Existence Fixed Point Solutions for C-Class Functions in Bipolar Metric Spaces With Applications

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DOI: https://doi.org/10.28924/2291-8639-21-2023-7
Published: Feb 1, 2023
Cite as:
G. Upender Reddy, C. Ushabhavani, B. Srinuvasa Rao, Existence Fixed Point Solutions for C-Class Functions in Bipolar Metric Spaces With Applications, Int. J. Anal. Appl., 21 (2023), 7.

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G. Upender Reddy, C. Ushabhavani, B. Srinuvasa Rao

Abstract

In this study, the idea of C-class functions is introduced in the process of building a bi-polar metric space, along with often coupled fixed point theorems for these mappings in complete bi-polar metric spaces that associate altering distance function and ultra-altering distance function. Furthermore, we provide applications to integral equations as well as homotopy and we give an interpretation that demonstrates the relevance of the results obtained.

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References

  1. D. Guo, V. Lakshmikantham, Coupled Fixed Points of Nonlinear Operators With Applications, Nonlinear Anal.: Theory Methods Appl. 11 (1987), 623-632. https://doi.org/10.1016/0362-546x(87)90077-0.
  2. T.G. Bhaskar, V. Lakshmikantham, Fixed Point Theorems in Partially Ordered Metric Spaces and Applications, Nonlinear Anal.: Theory Methods Appl. 65 (2006), 1379-1393. https://doi.org/10.1016/j.na.2005.10.017.
  3. M. Abbas, M. Ali Khan, S. Radenovic, Common Coupled Fixed Point Theorems in Cone Metric Spaces for wCompatible Mappings, Appl. Math. Comput. 217 (2010), 195-202. https://doi.org/10.1016/j.amc.2010.05.042.
  4. A. Aghajani, M. Abbas, E. Pourhadi Kallehbasti, Coupled Fixed Point Theorems in Partially Ordered Metric Spaces and Application, Math. Commun. 17 (2012), 497-509. https://hrcak.srce.hr/clanak/137302.
  5. E. Karapinar, Coupled Fixed Point on Cone Metric Spaces, Gazi Univ. J. Sci. 24 (2011), 51-58. https://dergipark.org.tr/en/pub/gujs/issue/7418/96917.
  6. M. Abbas, B. Ali, Y.I. Suleiman, Generalized Coupled Common Fixed Point Results in Partially Ordered A-Metric Spaces, Fixed Point Theory Appl. 2015 (2015), 64. https://doi.org/10.1186/s13663-015-0309-2.
  7. W. Long, B.E. Rhoades, M. Rajovic, Coupled Coincidence Points for Two Mappings in Metric Spaces and Cone Metric Spaces, Fixed Point Theory Appl. 2012 (2012), 66. https://doi.org/10.1186/1687-1812-2012-66.
  8. M. Jain, S. Kumar, R. Chugh, Coupled Fixed Point Theorems for Weak Compatible Mappings in Fuzzy Metric Spaces, Ann. Fuzzy Math. Inform. 5 (2013), 321-336.
  9. M. Kir, E. Yolacan, H. Kiziltunc, Coupled Fixed Point Theorems in Complete Metric Spaces Endowed With a Directed Graph and Application, Open Math. 15 (2017), 734-744. https://doi.org/10.1515/math-2017-0062.
  10. A.H. Ansari, Note on ϕ−ψ-Contractive Type Mappings and Related Fixed Point, In: The 2nd Regional Conference on Mathematics and Applications, Payame Noor University, 2014.
  11. A.H. Ansari, A. Kaewcharoen, C-Class Functions and Fixed Point Theorems for Generalized ℵ − η − ψ − ϕ − F - Contraction Type Mappings in ℵ − η-Complete Metric Spaces, J. Nonlinear Sci. Appl. 9 (2016), 4177-4190.
  12. H. Huang, G. Deng, S. Radenovic, Fixed Point Theorems for C-Class Functions in b-Metric Spaces and Applications, J. Nonlinear Sci. Appl. 10 (2017), 5853-5868.
  13. A.H. Ansari, W. Shatanawi, A. Kurdi, G. Maniu, Best Proximity Points in Complete Metric Spaces With (P)- Property via C-Class Functions, J. Math. Anal. 7 (2016), 54-67.
  14. V. Ozturk, A.H. Ansari, Common Fixed Point Theorems for Mappings Satisfying (E.A)-Property via C-Class Functions in b-Metric Spaces, Appl. Gen. Topol. 18 (2017), 45-52. https://doi.org/10.4995/agt.2017.4573.
  15. T. Hamaizia, Common Fixed Point Theorems Involving C-class Functions in Partial Metric Spaces, Sohag J. Math. 8 (2021), 23–28. https://doi.org/10.18576/sjm/080103.
  16. G.S. Saluja, Common Fixed Point Theorems on S-Metric Spaces via C-Class Functions, Int. J. Math. Combin. 3 (2022), 21-37.
  17. W. Shatanawi, M. Postolache, A. H. Ansari, W. Kassab, Common Fixed Points of Dominating and Weak Annihilators in Ordered Metric Spaces via C-Class Functions, J. Math. Anal. 8 (2017), 54-68.
  18. A. Mutlu, U. Gu¨rdal, Bipolar Metric Spaces and Some Fixed Point Theorems, J. Nonlinear Sci. Appl. 9 (2016), 5362-5373.
  19. A. Mutlu, K. O¨zkan, U. Gu¨rdal, Coupled Fixed Point Theorems on Bipolar Metric Spaces, Eur. J. Pure Appl. Math. 10 (2017), 655-667.
  20. G.N.V. Kishore, R.P. Agarwal, B. Srinuvasa Rao, R.V.N. Srinivasa Rao, Caristi Type Cyclic Contraction and Common Fixed Point Theorems in Bipolar Metric Spaces With Applications, Fixed Point Theory Appl. 2018 (2018), 21. https://doi.org/10.1186/s13663-018-0646-z.
  21. G.N.V. Kishore, B. Srinuvasa Rao, R.S. Rao, Mixed Monotone Property and Tripled Fixed Point Theorems in Partially Ordered Bipolar Metric Spaces, Italian J. Pure Appl. Math. 42 (2019), 598-615.
  22. G.N.V. Kishore, B.S. Rao, S. Radenovic´, H. Huang, Caristi Type Cyclic Contraction and Coupled Fixed Point Results in Bipolar Metric Spaces, Sahand Commun. Math. Anal. 17 (2020), 1-22. https://doi.org/10.22130/scma.2018.79219.369.
  23. G.N.V. Kishore, K.P.R. Rao, H. IsIk, B. Srinuvasa Rao, A. Sombabu, Covarian Mappings and Coupled Fixed Point Results in Bipolar Metric Spaces, Int. J. Nonlinear Anal. Appl. 12 (2021),1-15. https://doi.org/10.22075/ijnaa.2021.4650.
  24. G.N.V. Kishorea, H. Işık, , H. Aydic, B.S. Rao, D.R. Prasad, On New Types of Contraction Mappings in Bipolar Metric Spaces and Applications, J. Linear Topol. Algebra, 9 (2020), 253-266.
  25. M.S. Khan, M. Swaleh, S. Sessa, Fixed Point Theorems by Altering Distances Between the Points, Bull. Austral. Math. Soc. 30 (1984), 1-9. https://doi.org/10.1017/s0004972700001659.