Abstract
In this manuscript, we investigate certain conditions that imply the existence of fixed points for almost contraction mappings defined on compact metric spaces. Furthermore we introduce a criteria establishing the uniqueness of fixed points for the mentioned operators. As a result we obtain generalized results by unifying some recent related fixed point theorems on the topic.
Highlights
1 Introduction and Preliminaries In nonlinear functional analysis, fixed point theory is being investigated increasingly by reason of the fact that it has a wide range of applications in fields such as economics, computer science, and many others
One of the pioneering theorems in this direction is the Banach contraction mapping principle [ ] which states that each contraction defined on a complete metric space X has a unique fixed point
Main Theorems We start this section by proving the following theorem: Theorem Let T be a self mapping on a compact metric space (X, d)
Summary
Introduction and PreliminariesIn nonlinear functional analysis, fixed point theory is being investigated increasingly by reason of the fact that it has a wide range of applications in fields such as economics (see e.g. [ , ]), computer science (see e.g. [ – ]), and many others. One of the pioneering theorems in this direction is the Banach contraction mapping principle [ ] which states that each contraction defined on a complete metric space X has a unique fixed point. Every mapping T on X satisfying the following has a fixed point: There exists r ∈ [ , ) such that θ (r)d(x, Tx) ≤ d(x, y) implies d(Tx, Ty) ≤ rd(x, y) for all x, y ∈ X.
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