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Some new fixed point results under constraint inequalities in comparable complete partially ordered Menger PM-spaces

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Abstract

In this paper, we introduce the concept of comparable \({\cal T}\)-completeness of a partially ordered Menger PM-space and discuss the existence of fixed points for mappings satisfying certain conditions in the framework of a comparable \({\cal T}\)-complete partially ordered Menger PM-space. We obtain some new results which generalize many known ones in the literature. Moreover, we derive some consequent results and give an example to illustrate our main result.

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References

  1. B Alqahtani, R Lashkaripour, E Karapınar, J Hamzehnejadi. Discussion on the fixed point problems with constraint inequalities, J Inequal Appl, 2018, 2018: 224.

    Article  MathSciNet  MATH  Google Scholar 

  2. A H Ansari, P Kumam, B Samet. A fixed point problem with constraint inequalities via an implict contraction, J Fixed Point Theory Appl, 2017, 19: 1145–1163.

    Article  MathSciNet  MATH  Google Scholar 

  3. S K Bhandari, D Gopal, P Konar. Probabilistic α-min ciric type contraction results using a control function, AIMS Mathematics, 2020, 5(2): 1186–1198.

    Article  MathSciNet  MATH  Google Scholar 

  4. S Chang, Y J Cho, S M Kang. Nonlinear Operator Theory in Probabilistic Metric Spaces, Nova Science Publishers Inc, New York, 2001.

    MATH  Google Scholar 

  5. L Ćirić, D Mihet, R Saadati. Monotone generalized contractions in partially ordered probabilistic metric spaces, Topol Appl, 2009, 156(17): 2838–2844.

    Article  MathSciNet  MATH  Google Scholar 

  6. T Došenović, P Kumam, D Gopal, D K Patel, A Takači. On fixed point theorems involving altering distances in Menger probabilistic metric spaces, J Inequal Appl, 2013, 2013: 576.

    Article  MathSciNet  MATH  Google Scholar 

  7. J X Fang, Y Gao. Common fixed point theorems under strict contractive conditions in Menger spaces, Nonlinear Anal-Theor, 2009, 70(1): 184–193.

    Article  MathSciNet  MATH  Google Scholar 

  8. D Gopal, M Abbas, C Vetro. Some new fixed point theorems in Menger PM-spaces with application to Volterra type integral equation, Appl Math Comput, 2014, 232: 955–967.

    MathSciNet  MATH  Google Scholar 

  9. O Hadžić, E Pap. Fixed Point Theory in Probabilistic Metric Spaces, Kluwer Academic Publishers, Dordrecht, 2001.

    Book  MATH  Google Scholar 

  10. J Harjani, K Sadarangani. Fixed point theorems for weakly contractive mappings in partially ordered sets, Nonlinear Analysis, 2009, (7–8): 3403–3410.

  11. M Jleli, B Samet. A fixed point problem under two constraint inequalities, Fixed Point Theory Appl, 2016, 2016: 18.

    Article  MathSciNet  MATH  Google Scholar 

  12. E Karapınar, B Samet. Generalized α-ψ contractive type mappings and related fixed point theorems with applications, Abstr Appl Anal, 2012, 2012: 793486.

    Article  MathSciNet  MATH  Google Scholar 

  13. E Karapınar, P Kumam, P Salimi. On α-ψ-Meir-Keeler contractive mappings, Fixed Point Theory Appl, 2013, 2013: 94.

    Article  MathSciNet  MATH  Google Scholar 

  14. V Lakshmikantham, L Ćirić Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Analysis, 2009, 70(12): 4341–4349.

    Article  MathSciNet  MATH  Google Scholar 

  15. K Menger. Statistical metrics, Proc Natl Acad Sci USA, 1942, 28: 535–537.

    Article  MathSciNet  MATH  Google Scholar 

  16. A C M Ran, M C B Reurings. A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc Amer Math Soc, 2004, 132: 1435–1443.

    Article  MathSciNet  MATH  Google Scholar 

  17. B Samet, C Vetro. Coupled fixed point theorems for multi-valued nonlinear contraction mappings in partially ordered metric spaces, Nonlinear Analysis, 2011, 74(12): 4260–4268.

    Article  MathSciNet  MATH  Google Scholar 

  18. B Samet, C Vetro, P Vertro. Fixed point theorems for α-ψ contractive type mappings, Nonlinear Analysis, 2012, 75(4): 2154–2165.

    Article  MathSciNet  MATH  Google Scholar 

  19. B Schweizer, A Sklar. Statistical metric spaces, Pacific J Math, 1960, 10: 313–334.

    Article  MathSciNet  MATH  Google Scholar 

  20. B Schweizer, A Sklar. Probabilistic Metric Spaces, North-Holland, Amsterdam, 1983.

    MATH  Google Scholar 

  21. B Schweizer. Commentary on Probabilistic Geometry, in Karl Menger, Selecta Mathematica, Springer, Vienna, 2003, 409–432.

    Google Scholar 

  22. S Shukla, D Gopal, W Sintunavarat. A new class of fuzzy contractive mappings and fixed point theorems, Fuzzy Set Syst, 2018, 350: 85–94.

    Article  MathSciNet  MATH  Google Scholar 

  23. Q Tu, C Zhu, Z Wu, X Mu. Some new coupled fixed point theorems in partially ordered complete probabilistic metric spaces, J Nonlinear Sci Appl, 2016, 9: 1116–1128.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  25. J Wu. Some fixed point theorems for mixed monotone operators in partially ordered probabilistic metric spaces, Fixed Point Theory Appl, 2014, 2014: 49.

    Article  MathSciNet  MATH  Google Scholar 

  26. Z Wu, C Zhu, J Li. Common fixed point theorems for two hybrid pairs of mappings satisfying the common property (E.A) in Menger PM-spaces, Fixed Point Theory and Applications, 2013, 2013: 25.

    Article  MathSciNet  MATH  Google Scholar 

  27. Z Wu, C Zhu, X Zhang. Some new fixed point theorems for single and set-valued admissible mappings in Menger PM-spaces, RACSAM Rev R Acad A, 2016, 110: 755–769.

    MathSciNet  MATH  Google Scholar 

  28. Z Wu, C Zhu, C Yuan. Fixed point results for (α, η, ϕ, ξ)-contractive multi-valued mappings in Menger PM-Spaces and their applications, Filomat, 2017, 31(16): 5357–5368.

    Article  MathSciNet  MATH  Google Scholar 

  29. Z Wu, C Zhu, C Yuan. Fixed point results for cyclic contractions in Menger PM-spaces and generalized Menger PM-spaces, RACSAM Rev R Acad A, 2018, 112: 449–462.

    MathSciNet  MATH  Google Scholar 

  30. Z Wu, C Zhu, C Yuan. Fixed point results under constraint inequalities in Menger PM-spaces, J Comput Anal Appl, 2018, 25(7): 1324–1336.

    MathSciNet  Google Scholar 

  31. W Xu, C Zhu, Z Wu, L Zhu. Fixed point theorems for two new types of cyclic weakly contractive mappings in partially ordered Menger PM-spaces, J Nonlinear Sci Appl, 2015, 8: 412–422.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Nanchang University, Nanchang, 330031, China

    Zhao-qi Wu & Chuan-xi Zhu

  2. Institute of Mathematics, Hangzhou Dianzi University, Hangzhou, 310018, China

    Lin Zhang

  3. Department of Mathematics, Swansea University, Singleton Park, SA2 8PP, UK

    Cheng-gui Yuan

Authors
  1. Zhao-qi Wu
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  2. Lin Zhang
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  3. Chuan-xi Zhu
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  4. Cheng-gui Yuan
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Corresponding author

Correspondence to Zhao-qi Wu.

Additional information

Supported by the National Natural Science Foundation of China(12161056, 11701259, 11771198) and Natural Science Foundation of Jiangxi Province of China(20202BAB201001).

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Wu, Zq., Zhang, L., Zhu, Cx. et al. Some new fixed point results under constraint inequalities in comparable complete partially ordered Menger PM-spaces. Appl. Math. J. Chin. Univ. 37, 494–512 (2022). https://doi.org/10.1007/s11766-022-3685-5

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  • DOI: https://doi.org/10.1007/s11766-022-3685-5

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