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Fixed point results under various contractive conditions in partial metric spaces

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Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas Aims and scope Submit manuscript

Abstract

Some new fixed point and common fixed point results for mappings in partial metric spaces are obtained. Various conditions such as Hardy–Rogers-type, quasicontraction type and weak contractive type conditions are used. Moreover, properties (P) and (Q) are investigated. Examples are presented to show how these results can be used.

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References

  1. Abbas, M., Nazir, T., Romaguera, S.: Fixed point results for generalized cyclic contraction mappings in partial metric spaces. Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM. doi:10.1007/s13398-011-0051-5

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

  3. Altun I., Sadarangani K.: Corrigendum to “Generalized contractions on partial metric spaces” [Topol. Appl. 157 (2010) 2778–2785]. Topol. Appl. 158, 1738–1740 (2011)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  5. Samet Lj., 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)

    Article  MathSciNet  MATH  Google Scholar 

  6. Escardo H.: Pcf extended with real numbers. Theor. Comput. Sci. 162, 79–115 (1996)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  9. Jachymski J.: Equivalent conditions for generalized contractions on (ordered) metric spaces. Nonlinear Anal. 74, 768–774 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  10. Jeong G.S., Rhoades B.E.: Maps for which F(T) = F(T n). Fixed Point Theory Appl. 6, 87–131 (2005)

    Google Scholar 

  11. ÐJukić, D., Kadelburg, Z., Radenović S.: Fixed points of Geraghty-type mappings in variuos generalized metric spaces, Abstract Appl. Anal. (2011). doi:10.1155/2011/561245 (article ID 561245)

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

    Article  MathSciNet  Google Scholar 

  13. Nashine, H.K.: New fixed point theorems for mappings satisfying generalized weakly contractive condition with weaker control functions. Ann. Polonici Math. (2011, to appear)

  14. Oltra S., Romaguera S., Saánchez-Pérez E.A.: Bicompleting weightable quasi-metric spaces and partial metric spaces. Rend. Circ. Mat. Palermo 51(2), 151–162 (2002)

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  16. Radenović S., Kadelburg Z., Jandrlić D., Jandrlić A.: Some results on weak contraction maps. Bull. Iran. Math. Soc. (2012, to appear)

  17. Rhoades B.E.: A comparison of various definitions of contractive mappings. Trans. Am. Math. Soc 336, 257–290 (1977)

    Article  MathSciNet  Google Scholar 

  18. Rhoades B.E.: Some theorems on weakly contractive maps. Nonlinear Anal. 47, 2683–2693 (2001)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  20. Shatanawi W., Samet B., Abbas M.: Coupled fixed point theorems for mixed monotone mappings in ordered partial metric spaces. Math. Comput. Model. 55, 680–687 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  21. Sönmez, A.: Fixed point theorems in partial cone metric spaces. arXiv:11012741v1 [math.GN].

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

    MathSciNet  MATH  Google Scholar 

  23. Zhang Q., Song Y.: Fixed point theory for generalized φ-weak contractions. Appl. Math. Lett. 22, 75–78 (2009)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11000, Beograd, Serbia

    Zoran Kadelburg

  2. Department of Mathematics, Disha Institute of Management and Technology, Satya Vihar, Vidhansabha-Chandrakhuri Marg, Mandir Hasaud, Raipur, Chhattisgarh, 492101, India

    Hemant Kumar Nashine

  3. Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120, Beograd, Serbia

    Stojan Radenović

Authors
  1. Zoran Kadelburg
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  2. Hemant Kumar Nashine
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  3. Stojan Radenović
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Correspondence to Stojan Radenović.

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Kadelburg, Z., Nashine, H.K. & Radenović, S. Fixed point results under various contractive conditions in partial metric spaces. RACSAM 107, 241–256 (2013). https://doi.org/10.1007/s13398-012-0066-6

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  • DOI: https://doi.org/10.1007/s13398-012-0066-6

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