Abstract
Some new existence theorems concerning approximate coincidence point property and approximate fixed point property for nonlinear maps in metric spaces without global completeness are established in this paper. By exploiting these results, we prove some new coincidence point and fixed point theorems which generalize and improve Berinde-Berinde's fixed point theorem, Mizoguchi-Takahashi's fixed point theorem, Kikkawa-Suzuki's fixed point theorem, and some well known results in the literature. Moreover, some applications of our results to the existence of coupled coincidence point and coupled fixed point are also presented.
Highlights
Let us begin with some basic definitions and notations that will be needed in this paper
Let (X, d) be a metric space and Dp be a τ0-metric on CB(X) induced by a τ0-function p
Let (X, d) be a metric space, p be a τ0-function, Dp be a τ0-metric on CB(X) induced by p, T : X → CB(X) be a multivalued map and f : X → X be a self-map
Summary
Let us begin with some basic definitions and notations that will be needed in this paper. 2.2], the authors had shown that every generalized multivalued almost contraction in a metric space (X, d) has the approximate fixed point property. Kikkawa and Suzuki [8] proved an interesting generalization of both Theorem 1 and the Nadler fixed point theorem [9] which is an extension of the Banach contraction principle to multivalued maps. Let (X, d) be a complete metric space, α : [0, ∞) → [0, 1) be a MT-function and T : X → CB(X) be a multivalued map. In this paper, some of our results are original in the literature and we obtain many results in the literature as special cases; see for example, [4,5,6,7,8,9,10, 13, 14, 17,18,19,20,21,22,23, 30] and references therein
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