Open Access

ARTICLE

On Some Novel Fixed Point Results for Generalized -Contractions in -Metric-Like Spaces with Application

by Kastriot Zoto¹, Ilir Vardhami², Dušan Bajović³, Zoran D. Mitrović^3,*, Stojan Radenović⁴

1 Department of Mathematics and Computer Sciences, Faculty of Natural Sciences, University of Gjirokastra, Gjirokastra, 6001, Albania
2 Department of Mathematics, Faculty of Natural Sciences, University of Tirana, Tirana, 1001, Albania
3 Faculty of Electrical Engineering, University of Banja Luka, Banja Luka, 78000, Bosnia and Herzegovina
4 Department of Mathematics, Faculty of Mechanical Engineering, University of Belgrade, Beograd, 11120, Serbia

* Corresponding Author: Zoran D. Mitrović. Email:

(This article belongs to the Special Issue: Computational Aspects of Nonlinear Operator and Fixed Point Theory with Applications)

Computer Modeling in Engineering & Sciences 2023, 135(1), 673-686. https://doi.org/10.32604/cmes.2022.022878

Received 30 March 2022; Accepted 17 May 2022; Issue published 29 September 2022

Abstract

The focus of our work is on the most recent results in fixed point theory related to contractive mappings. We describe variants of -contractions that expand, supplement and unify an important work widely discussed in the literature, based on existing classes of interpolative and -contractions. In particular, a large class of contractions in terms of and F for both linear and nonlinear contractions are defined in the framework of -metric-like spaces. The main result in our paper is that --weak contractions have a fixed point in -metric-like spaces if function F or the specified contraction is continuous. As an application of our results, we have shown the existence and uniqueness of solutions of some classes of nonlinear integral equations.

---

Keywords

---