Interpolative Contractive Results for $m$-Metric Spaces

Yıl 2023, Cilt: 7 Sayı: 2, 336 - 347, 23.07.2023

Safeer Khan , Ali Raza

https://doi.org/10.31197/atnaa.1220114

Cited By: 6

Öz

In this paper, we initiate the study of fixed points for interpolative mappings in m-metric spaces. We discuss
three different cases: the sum of interpolative exponents" is less than, equal to or greater than 1. We support
each of our result by examples in m-metric spaces. In the last section, we obtain our results in p-metric
spaces. Finally we note that our results generalize results of [3], [4] and [5] from ordinary metric to m- and
p-metrics.

Anahtar Kelimeler

$m$-metric , $p$-metric , Fixed point , Interpolative contractions. , $m$-metric, $p$-metric, Fixed point, Interpolative contractions

Kaynakça

• [1] Asadi, M., Karapınar, E. and Salimi, P., 2014. New extension of p-metric spaces with some fixed-point results on M-metric spaces. Journal of Inequalities and Applications, 2014(1), pp.1-9.
• [2] Banach, S., 1922. Sur les op´erations dans les ensembles abstraits et leur application aux ´equations int´egrales. Fund. math, 3(1), pp.133-181.
• [3] Errai, Y., Marhrani, E.M. and Aamri, M., 2020. Some remarks on fixed point theorems for interpolative Kannan contraction. Journal of Function Spaces, 2020.
• [4] Gaba, Y.U., Aydi, H. and Mlaiki, N., 2021. (ρ, η, µ)−Interpolative Kannan Contractions I. Axioms, 10(3), p.212.
• [5] Karapinar, E., Revisiting the Kannan type contractions via interpolation. Adv. Theory Nonlinear Anal. Appl. 2, no. 2 (2018), 85–87.
• [6] Matthews, S.G., 1994. Partial metric topology. Annals of the New York Academy of Sciences, 728(1), pp.183-197.
• [7] Asadi, M., 2015. Fixed point theorems for Meir-Keeler type mappings in M-metric spaces with applications. Fixed Point Theory and Applications, 2015, pp.1-10.
• [8] Asadi, M., Azhini, M., Karapinar, E. and Monfared, H., 2017. Simulation functions over M-metric spaces. East Asian mathematical journal, 33(5), pp.559-570.
• [9] Monfared, H., Asadi, M., Azhini, M. and O’Regan, D., 2018. F(ψ, φ)- Contractions for α-admissible mappings on M-metric spaces. Fixed Point Theory and Applications, 2018(1), pp.1-17.
• [10] Monfared, H., Azhini, M. and Asadi, M., 2017. A generalized contraction principle with control function on M-metric spaces. Nonlinear Functional Analysis and Applications, 22(2), pp.395-402.
• [11] Asadi, M., 2016. On Ekeland’s variational principle in M-metric spaces. Journal of nonlinear and convex analysis, 17(6), pp.1151-1158.
• [12] Monfared, H., Azhini, M. and Asadi, M., 2017. C-class and F(ψ, φ)-contractions on M-metric spaces. International Journal of Nonlinear Analysis and Applications, 8(1), pp.209-224.
• [13] Asadi, M., Moeini, B.., Mukheimer, A. and Aydi, H., 2019. Complex valued M- metric spaces and related fixed point results via complex C- class function. Journal of Inequalities and Special Functions, 10(1), pp.101-110.
• [14] Moeini, B., Asadi, M., Aydi, H. and Noorani, M.S., 2019. C∗-algebra-valued M-metric spaces and some related fixed point results. Italian Journal of Pure and Applied Mathematics, 41, pp.708-723