Abstract
Abstract In this paper, we prove some coincidence and fixed point theorems for a new type of multi-valued weak G-contraction mapping with compact values. The results of this paper extend and generalize several known results from a complete metric space endowed with a graph. Some examples are given to illustrate the usability of our results. MSC:47H04, 47H10.
Highlights
The classical contraction mapping principle of Banach states that if (X, d) is a complete metric space and f : X → X is a contraction mapping, i.e., d(f (x), f (y)) ≤ αd(x, y) for all x, y ∈ X, where α ∈ [, ), f has a unique fixed point
Banach fixed point theorem plays an important role in several branches of mathematics
Because of its usefulness for mathematical theory, Banach fixed point theorem has been extended in many directions; see [ – ]
Summary
The classical contraction mapping principle of Banach states that if (X, d) is a complete metric space and f : X → X is a contraction mapping, i.e., d(f (x), f (y)) ≤ αd(x, y) for all x, y ∈ X, where α ∈ [ , ), f has a unique fixed point. They showed that in a complete metric space, every generalized multi-valued (α, L)weak contraction has a fixed point.
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