Abstract
In this paper, we present the notion of generalized \(F\)-expansive mapping incomplete rectangular metric spaces and study various fixed point theorems for such mappings. The findings of this paper, generalize and improve many existing results in the literature.
Highlights
The fixed point theory is a very interesting research area in due to its wide range of applicability, to resolve diverse problems emanating from the theory of nonlinear differential equations and integral equations.Wardowski [1], generalized the famous Banach theorem [2] for F−contraction on metric spaces, several mathematicians extended this new notion for contraction on metric spaces [3–6].The concept of a rectangular metric space was introduced by Branciari in [7]
In this paper, we present the notion of generalized F-expansive mapping in complete rectangular metric spaces and study various fixed point theorems for such mappings
In this paper, inspired by the idea of F−contraction introduced by Wardowski [1] in metric spaces, we presented generalized F−expansive mapping and establish various fixed point theorems for such mappings in complete rectangular metric spaces
Summary
The fixed point theory is a very interesting research area in due to its wide range of applicability, to resolve diverse problems emanating from the theory of nonlinear differential equations and integral equations. Wardowski [1], generalized the famous Banach theorem [2] for F−contraction on metric spaces, several mathematicians extended this new notion for contraction on metric spaces [3–6]. The concept of a rectangular metric space was introduced by Branciari in [7]. Several interesting results about the existence of fixed points in rectangular metric spaces have been obtained [8–11]. Kari et al, [12], obtained some results for generalized θ − φ−expansive mapping in rectangular metric spaces. Kumar et al, [14], introduced a new concept of (α, ψ)−expansive mappings and established some fixed point theorems for such mapping in complete rectangular metric spaces. In this paper, inspired by the idea of F−contraction introduced by Wardowski [1] in metric spaces, we presented generalized F−expansive mapping and establish various fixed point theorems for such mappings in complete rectangular metric spaces.
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