Abstract
In this paper, we introduce α-admissible mappings on product spaces and obtain fixed point results for α-admissible Prešić type operators. Our results extend, unify and generalize some known results of the literature. We also provide examples which illustrate the results proved herein and show that how the new results are different from the existing ones.
Highlights
Let X be a nonempty set and f : X → X be a mapping
The famous Banach contraction principle ensures the existence and uniqueness of the fixed point of a mapping defined on a complete metric space
We define α-admissible mappings on product spaces and prove some fixed point results for α-admissible Prešictype operators
Summary
Let X be a nonempty set and f : X → X be a mapping. An element x∗ ∈ X is called a fixed point of f if f x∗ = x∗. The famous Banach contraction principle ensures the existence and uniqueness of the fixed point of a mapping defined on a complete metric space. Let (X, d) be a complete metric space with a contraction mapping f : X → X, that is, f satisfies the following condition: d(f x, f y) λd(x, y) for all x, y ∈ X, where λ ∈ [0, 1). Let (X, d) be a complete metric space, k a positive integer and T : Xk → X be a mapping satisfying the following contractive type condition: k d T
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