Abstract
In this article, we first introduce the concept of directional hidden contractions in metric spaces. The existences of generalized approximate fixed point property for various types of nonlinear contractive maps are also given. From these results, we present some new fixed point theorems for directional hidden contractions which generalize Berinde-Berinde's fixed point theorem, Mizoguchi-Takahashi's fixed point theorem and some well-known results in the literature.
Highlights
Introduction and preliminariesLet (X, d) be a metric space
The set of fixed points of T is denoted by F (T)
We present some existence theorems for directional hidden contractions
Summary
Introduction and preliminariesLet (X, d) be a metric space. The open ball centered in x Î X with radius r > 0 is denoted by B(x, r). A multivalued map T : K → N (X) is said to have the p-approximate fixed point property in provided inf p(x, Tx) be a function and g
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