Abstract
In this paper, we present the notion ofθ−ϕ−expansive mapping in complete rectangular metric spaces and study various fixed point theorems for such mappings. The presented theorems extend, generalize, and improve many existing results in the literature.
Highlights
The problem of fixed points of mapping with an adequate contractive condition has been the focal point of a rigorous research activity
We present the notion of θ − φ − expansive mapping in complete rectangular metric spaces and study various fixed point theorems for such mappings
Kumar et al [9] introduced a new notion of generalized ðα, ψÞ − expansive mappings and established some fixed point theorems for such mappings in complete generalized metric spaces
Summary
The problem of fixed points of mapping with an adequate contractive condition has been the focal point of a rigorous research activity. It has an extensive applications in different areas such as nonlinear and adaptive control systems, parametrized estimation problems, fractal image decoding, and convergence of recurrent networks. Kumar et al [9] introduced a new notion of generalized ðα, ψÞ − expansive mappings and established some fixed point theorems for such mappings in complete generalized metric spaces. In this paper, inspired by the idea of θ − φ − contraction introduced by Zheng et al [10] in metric spaces, we presented θ − φ − expansive mapping and establish various fixed point theorems for such mappings in complete rectangular metric spaces.
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