Abstract
We recall the concepts of -contractive and α-admissible mappings on complete metric spaces to state related fixed point theorems. In this paper, we obtain some fixed point results for -expansive locally contractive mappings in complete metric spaces. The contractiveness of the mapping is only on a closed ball instead of the whole space. Our results unify, generalize, and complement various well-known comparable results in the literature. MSC:46S40, 47H10, 54H25.
Highlights
1 Introduction and preliminaries The main revolution in the existence theory of many linear and nonlinear operators happened after the Banach contraction principle [ ]
Samet et al in [ ] introduced the concepts of (α-ψ)-contractive and α-admissible mappings in complete metric spaces. They proved a fixed point theorem for (α-ψ)-contractive mappings in complete metric spaces using the concept of α-admissible mapping
We use the concept of α-admissible to study fixed point theorems for expansive mappings satisfying {α, ξ }-contractive conditions in a complete metric spaces
Summary
Introduction and preliminariesThe main revolution in the existence theory of many linear and nonlinear operators happened after the Banach contraction principle [ ]. They proved a fixed point theorem for (α-ψ)-contractive mappings in complete metric spaces using the concept of α-admissible mapping. Theorem [ ] Let (X, d) be a complete metric space and F be α-admissible mapping.
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