Common Fixed Point Techniques in Bipolar Orthogonal Metric Space With Applications to Economic Problem and Integral Equation

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-23-2025-52
Published: Mar 3, 2025
Cite as:
Gunaseelan Mani, Gopinath Janardhanan, Sabri T.M. Thabet, Imed Kedim, Miguel Vivas-Cortez, Common Fixed Point Techniques in Bipolar Orthogonal Metric Space With Applications to Economic Problem and Integral Equation, Int. J. Anal. Appl., 23 (2025), 52.

Main Article Content

Gunaseelan Mani, Gopinath Janardhanan, Sabri T.M. Thabet, Imed Kedim, Miguel Vivas-Cortez

Abstract

This article proves a new common fixed point theorems in bipolar orthogonal metric space in the context of the Meir-Keeler contraction type. We have given some suitable examples based on our obtain theorems. Finally, we provide an application to the integral equation and an application to the production-consumption equilibrium problem.

Article Details

References

  1. S. Banach, Sur les Opérations dans les Ensembles Abstraits et leur Application aux Équations Intégrales, Fundam. Math. 3 (1922), 133–181. https://doi.org/10.4064/fm-3-1-133-181.
  2. A. Mutlu, U. Gürdal, Bipolar Metric Spaces and Some Fixed Point Theorems, J. Nonlinear Sci. Appl. 09 (2016), 5362–5373. https://doi.org/10.22436/jnsa.009.09.05.
  3. G. Mani, A.J. Gnanaprakasam, K. Javed, E. Ameer, S. Mansour, H. Aydi, W. Kallel, On a Fuzzy Bipolar Metric Setting with a Triangular Property and an Application on Integral Equations, AIMS Math. 8 (2023), 12696–12707. https://doi.org/10.3934/math.2023639.
  4. B. Srinuvasa Rao, G. N.V.Kishore, Common Fixed Point Theorems in Bipolar Metric Spaces with Applications to Integral Equations, Int. J. Eng. Technol. 7 (2018), 1022–1026. https://doi.org/10.14419/ijet.v7i4.10.26662.
  5. E. Karapınar, M. Cvetkovi´c, An Inevitable Note on Bipolar Metric Spaces, AIMS Math. 9 (2024), 3320–3331. https://doi.org/10.3934/math.2024162.
  6. Sunita Soni, Common Fixed Point Theorems in Bipolar Metric Spaces, Int. J. Sci. Res. Arch. 9 (2023), 741–746. https://doi.org/10.30574/ijsra.2023.9.1.0713.
  7. H. Ahmad, M. Younis, A.A.N. Abdou, Bipolar B-Metric Spaces in Graph Setting and Related Fixed Points, Symmetry 15 (2023), 1227. https://doi.org/10.3390/sym15061227.
  8. 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.
  9. A. Meir, E. Keeler, A Theorem on Contraction Mappings, J. Math. Anal. Appl. 28 (1969), 326–329. https://doi.org/10.1016/0022-247X(69)90031-6.
  10. M.S. Sezen, Some Special Functions in Orthogonal Fuzzy Bipolar Metric Spaces and Their Fixed Point Applications, Numer. Methods Partial Differ. Equ. 38 (2022), 794–802. https://doi.org/10.1002/num.22701.
  11. J.U. Maheswari, K. Dillibabu, G. Mani, S.T.M. Thabet, I. Kedim, M. Vivas-Cortez, On New Common Fixed Point Theorems via Bipolar Fuzzy b-Metric Space with Their Applications, PLOS ONE 19 (2024), e0305316. https://doi.org/10.1371/journal.pone.0305316.
  12. K. Javed, A. Asif, E. Savas, A Note on Orthogonal Fuzzy Metric Space, Its Properties, and Fixed Point Theorems, J. Funct. Spaces 2022 (2022), 5863328. https://doi.org/10.1155/2022/5863328.
  13. A.J. Gnanaprakasam, G. Mani, O. Ege, A. Aloqaily, N. Mlaiki, New Fixed Point Results in Orthogonal b-Metric Spaces with Related Applications, Mathematics 11 (2023), 677. https://doi.org/10.3390/math11030677.
  14. G. Janardhanan, G. Mani, O. Ege, V. Varadharajan, R. George, Orthogonal Neutrosophic 2-Metric Spaces, J. Inequal. Appl. 2023 (2023), 112. https://doi.org/10.1186/s13660-023-03024-x.
  15. G.Mani, A.J. Gnanaprakasam, K. Javed, S. Kumar, On Orthogonal Coupled Fixed Point Results with an Application, J. Funct. Spaces 2022 (2022), 5044181. https://doi.org/10.1155/2022/5044181.
  16. G. Mani, S.K. Prakasam, A.J. Gnanaprakasam, R. Ramaswamy, O.A.A. Abdelnaby, K.H. Khan, S. Radenovi´c, Common Fixed Point Theorems on Orthogonal Branciari Metric Spaces with an Application, Symmetry 14 (2022), 2420. https://doi.org/10.3390/sym14112420.
  17. Y. Touail, D. El Moutawakil, Fixed Point Theorems on Orthogonal Complete Metric Spaces with an Application, Int. J. Nonlinear Anal. Appl. 12 (2021), 1801-1809. https://doi.org/10.22075/ijnaa.2021.23033.2464.
  18. P.P. Murthy, C.P. Dhuri, S. Kumar, R. Ramaswamy, M.A.S. Alaskar, S. Radenovi’c, Common Fixed Point for Meir–Keeler Type Contraction in Bipolar Metric Space, Fractal Fract. 6 (2022), 649. https://doi.org/10.3390/fractalfract6110649.
  19. 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.
  20. M.E. Gordji, M. Rameani, M. de la Sen, Y.J. Cho, On Orthogonal Sets and Banach Fixed Point Theorem, Fixed Point Theory 18 (2017), 569–578. https://doi.org/10.24193/fpt-ro.2017.2.45.
  21. M. Nazam, H. Aydi, A. Hussain, Existence Theorems for (Ψ, Φ)-Orthogonal Interpolative Contractions and an Application to Fractional Differential Equations, Optimization 72 (2023), 1899–1929. https://doi.org/10.1080/02331934.2022.2043858.
  22. M. Mudhesh, A. Hussain, M. Arshad, H. Alsulami, A Contemporary Approach of Integral Khan-Type Multivalued Contractions with Generalized Dynamic Process and an Application, Mathematics 11 (2023), 4318. https://doi.org/10.3390/math11204318.
  23. A. Hussain, Fractional Differential Boundary Value Equation Utilizing the Convex Interpolation for Symmetry of Variables, Symmetry 15 (2023), 1189. https://doi.org/10.3390/sym15061189.
  24. R.K. Sharma, S. Chandok, Multivalued Problems, Orthogonal Mappings, and Fractional Integro-Differential Equation, J. Math. 2020 (2020), 6615478. https://doi.org/10.1155/2020/6615478.
  25. R. K. Sharma, S. Chandok, Existence, Stability and Well-Posedness of Fixed Point Problem With Application to Integral Equation, U.P.B. Sci. Bull., Ser. A 83 (2021), 59–68.
  26. S. Chandok, R.K. Sharma, S. Radenovi´c, Multivalued Problems via Orthogonal Contraction Mappings with Application to Fractional Differential Equation, J. Fixed Point Theory Appl. 23 (2021), 14. https://doi.org/10.1007/s11784-021-00850-8.
  27. R. Sharma, S. Chandok, Well-Posedness and Ulam’s Stability of Functional Equations in F-Metric Space with an Application, Filomat 36 (2022), 5573–5589. https://doi.org/10.2298/FIL2216573S.
  28. Godwin Amechi O, G.A. Okeke, D. Francis, Some Common Fixed Point Theorems in Generalized Modular Metric Spaces with Applications, Sci. Afr. 23 (2024), e02018. https://doi.org/10.1016/j.sciaf.2023.e02018.
  29. G.A. Okeke, D. Francis, A. Gibali, On Fixed Point Theorems for a Class of α-vˆ-Meir–Keeler-Type Contraction Mapping in Modular Extended b-Metric Spaces, J. Anal. 30 (2022), 1257–1282. https://doi.org/10.1007/s41478-022-00403-3.
  30. A.A. Thirthar, H. Abboubakar, A.L. Alaoui, K.S. Nisar, Dynamical Behavior of a Fractional-Order Epidemic Model for Investigating Two Fear Effect Functions, Results Control Optim. 16 (2024), 100474. https://doi.org/10.1016/j.rico.2024.100474.
  31. K. Muthuvel, K. Kaliraj, K.S. Nisar, V. Vijayakumar, Relative Controllability for ψ-Caputo Fractional Delay Control System, Results Control Optim. 16 (2024), 100475. https://doi.org/10.1016/j.rico.2024.100475.
  32. K.S. Nisar, A Constructive Numerical Approach to Solve the Fractional Modified Camassa–Holm Equation, Alex. Eng. J. 106 (2024), 19–24. https://doi.org/10.1016/j.aej.2024.06.076.