Fixed Point Results for w-Distance Functions via Altering Distance Functions on Orthogonal Metric Spaces

Year 2024, Volume: 7 Issue: 2, 1 - 8, 01.06.2024

Nurcan Bilgili Güngör

Abstract

In 2018, Senapati et al. respectively defined the orthogonal lower semi continuity and presented the notion w-distance in orthogonal metric space. Also they gave a fixed point theorem which is the version of Banach fixed point theorem in orthogonal metric spaces thanks to the concept of w-distance. A fixed point theorem for w-distance functions on orthogonal metric spaces are presented in this work. This theorem is a generalization of the version of Banach fixed point theorem in orthogonal metric spaces owing to the concept of w-distance.

Keywords

w-distance , orthogonal metric space , fixed point theorems , orthogonal p-contraction

References

• [1] Acar, Ö. and Esref, Erdogan, 2022, Some fixed point results for almost contraction on
• orthogonal metric space. Creative Mathematics & Informatics, 31(2).
• [2] Acar, Ö., Erdoğan, E. and Özkapu, A. S., 2022, Generalized integral type mappings on
• orthogonal metric spaces, Carpathian Mathematical Publications, 14(2), 485-492.
• [3] Acar, Ö. and Özkapu, A. S. , 2023, Multivalued rational type F-contraction on orthogonal
• metric space. Mathematical Foundations of Computing, 6(3), 303-312.
• [4] Alber, Y. I. and Guerre-Delabriere, S. , 1997, Principle of weakly contractive maps in
• Hilbert spaces, In New results in operator theory and its applications (pp. 7-22),
• Birkh¨auser, Basel.
• [5] Baghani, H.; Gordji, M.E.; Ramezani, M., 2016, Orthogonal sets: The axiom of choice
• and proof of a fixed-point theorem, J. Fixed Point Theory Appl., 18, 465–477.
• [6] Banach, S., 1922, Surles operations dans les ensembles abstraits et leur application aux
• equationsitegrales, Fund. Math., 3, 133–181.
• [7] Bilgili Gungor, N. and Turkoglu, D. , 2019, Fixed Point Theorems on Orthogonal Metric
• Spaces via Altering Distance Functions, 3rd International Conference on Mathematical Sciences (ICMS 2019), 4-8 September 2019, Maltepe University.
• [8] Bilgili Gungor, N., 2022, Extensions of orthogonal p-contraction on orthogonal metric
• spaces, Symmetry, 14(4), 746.
• [9] Eshaghi Gordji, M. and Habibi, H. , 2017, Fixed point theory in generalized orthogonal metric space, Journal of Linear and Topological Algebra (JLTA), 6(3), 251-260.
• [10] Gordji, M. E., Ramezani, M., De La Sen, M. and Cho, Y. J., 2017, On orthogonal sets
• and Banach fixed point theorem, Fixed Point Theory, 18(2), 569-578.
• [11]Gungor, N. B. (2022). Some fixed point results via auxiliary functions on orthogonal
• metric spaces and application to homotopy. AIMS Mathematics, 7(8), 14861-14874.
• [12] Gungor, N. B. , 2022, Some fixed point theorems on orthogonal metric spaces via
• extensions of orthogonal contractions. Communications Faculty of Sciences University of
• Ankara Series A1 Mathematics and Statistics, 71(2), 481-489.
• [13] Kada, O.; Suzuki, T.; Takahashi, W. , 1996, Nonconvex minimization theorems and fixed-point theorems in complete metric spaces, Math. Jpn. , 44, 381–391.
• [14] Khan, M. S., Swaleh, M. and Sessa, S. , 1984, Fixed point theorems by altering distances between the points, Bulletin of the Australian Mathematical Society, 30(1), 1-9.
• [15] Nazam, M., Chandok, S., Hussain, A. and Sulmi, H. H. A. , 2023, On the Iterative
• Multivalued⊥-Preserving Mappings and an Application to Fractional Differential Equation. Axioms, 12(1), 53.
• [16] Ramezani, M. , 2015, Orthogonal metric space and convex contractions, Int. J.
• Nonlinear Anal. Appl. , 6, 127–132.
• [17] Ramezani, M.; Baghani, H., 2017, Contractive gauge functions in strongly orthogonal
• metric spaces, Int. J. Nonlinear Anal. Appl. , 8, 23–28.
• [18] Rhoades, B. E. , 2001, Some theorems on weakly contractive maps, Nonlinear Analysis:
• Theory, Methods and Applications, 47(4), 2683-2693.
• [19] Sawangsup, K. and Sintunavarat, W., 2020, Fixed point results for orthogonal Z-
• contraction mappings in O-complete metric space. Int. J. Appl. Phys. Math, 10(1), 33-40.
• [20] Senapati, T., Dey, L. K., Damjanovi´c, B. and Chanda, A. , 2018, New fixed point results
• in orthogonal metric spaces with an application, Kragujevac Journal of Mathematics, 42(4), 505-516.