Skip to main content

Advances on Fixed Point Results on Partial Metric Spaces

  • Chapter
  • First Online:

Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 23))

Abstract

In this note, we shall consider recent advances and improvements on fixed point theory in the setting of partial metric spaces. We investigate the existence and uniqueness of several distinct type contractive mapping in the context of complete partial metric space. We also recollect sum existing results to give complete survey for this topic.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Abedeljawad, T., Karapınar, E., Taş, K.: Existence and uniqueness of common fixed point on partial metric spaces. Appl. Math. Lett. 24, 1894–1899 (2011)

    Article  MathSciNet  Google Scholar 

  2. Abdeljawad, T., Karapınar, E., Tas, K.: A generalized contraction principle with control functions on partial metric spaces. Comput. Math. Appl. 63(3), 716–719 (2012)

    Article  MathSciNet  Google Scholar 

  3. Achari, J.: Results on non-unique fixed points. Publ. L’Institut Math. 26, 5–9 (1978)

    MATH  Google Scholar 

  4. Agarwal, R.P., Alghamdi, M.A., Shahzad, N.: Fixed point theory for cyclic generalized contractions in partial metric spaces. Fixed Point Theory Appl. 2012, 40 (2012)

    Google Scholar 

  5. Alghamdi, M.A., Karapınar, E.: G − β − ψ Contractive type mappings and related fixed point theorems. J. Inequal. Appl. 2013, Article ID 70 (2013)

    Google Scholar 

  6. Alghamdi, M.A., Karapınar, E.: G − β − ψ Contractive type mappings in G-metric spaces. Fixed Point Theory Appl. 2013, Article ID 123 (2013)

    Article  MathSciNet  Google Scholar 

  7. Ali, M.U., Kamran, T., Karapınar, E.: On (α, ψ, η)-contractive multivalued mappings. Fixed Point Theory Appl. 2014, 7 (2014)

    Google Scholar 

  8. Aliouche, A., Popa, V.: General common fixed point theorems for occasionally weakly compatible hybrid mappings and applications. Novi Sad. J. Math. 39(1), 89–109 (2009)

    MathSciNet  MATH  Google Scholar 

  9. Altun, I., Acar, O.: Fixed point theorems for weak contractions in the sense of Berinde on partial metric spaces. Topol. Appl. 159, 2642–2648 (2012)

    Article  MathSciNet  Google Scholar 

  10. Altun, I., Erduran, A.: Fixed point theorems for monotone mappings on partial metric spaces. Fixed Point Theory Appl. Article ID 508730 (2011)

    Google Scholar 

  11. Altun, I., Simsek, H.: Some fixed point theorems on dualistic partial metric spaces. J. Adv. Math. Stud. 1, 1–8 (2008)

    MathSciNet  MATH  Google Scholar 

  12. Altun, I., Sola, F., Simsek, H.: Generalized contractions on partial metric spaces. Topol. Appl. 157, 2778–2785 (2010)

    Article  MathSciNet  Google Scholar 

  13. Aydi, H.: Fixed point results for weakly contractive mappings in ordered partial metric spaces. J. Adv. Math. Stud. 4(2), 1–12 (2011)

    MathSciNet  MATH  Google Scholar 

  14. Aydi, H.: Some fixed point results in ordered partial metric spaces. J. Nonlinear Sci. Appl. 4(2), 210–217 (2011)

    Article  MathSciNet  Google Scholar 

  15. Aydi, H.: Some coupled fixed point results on partial metric spaces. Int. J. Math. Math. Sci. Article ID 647091 (2011)

    Google Scholar 

  16. Aydi, H.: Fixed point results for weakly contractive mappings in ordered partial metric spaces. J. Adv. Math. Stud. 4(2), 1–12 (2011)

    MathSciNet  MATH  Google Scholar 

  17. Aydi, H.: Fixed point theorems for generalized weakly contractive condition in ordered partial metric spaces. J. Nonlinear Anal. Optim. Theory Appl. 2(2), 33–48 (2011)

    MathSciNet  Google Scholar 

  18. Aydi, H.: Common fixed point results for mappings satisfying (ψ, ϕ)-weak contractions in ordered partial metric space. Int. J. Math. Stat. 12(2), 53–64 (2012)

    MathSciNet  MATH  Google Scholar 

  19. Aydi, H., Karapınar, E.: A Meir-Keeler common type fixed point theorem on partial metric spaces. Fixed Point Theory Appl. 2012, 26 (2012)

    Google Scholar 

  20. Aydi, H., Karapınar, E., Shatanawi, W.: Coupled fixed point results for (ψ, φ)-weakly contractive condition in ordered partial metric spaces. Comput. Math. Appl. 62(12), 4449–4460 (2011)

    Article  MathSciNet  Google Scholar 

  21. Aydi, H., Abbas, M., Vetro, C.: Partial Hausdorff metric and Nadler’s fixed point theorem on partial metric spaces. Topol. Appl. 159, 3234–3242 (2012)

    Article  MathSciNet  Google Scholar 

  22. Aydi, H., Vetro, C., Sintunavarat, W., Kumam, P.: Coincidence and fixed points for contractions and cyclical contractions in partial metric spaces. Fixed Point Theory Appl. 2012(124) (2012)

    Google Scholar 

  23. Aydi, H., Bilgili, N., Karapınar, E.: Common fixed point results from quasi-metric spaces to G-metric spaces. J. Egypt. Math. Soc. 23(2), 356–361 (2015)

    Article  MathSciNet  Google Scholar 

  24. Aydi, H., Vetro, C., Karapınar, E.: On Ekeland’s variational principle in partial metric spaces. Appl. Math. Inf. Sci. 9(1), 257–262 (2015)

    Article  MathSciNet  Google Scholar 

  25. Aydi, H., Jellali, M., Karapinar, E.: Common fixed points for generalized α-implicit contractions in partial metric spaces: consequences and application. RACSAM - Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 109(2), 367–384 (2015)

    Google Scholar 

  26. Bae, I., Kim, K.: Common fixed point theorems without commuting conditions. Korean J. Math. Sci. 8, 147–155 (2001)

    Google Scholar 

  27. Banach, S.: Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fund. Math. 3, 133–181 (1922)

    Article  Google Scholar 

  28. Baskaran, R., Subrahmanyam, P.V.: A note on the solution of a class of functional equations. Appl. Anal. 22, 235–241 (1986)

    Article  MathSciNet  Google Scholar 

  29. Bellman, R.: Methods of nonliner analysis. Mathematics in Science and Engineering, vol. II, 61. Academic, New York (1973)

    Google Scholar 

  30. Bellman, R., Lee, E.S.: Functional equations in dynamic programming. Aequationes Math. 17, 1–18 (1978)

    Article  MathSciNet  Google Scholar 

  31. Berinde, V.: Some remarks on a fixed point theorem for Ćirić-type almost contractions. Carpathian J. Math. 25(2), 157–162 (2009)

    MathSciNet  MATH  Google Scholar 

  32. Berinde, V.: Common fixed points of noncommuting almost contractions in cone metric spaces. Math. Commun. 15(1), 229–241 (2010)

    MathSciNet  MATH  Google Scholar 

  33. Berinde, V.: Approximating common fixed points of noncommuting almost contractions in metric spaces. Fixed Point Theory 11(2), 179–188 (2010)

    MathSciNet  MATH  Google Scholar 

  34. Berinde, V.: Common fixed points of noncommuting discontinuous weakly contractive mappings in cone metric spaces. Taiwan. J. Math. 14(5), 1763–1776 (2010)

    Article  MathSciNet  Google Scholar 

  35. Berinde, V., Vetro, F.: Common fixed points of mappings satisfying implicit contractive conditions. Fixed Point Theory Appl. 2012, 105 (2012)

    Google Scholar 

  36. Bhakta, T.C., Mitra, S.: Some existence theorems for functional equations arising in dynamic programming. J. Math. Anal. Appl. 98, 348–362 (1984)

    Article  MathSciNet  Google Scholar 

  37. Bianchini, R.M., Grandolfi, M.: Transformazioni di tipo contracttivo generalizzato in uno spazio metrico. Atti Acad. Naz. Lincei, VII. Ser. Rend. Cl. Sci. Fis. Mat. Natur. 45, 212–216 (1968)

    Google Scholar 

  38. Border, K.C.: Fixed Point Theorems with Applications to Economics and Game Theory. Cambridge University Press, New York (1985)

    Book  Google Scholar 

  39. Borwein, J.M., Zhu, Q.J.: Techniques of Variational Analysis. Springer, New York (2005)

    MATH  Google Scholar 

  40. Branciari, A.: A fixed point theorem for mappings satisfying a general contractive condition of integral type. Int. J. Math. Math. Sci. 29, 531–536 (2002)

    Article  MathSciNet  Google Scholar 

  41. Bukatin, M., Kopperman, R., Matthews, S., Pajoohesh, H.: Partial metric spaces. Am. Math. Mon. 116(8), 708–718 (2009)

    Article  MathSciNet  Google Scholar 

  42. Caristi, J.: Fixed point theorems for mapping satisfying inwardness conditions. Trans. Am. Math. Soc. 215, 241–251 (1976)

    Article  MathSciNet  Google Scholar 

  43. Chen, C.-M., Karapınar, E.: Fixed point results for the α-Meir-Keeler contraction on partial Hausdorff metric spaces. J. Inequal. Appl. 2013, 410 (2013)

    Google Scholar 

  44. Chi, K.P., Karapınar, E., Thanh, T.D.: A generalized contraction principle in partial metric spaces. Math. Comput. Model. 55, 1673–1681 (2012). https://doi.org/10.1016/j.mcm.2011.11.005

    Article  MathSciNet  Google Scholar 

  45. Ćirić, L.B.: On some maps with a nonunique fixed point. Publ. L’Institut Math. 17, 52–58 (1974)

    MathSciNet  MATH  Google Scholar 

  46. Ćirić, L.B.: A generalization of Banach’s contraction principle. Proc. Am. Math. Soc. 45(2), 267–273 (1974)

    Article  MathSciNet  Google Scholar 

  47. Ćirić, L.j., Samet, B., Aydi, H., Vetro, C.: Common fixed points of generalized contractions on partial metric spaces and an application. Appl. Math. Comput. 218, 2398–2406 (2011)

    Google Scholar 

  48. Clarke, F.: Pointwise contraction criteria for the existence of fixed points. MRC Technical Report 1658. University of Wisconsin, Madison, Wisconsin; Bull. Canad. Math. Soc. July 1976

    Google Scholar 

  49. Czerwik, S.: Contraction mappings in b-metric spaces. Acta Math. Inform. Univ. Ostraviensis 1, 5–11 (1993)

    MathSciNet  MATH  Google Scholar 

  50. Ekeland, I.: Sur les prob‘ emes variationnels. C.R. Acad. Sci. Paris 275, 1057–1059 (1972)

    Google Scholar 

  51. Escardo, M.H.: Pcf Extended with real numbers. Theor. Comput. Sci. 162, 79–115 (1996)

    Article  MathSciNet  Google Scholar 

  52. Fréchet, M.R.: Sur quelques points du calcul fonctionnel. Rend. Circ. Mat. Palermo 22, 1–74 (1906). https://doi.org/10.1007/BF03018603

    Article  Google Scholar 

  53. Gillespie, J.B., Houghton, C.J.: A metric space approach to the information channel capacity of spike trains. J. Comput. Neurosci. 30(1), 201–209 (2011)

    Article  MathSciNet  Google Scholar 

  54. Gulyaz, S., Karapınar, E.: Coupled fixed point result in partially ordered partial metric spaces through implicit function. Hacet. J. Math. Stat. 42(4), 347–357 (2013)

    MathSciNet  MATH  Google Scholar 

  55. Haghi, R.H., Rezapour, Sh., Shahzad, N.: Be careful on partial metric fixed point results. Topol. Appl. 160(3), 450–454 (2013)

    Article  MathSciNet  Google Scholar 

  56. Heckmann, R.: Approximation of metric spaces by partial metric spaces. Appl. Categ. Struct. 7, 71–83 (1999)

    Article  MathSciNet  Google Scholar 

  57. Hitzler, P., Seda, A.: Mathematical Aspects of Logic Programming Semantics. Studies in Informatics Series. Chapman and Hall/CRC Press, Taylor and Francis Group, Boca Raton (2011)

    MATH  Google Scholar 

  58. Huang, L.G., Zhang, X.: Cone metric spaces and fixed point theorems of contractive mappings. J. Math. Anal. Appl. 332(2), 1468–1476 (2007)

    Article  MathSciNet  Google Scholar 

  59. Ilić, D., Pavlović, V., Rakoc̆ević, V.: Some new extensions of Banach’s contraction principle to partial metric space. Appl. Math. Lett. 24(8), 1326–1330 (2011)

    Google Scholar 

  60. Ilić, D., Pavlović, V., Rakoc̆ević, V.: Extensions of the Zamfirescu theorem to partial metric spaces. Original Research Article Math. Comput. Model. 55(3–4), 801–809 (2012)

    Google Scholar 

  61. Imdad, M., Kumar, S., Khan, M.S.: Remarks on some fixed point theorems satisfying implicit relations. Radovi Math. 1, 35–143 (2002)

    MathSciNet  MATH  Google Scholar 

  62. Jleli, M., Karapınar, E., Samet, B.: Best proximity points for generalized α − ψ-proximal contractive type mappings. J. Appl. Math. Article ID 534127 (2013)

    Google Scholar 

  63. Jleli, M., Karapınar, E., Samet, B.: Fixed point results for α − ψ λ contractions on gauge spaces and applications. Abstr. Appl. Anal. Article ID 730825 (2013)

    Google Scholar 

  64. Jleli, M., Karapınar, E., Samet, B.: Further remarks on fixed point theorems in the context of partial metric spaces. Abstr. Appl. Anal. Article ID: 715456 (2013)

    Google Scholar 

  65. Kannan, R.: Some results on fixed points. Bull. Calcutta Math. Soc. 60, 71–76 (1968)

    MathSciNet  MATH  Google Scholar 

  66. Karapınar, E.: Generalizations of Caristi Kirk’s theorem on partial metric spaces. Fixed Point Theory Appl. 2011(4) (2011)

    Google Scholar 

  67. Karapınar, E.: A note on common fixed point theorems in partial metric spaces. Miskolc Math. Notes 12(2), 185–191 (2011)

    MathSciNet  MATH  Google Scholar 

  68. Karapınar, E.: Some fixed point theorems on the class of comparable partial metric spaces on comparable partial metric spaces. Appl. General Topol. 12(2), 187–192 (2011)

    MathSciNet  MATH  Google Scholar 

  69. Karapinar, E.: Ćirić types nonunique fixed point theorems on partial metric spaces. J. Nonlinear Sci. Appl. 5, 74–83 (2012)

    Article  MathSciNet  Google Scholar 

  70. Karapınar, E.: Weak ϕ-contraction on partial metric spaces. J. Comput. Anal. Appl. 16(6), 14(2), 206–210 (2012)

    Google Scholar 

  71. Karapınar, E., Erhan, I.M.: Fixed point theorems for operators on partial metric spaces. Appl. Math. Lett. 24, 1900–1904 (2011)

    Article  MathSciNet  Google Scholar 

  72. Karapınar, E., Erhan, I.M.: Fixed point theorem for cyclic maps on partial metric spaces. Appl. Math. Inform. Sci. 6, 239–244 (2012)

    MathSciNet  Google Scholar 

  73. Karapınar, E., Romaguera, S.: Nonunique fixed point theorems in partial metric spaces. Filomat 27(7), 1305–1314 (2013)

    Article  MathSciNet  Google Scholar 

  74. Karapınar, E., Samet, B.: Generalized (α − ψ)-contractive type mappings and related fixed point theorems with applications. Abstr. Appl. Anal. 2012, Article ID 793486, 17 p. (2012)

    Google Scholar 

  75. Karapınar, E., Yuksel, U.: Some common fixed point theorems in partial metric spaces. J. Appl. Math. Article ID 263621, 17 p. (2011). https://doi.org/10.1155/2011/263621

  76. Karapınar, E., Shobkolaei, N., Sedghi, S., Vaezpour, S.M.: A common fixed point theorem for cyclic operators on partial metric spaces. Filomat 26(2), 407–414 (2012)

    Article  MathSciNet  Google Scholar 

  77. Karapınar, E., Erhan, I., Ozturk, A.: Fixed point theorems on quasi-partial metric spaces. Math. Comput. Model. 57(9–10), 2442–2448 (2013)

    Article  MathSciNet  Google Scholar 

  78. Karapınar, E., Kuman, P., Salimi, P.: On α − ψ-Meri-Keeler contractive mappings. Fixed Point Theory Appl. 2013, 94 (2013)

    Google Scholar 

  79. Karapınar, E., Alsulami, H.H., Noorwali, M.: Some extensions for Geragthy type contractive mappings. J. Inequal. Appl. 2015, 303 (2015)

    Google Scholar 

  80. Kirk, W.A., Srinivasan, P.S., Veeramani, P.: Fixed points for mappings satisfying cyclical contractive conditions. Fixed Point Theory 4(1), 79–89 (2003)

    MathSciNet  MATH  Google Scholar 

  81. Kopperman, R.D., Matthews, S.G., Pajoohesh, H.: What do partial metrics represent? Notes distributed at the 19th Summer Conference on Topology and its Applications, University of CapeTown (2004)

    Google Scholar 

  82. Kramosil, O., Michalek, J.: Fuzzy metric and statistical metric spaces. Kybernetika 11, 326–334 (1975)

    MathSciNet  MATH  Google Scholar 

  83. Künzi, H.P.A., Pajoohesh, H., Schellekens, M.P.: Partial quasi-metrics. Theor. Comput. Sci. 365(3), 237–246 (2006)

    Article  MathSciNet  Google Scholar 

  84. Matthews, S.G.: Partial metric topology. Research Report 212. Dept. of Computer Science. University of Warwick (1992)

    Google Scholar 

  85. Matthews, S.G.: Partial metric topology. Proc. 8th Summer of Conference on General Topology and Applications. Ann. New York Acad. Sci. 728, 183–197 (1994)

    Google Scholar 

  86. Meir, A., Keeler, E.: A theorem on contraction mappings. J. Math. Anal. Appl. 28, 326–329 (1969)

    Article  MathSciNet  Google Scholar 

  87. Menger, K.: Statistical metrics. Proc. Nat. Acad. Sci. USA 28, 535–537 (1942)

    Article  MathSciNet  Google Scholar 

  88. Mohammadi, B., Rezapour, Sh., Shahzad, N.: Some results on fixed points of α-ψ-Ciric generalized multifunctions. Fixed Point Theory Appl. 2013, 24 (2013)

    Google Scholar 

  89. Mustafa, Z., Sims, B.: A new approach to generalized metric spaces. J. Nonlinear Convex Anal. 7(2), 289–297 (2006)

    MathSciNet  MATH  Google Scholar 

  90. Nadler, S.B.: Multi-valued contraction mappings. Pac. J. Math. 30, 475–488 (1969)

    Article  MathSciNet  Google Scholar 

  91. Ok, E.A.: Real Analysis with Economic Applications. Princeton University Press, Princeton (2007)

    MATH  Google Scholar 

  92. Oltra, S., Valero, O.: Banach’s fixed point theorem for partial metric spaces. Rend. Istid. Math. Univ. Trieste 36, 17–26 (2004)

    MathSciNet  MATH  Google Scholar 

  93. Pachpatte, B.G.: On Ćirić type maps with a nonunique fixed point. Indian J. Pure Appl. Math. 10, 1039–1043 (1979)

    MathSciNet  MATH  Google Scholar 

  94. Paesano, D., Vetro, P.: Suzuki’s type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces. Topol. Appl. 159(3), 911–920 (2012)

    Article  MathSciNet  Google Scholar 

  95. Popa, V.: Fixed point theorems for implicit contractive mappings. Stud. Cerc. St. Ser. Mat. Univ. Bacau. 7, 129–133 (1997)

    MATH  Google Scholar 

  96. Popa, V.: Some fixed point theorems for compatible mappings satisfying an implicit relation. Demonstratio Math. 32, 157–163 (1999)

    MathSciNet  MATH  Google Scholar 

  97. Popa, V.: A general fixed point theorem for four weakly compatible mappings satisfying an implicit relation. Filomat. 19, 45–51 (2005)

    Article  MathSciNet  Google Scholar 

  98. Popa, V., Patriciu, A.M.: A general fixed point theorem for mappings satisfying an ϕ-implicit relation in complete G-metric spaces. Gazi Univ. J. Sci. 25(2), 403–408 (2012)

    Google Scholar 

  99. Popa, V., Patriciu, A.M.: A general fixed point theorem for pairs of weakly compatible mappings in G-metric spaces. J. Nonlinear Sci. Appl. 5, 151–160 (2012)

    Article  MathSciNet  Google Scholar 

  100. Popescu, O.: Some new fixed point theorems for α-Geraghty contractive type maps in metric spaces. Fixed Point Theory Appl. 2014, 190 (2014)

    Google Scholar 

  101. Proinov, P.D.: A generalization of the Banach contraction principle with high order of convergence of successive approximations. Nonlinear Anal. (TMA) 67, 2361–2369 (2007)

    Google Scholar 

  102. Proinov, P.D.: New general convergence theory for iterative processes and its applications to Newton Kantorovich type theorems. J. Complex. 26, 3–42 (2010)

    Article  MathSciNet  Google Scholar 

  103. Ran, A.C.M., Reurings, M.C.B.: A fixed point theorem in partially ordered sets and some applications to matrix equations. Proc. Am. Math. Soc. 132, 1435–1443 (2003)

    Article  MathSciNet  Google Scholar 

  104. Reich, S.: Kannan’s fixed point theorem. Boll. Un. Mat. Ital. 4(4), 1–11(1971)

    Google Scholar 

  105. Roldan, A., Martinez-Moreno, J., Roldan, C., Karapınar, E.: Multidimensional fixed point theorems in partially ordered complete partial metric spaces under (psi,varphi)-contractivity conditions. Abstr. Appl. Anal. Article ID: 634371 (2013)

    Google Scholar 

  106. Romaguera, S.: A Kirk type characterization of completeness for partial metric spaces. Fixed Point Theory Appl. 2010, Article ID 493298, 6 p. (2010)

    Google Scholar 

  107. Romaguera, S.: Matkowski’s type theorems for generalized contractions on (ordered) partial metric spaces. Appl. General Topol. 12(2), 213–220 (2011)

    MathSciNet  MATH  Google Scholar 

  108. Romaguera, S.: Fixed point theorems for generalized contractions on partial metric spaces. Topol. Appl. 159, 194–199 (2012)

    Article  MathSciNet  Google Scholar 

  109. Romaguera, S., Schellekens, M.: Duality and quasi-normability for complexity spaces. Appl. General Topol. 3, 91–112 (2002)

    Article  MathSciNet  Google Scholar 

  110. Romaguera, S., Schellekens, M.: Partial metric monoids and semivaluation spaces. Topol. Appl. 153(5–6), 948–962 (2005)

    Article  MathSciNet  Google Scholar 

  111. Romaguera, S., Valero, O.: A quantitative computational model for complete partial metric spaces via formal balls. Math. Struct. Comput. Sci. 19(3), 541–563 (2009)

    Article  MathSciNet  Google Scholar 

  112. Rus, I.A.: Generalized Contractions and Applications. Cluj University Press, Cluj-Napoca (2001)

    MATH  Google Scholar 

  113. Samet, B., Rajović, M., Lazović, R., Stoiljković, R.: Common fixed point results for nonlinear contractions in ordered partial metric spaces. Fixed Point Theory Appl. 2011, 71 (2011)

    Google Scholar 

  114. Samet, B., Vetro, C., Vetro, P.: Fixed point theorem for α − ψ contractive type mappings. Nonlinear Anal. 75, 2154–2165 (2012)

    Article  MathSciNet  Google Scholar 

  115. Samet, B., Vetro, C., Vetro, F.: From metric spaces to partial metric spaces. Fixed Point Theory Appl. 2013, 5 (2013)

    Google Scholar 

  116. Schellekens, M.P.: A characterization of partial metrizability: domains are quantifiable. Theor. Comput. Sci. 305(1–3), 409–432 (2003)

    Article  MathSciNet  Google Scholar 

  117. Schellekens, M.P.: The correspondence between partial metrics and semivaluations. Theor. Comput. Sci. 315(1), 135–149 (2004)

    Article  MathSciNet  Google Scholar 

  118. Sehgal, V.M.: Some fixed and common fixed point theorems in metric spaces. Can. Math. Bull. 17(2), 257–259 (1974)

    Article  MathSciNet  Google Scholar 

  119. Shatanawi, W., Samet, B., Abbas, M.: Coupled fixed point theorems for mixed monotone mappings in ordered partial metric spaces. Math. Comput. Model. (2011). https://doi.org/10.1016/j.mcm.2011.08.042

    MATH  Google Scholar 

  120. Shobkolaei, N., Vaezpour, S.M., Sedghi, S.: A common fixed point theorem on ordered partial metric spaces. J. Basic. Appl. Sci. Res. 1(12), 3433–3439 (2011)

    Google Scholar 

  121. Stoy, J.E.: Denotational Semantics: The Scott-Strachey Approach to Programming Language Theory. MIT Press, Cambridge (1981)

    MATH  Google Scholar 

  122. Squassina, M.: On Ekeland’s variational principle. J. Fixed Point Theory Appl. 10, 191–195 (2011)

    Article  MathSciNet  Google Scholar 

  123. Turinici, M.: Abstract comparison principles and multivariable Gronwall-Bellman inequalities. J. Math. Anal. Appl. 117, 100–127 (1986)

    Article  MathSciNet  Google Scholar 

  124. Valero, O.: On Banach fixed point theorems for partial metric spaces. Appl. Gen. Topol. 6(2), 229–240 (2005)

    Article  MathSciNet  Google Scholar 

  125. Vetro, F., Radenović, S.: Nonlinear ψ-quasi-contractions of Ćirić-type in partial metric spaces. Appl. Math. Comput. 219(4), 1594–1600 (2012)

    MathSciNet  MATH  Google Scholar 

  126. Vetro, C., Vetro, F.: Common fixed points of mappings satisfying implicit relations in partial metric spaces. J. Nonlinear Sci. Appl. 6(3), 152–161 (2013)

    Article  MathSciNet  Google Scholar 

  127. Vetro, C., Vetro, F.: Metric or partial metric spaces endowed with a finite number of graphs: a tool to obtain fixed point results. Topol. Appl. 164, 125–137 (2014)

    Article  MathSciNet  Google Scholar 

  128. Waszkiewicz, P.: Quantitative continuous domains. Appl. Categ. Struct. 11, 41–67 (2003)

    Article  MathSciNet  Google Scholar 

  129. Waszkiewicz, P.: Partial metrisability of continuous posets. Math. Struct. Comput. Sci. 16(2), 359–372 (2006)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Karapınar, E., Taş, K., Rakočević, V. (2019). Advances on Fixed Point Results on Partial Metric Spaces. In: Taş, K., Baleanu, D., Machado, J. (eds) Mathematical Methods in Engineering. Nonlinear Systems and Complexity, vol 23. Springer, Cham. https://doi.org/10.1007/978-3-319-91065-9_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-91065-9_1

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-91064-2

  • Online ISBN: 978-3-319-91065-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics