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

Year 2020, Volume: 4 Issue: 3, 167 - 175, 31.08.2020

Sirous Moradi

https://doi.org/10.31197/atnaa.773720

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

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