Abstract
Abstract In this paper, we introduce a new class of expansive mappings called generalized ( ξ , α ) -expansive mappings and investigate the existence of a fixed point for the mappings in this class. We conclude that several fixed-point theorems can be considered as a consequence of main results. Moreover, some examples are given to illustrate the usability of the obtained results. MSC:46T99, 54H25, 47H10, 54E50.
Highlights
1 Introduction Fixed-point theory has attracted many mathematicians since it provides a simple proof for the existence and uniqueness of the solutions to various mathematical models
We mention the α-ψ -contractive mapping, which was introduced by Samet et al [ ] via α-admissible mappings
Samet et al [ ] stated that several existing results can be concluded from their main results
Summary
Fixed-point theory has attracted many mathematicians since it provides a simple proof for the existence and uniqueness of the solutions to various mathematical models (integral and partial differential equations, variational inequalities etc.). [ ] Let (X, d) be a complete metric space and T : X → X be an α-ψ contractive mapping satisfying the following conditions: (i) T is α-admissible; (ii) there exists x ∈ X such that α(x , Tx ) ≥ ; (iii) T is continuous.
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