Abstract
In this paper, we introduce a new type of a generalized- -Meir-Keeler contractive mapping and establish some interesting theorems on the existence of fixed points for such mappings via admissible mappings. Applying our results, we derive fixed point theorems in ordinary metric spaces and metric spaces endowed with an arbitrary binary relation. MSC:47H10, 54H25.
Highlights
Fixed points and fixed point theorems have countless applications and have become a major theoretical tool in many fields such as differential equations, mathematical economics, game theory, dynamics, optimal control, functional analysis, and operator theory
The well-known Banach contraction principle is one of the forceful tools in nonlinear analysis, which states that every contraction self-mapping T on complete metric spaces (X, d) (i.e., d(Tx, Ty) ≤ kd(x, y) for all x, y ∈ X, where k ∈ [, )) has a unique fixed point
In Meir and Keeler [ ] established a fixed point theorem in a metric space (X, d) for mappings satisfying the condition that for each ε > there exists δ(ε) > such that ε ≤ d(x, y) < ε + δ(ε) implies d(Tx, Ty) < ε for all x, y ∈ X
Summary
Fixed points and fixed point theorems have countless applications and have become a major theoretical tool in many fields such as differential equations, mathematical economics, game theory, dynamics, optimal control, functional analysis, and operator theory. In Meir and Keeler [ ] established a fixed point theorem in a metric space (X, d) for mappings satisfying the condition that for each ε > there exists δ(ε) > such that ε ≤ d(x, y) < ε + δ(ε) implies d(Tx, Ty) < ε for all x, y ∈ X.
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