Abstract
AbstractIn this paper, we state and prove Wardowski type fixed point theorems in metric space by using a modified generalized F-contraction maps. These theorems extend other well-known fundamental metrical fixed point theorems in the literature (Dung and Hang in Vietnam J. Math. 43:743-753, 2015 and Piri and Kumam in Fixed Point Theory Appl. 2014:210, 2014, etc.). Examples are provided to support the usability of our results.
Highlights
Introduction and preliminariesOne of the most well-known results in generalizations of the Banach contraction principle is the Wardowski fixed point theorem [ ]
Before providing the Wardowski fixed point theorem, we recall that a self-map T on a metric space (X, d) is said to be an F-contraction if there exist F ∈ F and τ ∈ (, ∞) such that
By adding values d(T x, x), d(T x, Tx), d(T x, y), d(T x, Ty) to ( ), Dung and Hang [ ] introduced the notion of a modified generalized F-contraction and proved a fixed point theorem for such maps
Summary
Introduction and preliminariesOne of the most well-known results in generalizations of the Banach contraction principle is the Wardowski fixed point theorem [ ]. Before providing the Wardowski fixed point theorem, we recall that a self-map T on a metric space (X, d) is said to be an F-contraction if there exist F ∈ F and τ ∈ ( , ∞) such that By using the notion of F-weak contraction, Wardowski and Van Dung [ ] have proved a fixed point theorem which generalizes the result of Wardowski as follows.
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