On Some Applications of P-Contraction Fixed Point Theorems in Bipolar Metric Spaces

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DOI: https://doi.org/10.28924/2291-8639-22-2024-159
Published: Sep 16, 2024
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K. Varalakshmi, G. Upender Reddy, On Some Applications of P-Contraction Fixed Point Theorems in Bipolar Metric Spaces, Int. J. Anal. Appl., 22 (2024), 159.

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K. Varalakshmi, G. Upender Reddy

Abstract

In this paper, we have discussed the P-contraction type fixed point theorems of covariant mappings in bipolar metric spaces, and we have shown an example which supports our results. Also we discussed applications to integral equations and Homotopy theory.

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References

  1. A. Mutlu, U. Gürdal, Bipolar Metric Spaces and Some Fixed Point Theorems, J. Nonlinear Sci. Appl. 9 (2016), 5362–5373.
  2. A. Mutlu, K. Özkan, U. Gürdal, Coupled Fixed Point Theorems on Bipolar Metric Spaces, Eur. J. Pure Appl. Math. 10 (2017), 655–667.
  3. G.N.V. Kishore, R.P. Agarwal, B.S. Rao, R.V.N.S. 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.
  4. G.N.V. Kishore, B.S. 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.
  5. 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.
  6. G.N.V. Kishore, K.P.R. Rao, H. IsIk, B.S. Rao, A. Sombabu, Covarian Mappings and Coupled Fiexd Point Results in Bipolar Metric Spaces, Int. J. Nonlinear Anal. Appl. 12 (2021), 1–15. https://doi.org/10.22075/ijnaa.2021.4650.
  7. G.N.V. Kishorea, H. I¸sık, , 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.
  8. J. Paul, M. Sajid, N. Chandra, U.C. Gairola, Some Common Fixed Point Theorems in Bipolar Metric Spaces and Applications, AIMS Math. 8 (2023), 19004–19017. https://doi.org/10.3934/math.2023969.
  9. A. Mutlu, K. Özkan, U. Gürdal, Locally and Weakly Contractive Principle in Bipolar Metric Spaces, TWMS J. Appl. Eng. Math. 10 (2020), 379–388.
  10. G.N.V. Kishore, D.R. Prasad, B.S. Rao, V.S. Baghavan, Some Applications via Common Coupled Fixed Point Theorems in Bipolar Metric Spaces, J. Crit. Rev. 7 (2020), 601–607.
  11. G.N.V. Kishore, K.P.R. Rao, A. Sombabu, R.V.N.S. Rao, Related Results to Hybrid Pair of Mappings and Applications in Bipolar Metric Spaces, J. Math. 2019 (2019), 8485412. https://doi.org/10.1155/2019/8485412.
  12. P.P. Murthy, Z. Mitrovic, C.P. Dhuri, S. Radenovic, The Common Fixed Points in a Bipolar Metric Space, Gulf J. Math. 12 (2022), 31–38. https://doi.org/10.56947/gjom.v12i2.741.
  13. B.S. Rao, E. Gouthami, C. Maheswari, M.S. Shaik, Coupled Coincidence Points for Hybrid Pair of Mappings via Mixed Monotone Property in Bipolar Metric Spaces, Adv. Fixed Point Theory, 12 (2022), 3. https://doi.org/10.28919/afpt/7034.
  14. N. Parkala, U.R. Gujjula, S.R. Bagathi, Some Quadruple Fixed Points of Integral Type Contraction Mappings in Bipolar Metric Spaces with Application, Indian J. Sci. Technol. 16 (2023), 1843–1856. https://doi.org/10.17485/ijst/v16i25.2058.
  15. G.U. Reddy, C. Ushabhavani, B.S. Rao, Existence Fixed Point Solutions for C-Class Functions in Bipolar Metric Spaces With Applications, Int. J. Anal. Appl. 21 (2023), 7. https://doi.org/10.28924/2291-8639-21-2023-7.
  16. M.G. Tas, , D. Türko ˘glu, I. Altun, Fixed Point Results for P-Contractive Mappings on M-Metric Space and Application, AIMS Math. 9 (2024), 9770–9784. https://doi.org/10.3934/math.2024478.
  17. ˙I. Altun, H. Aslan Hançer, M.D. Ate¸s, Enriched P-Contractions on Normed Space and a Fixed Point Result, Turk. J. Math. Comp. Sci. 16 (2024), 64–69. https://doi.org/10.47000/tjmcs.1391969.
  18. H. Alamri, N. Hussain, I. Altun, Proximity Point Results for Generalized p-Cyclic Reich Contractions: An Application to Solving Integral Equations, Mathematics 11 (2023), 4832. https://doi.org/10.3390/math11234832.
  19. P. Mondal, H. Garai, L. K. Dey, On Contractive Mappings in bv(s)-Metric Spaces, Fixed Point Theory, 23 (2022), 573–590. https://doi.org/10.24193/fpt-ro.2022.2.10.
  20. M.A. Alghamdi, N. Hussain, P. Salimi, Fixed Point and Coupled Fixed Point Theorems on b-Metric-Like Spaces, J. Inequal. Appl. 2013 (2013), 402. https://doi.org/10.1186/1029-242x-2013-402.