Common Fixed Point Results for Interpolative Kannan Type Contraction over $m$-Metric Spaces
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Authors: N. SHABIR, A. RAZA AND S. H. KHAN
DOI: 10.46793/KgJMat2604.633S
Abstract:
The objective of this paper is to derive common fixed point results in m-metric spaces by using the interpolative condition proposed by Karapınar. We discuss three distinct scenarios: when the sum of the “interpolative exponents” is less than, equal to, or greater than 1. The validity of each result is supported by illustrative examples.
Keywords:
Common fixed point, m-interpolative Kannan type contraction (IKTC), m-metric space(m-MS).
References:
[1] M. Asadi, E. Karapınar and P. Salimi, New extension of p-metric spaces with some fixed-point results on M-metric spaces, J. Inequal. Appl. 2014(1) (2014), 1–9. http://www.journalofinequalitiesandapplications.com/content/2014/1/18
[2] S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math. 3(1) (1922), 133–181.
[3] Y. Errai, E. M. Marhrani and M. Aamri, Some remarks on fixed point theorems for interpolative Kannan contraction, J. Funct. Spaces (2020). https://doi.org/10.1155/2020/2075920
[4] Y. U. Gaba, H. Aydi and N. Mlaiki, (ρ,η,μ)−Interpolative Kannan contractions I, Axioms (3) (2021), Article ID 212. https://doi.org/10.3390/axioms10030212
[5] Y. U. Gaba, and E. Karapınar, A new approach to the interpolative contractions, Axioms 8(4) (2019), Article ID 110. https://doi.org/10.3390/axioms8040110
[6] E. Karapınar, Revisiting the Kannan type contractions via interpolation, Adv. Nonlinear Anal. Appl. 2(2) (2018), 85–87. https://doi.org/10.31197/atnaa.431135
[7] E. Karapınar, R. P. Agarwal, S. S. Yeşilkaya and C. Wang, Fixed-point results for Meir-Keeler type contractions in partial metric apaces: A survey, Mathematics 10(17) (2022), Article ID 3109. https://doi.org/10.3390/math10173109
[8] S. H. Khan and A. Raza, Interpolative contractive results for m-metric spaces, Adv. Nonlinear Anal. Appl. 2 (2023), 336–347. https://doi.org/10.31197/atnaa.1220114
[9] S. G. Matthews, Partial metric topology, Ann. N. Y. Acad. Sci. 728(1) (1994), 183–197.
[10] M. Noorwal, Common fixed point for Kannan type contractions via interpolation, J. Math. Anal. 9(6) (2018), 92–94.
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