Abstract
In this paper, we first give a new fixed point theorem for generalized Ćirić quasi-contraction maps in generalized metric spaces. Then we derive a common fixed point result for quasi-contractive type maps. Some examples are given to support our results. Our results extend and improve some fixed point and common fixed point theorems in the literature.MSC:47H10.
Highlights
Introduction and preliminariesThe well-known Banach fixed point theorem asserts that if (X, d) is a complete metric space and T : X → X is a map such that d(Tx, Ty) ≤ cd(x, y) for each x, y ∈ X, where ≤ c
We introduce the concept of a generalized Ćirić quasi-contraction map in generalized metric spaces
We show that there exists < c < such that α d Tn– x, Tnx < c for each n =
Summary
Introduction and preliminariesThe well-known Banach fixed point theorem asserts that if (X, d) is a complete metric space and T : X → X is a map such that d(Tx, Ty) ≤ cd(x, y) for each x, y ∈ X, where ≤ c < , T has a unique fixed point x ∈ X and for any x ∈ X, the sequence {Tnx } converges to x.In recent years, a number of generalizations of the above Banach contraction principle have appeared. 1 Introduction and preliminaries The well-known Banach fixed point theorem asserts that if (X, d) is a complete metric space and T : X → X is a map such that d(Tx, Ty) ≤ cd(x, y) for each x, y ∈ X, where ≤ c < , T has a unique fixed point x ∈ X and for any x ∈ X, the sequence {Tnx } converges to x. Let T : X → X be a Ćirić quasicontraction map, that is, there exists c < such that d(Tx, Ty) ≤ c max d(x, y), d(x, Tx), d(y, Ty), d(x, Ty), d(y, Tx) for any x, y ∈ X.
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