Abstract
In this article, we study a new generalized multivalued Khan-type (psi ,phi )-contraction. We obtain some fixed point theorems related to the introduced contraction for multivalued mappings in complete metric spaces. Our theorems extend and improve some previous known results with less conditions. Also, we give some illustrative examples.
Highlights
Throughout this paper, N and N0 denote the set of positive integers and the set of nonnegative integers, respectively
R, R+ and R+0 represent the set of real numbers, positive real numbers and non-negative real numbers, respectively
In 1922, Banach [1] proved a famous result known as the Banach contraction principle, which states that every contractive mapping has a unique fixed point
Summary
Throughout this paper, N and N0 denote the set of positive integers and the set of nonnegative integers, respectively. Piri, Rahrovi and Kumamet [15] extended the work of both Khan [13] and Fisher [14] They accomplished the work by introducing a new general contractive condition with a symmetric expression and established a corresponding fixed point theorem. Another direction of generalizations of Banach’s work is to express both sides of the inequality in the Banach result by forms involving functions. Wardowski introduced the notion of the F-contraction in ([16], 2012) and Jleli and Samet addressed the so-called θ contraction in ([17, 18], 2014) As a result, they all extended and improved Banach’s work
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