Interpolative Contractive Results for $m$-Metric Spaces-Reference-Cited by-同舟云学术

Interpolative Contractive Results for $m$-Metric Spaces

Published:2023-07-23 Issue:2 Volume:7 Page:336-347
ISSN:2587-2648
Container-title:Advances in the Theory of Nonlinear Analysis and its Application
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Author:

KHAN Safeer¹^ORCID,RAZA Ali¹^ORCID

Affiliation:

1. Abdus Salam School of Mathematical Sciences, Government College University Lahore

Abstract

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.

Publisher

Erdal Karapinar

Subject

Applied Mathematics,Analysis

Reference14 articles.

1. [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. [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. [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. [4] Gaba, Y.U., Aydi, H. and Mlaiki, N., 2021. (ρ, η, µ)−Interpolative Kannan Contractions I. Axioms, 10(3), p.212.

5. [5] Karapinar, E., Revisiting the Kannan type contractions via interpolation. Adv. Theory Nonlinear Anal. Appl. 2, no. 2 (2018), 85–87.

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