Common Fixed Point Theorems in Orthogonal Sets

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V. Pragadeeswarar, V. Vishnu KS, Manuel De la Sen

Abstract

In this paper, we introduce new notions of ⊥ Λ-quasicontraction and ⊥ Λ-preserving in the setting of orthogonal sets and prove respective common fixed point theorems. Furthermore, we provide an example to clarify our main result. Our results extend, improve, and generalize several known results in the literature.

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References

  1. M. Abbas, A.R. Khan, T. Nazir, Coupled Common Fixed Point Results in Two Generalized Metric Spaces, Appl. Math. Comput. 217 (2011), 6328–6336. https://doi.org/10.1016/j.amc.2011.01.006.
  2. A. Abkar, M. Eslamian, Common Fixed Point Results in Cat(0) Spaces, Nonlinear Anal.: Theory Methods Appl. 74 (2011), 1835–1840. https://doi.org/10.1016/j.na.2010.10.056.
  3. H. Baghani, M. Eshaghi Gordji, M. Ramezani, Orthogonal Sets: the Axiom of Choice and Proof of a Fixed Point Theorem, J. Fixed Point Theory Appl. 18 (2016), 465–477. https://doi.org/10.1007/s11784-016-0297-9.
  4. P. Dhivya, M. Marudai, Common Fixed Point Theorems for Mappings Satisfying a Contractive Condition of Rational Expression on a Ordered Complex Partial Metric Space, Cogent Math. 4 (2017), 1389622. https://doi.org/10.1080/23311835.2017.1389622.
  5. M. 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.
  6. M.E. Gordji, H. Habibi, M.B. Sahabi, Orthogonal Sets; Orthogonal Contractions, Asian-Eur. J. Math. 12 (2019), 1950034. https://doi.org/10.1142/s1793557119500347.
  7. H. Guan, J. Li, Common Fixed-Point Theorems of Generalized (ψ, φ)-Weakly Contractive Mappings in b-MetricLike Spaces and Application, J. Math. 2021 (2021), 6680381. https://doi.org/10.1155/2021/6680381.
  8. N.B. Gungor, D. Turkoglu, Fixed Point Theorems on Orthogonal Metric Spaces via Altering Distance Functions, AIP Conf. Proc. 2183 (2019), 040011. https://doi.org/10.1063/1.5136131.
  9. G. Jungck, Common Fixed Points for Noncontinuous Nonself Maps on Nonmetric Spaces, Far East. J. Math. Sci. 4 (1996), 199–215.
  10. Z. Kadelburg, M. Pavlovi´c, S. Radenovi´c, Common Fixed Point Theorems for Ordered Contractions and Quasicontractions in Ordered Cone Metric Spaces, Comput. Math. Appl. 59 (2010), 3148–3159. https://doi.org/10.1016/j.camwa.2010.02.039.
  11. V. Pragadeeswarar, G. Poonguzali, M. Marudai, S. Radenovi´c, Common Best Proximity Point Theorem for Multivalued Mappings in Partially Ordered Metric Spaces, Fixed Point Theory Appl. 2017 (2017), 22. https://doi.org/10.1186/s13663-017-0615-y.
  12. V. Pragadeeswarar, R. Gopi, Existence and Uniqueness of a Common Best Proximity Point on Fuzzy Metric Space, Fuzzy Inf. Eng. 11 (2019), 54–63. https://doi.org/10.1080/16168658.2020.1746484.
  13. A.S. Unni, V. Pragadeeswarar, Proximal Iterated Function Systems Using Cyclic Meir-Keeler Contractions and an Application to Fractal Theory, Fixed Point Theory Algorithms Sci. Eng. 2025 (2025), 3. https://doi.org/10.1186/s13663-025-00784-7.
  14. M. Sarwar, M.B. Zada, ˙I.M. Erhan, Common Fixed Point Theorems of Integral Type Contraction on Metric Spaces and Its Applications to System of Functional Equations, Fixed Point Theory Appl. 2015 (2015), 217. https://doi.org/10.1186/s13663-015-0466-3.
  15. K. Sawangsup, W. Sintunavarat, Y.J. Cho, Fixed Point Theorems for Orthogonal F-Contraction Mappings on OComplete Metric Spaces, J. Fixed Point Theory Appl. 22 (2019), 10. https://doi.org/10.1007/s11784-019-0737-4.