New Fixed Point Theorem for generalized T_F -contractive Mappings and its Application for Solving Some Polynomials

Open Access

Original research article

Author(s):

Sirous Moradi

Department of Mathematics, Faculty of Sciences, Lorestan University, Khorramabad, 68151-4-4316, Iran

Advances in the Theory of Nonlinear Analysis and its Applications 4(3), 167–175.

Received: July 24, 2020

Accepted: August 25, 2020

Published: August 27, 2020

Abstract

Let (X, d) be a complete metric space. In this paper, we study some new fixed point theorems for generalized T_F -contractive mapping defined on complete metric spaces by using graph closed concept and we proved the existence and uniqueness of a fixed point. These conditions are analogous to Ćirić conditions. In this paper, we compare the two concepts of graph closed and sequentially convergent, and we show that the concept of sequentially convergent is a special case of the concept of graph closed. Also, we provide an counterexample for Dubey et. al. and provide an example in support of our main results. Finally, by using our main results, we present an application to solving some polynomials. Our results, extend several results on the topic in the corresponding literature.

Keywords: Fixed point, contractive mapping, generalized T_F-contractive mapping, graph closed

Share & Cite

APA Style

Moradi, S. (2023). New fixed point theorem for generalized $T_F$ -contractive mappings and its application for solving some polynomials. Advances in the Theory of Nonlinear Analysis and Its Application, 4(3), 167–175.