Abstract
In this article, we have designed two existence of fixed point theorems which are regarding to set-valued SU-type θ η -contraction and Γ α -contraction via gauge function in the setting of metric spaces. An extensive set of nontrivial example will be given to justify our claim. At the end, we will give an application to prove the existence behavior for the system of functional equation in dynamical system and integral inclusion.
Highlights
Introduction andPreliminaries e most publicized famous result in nonlinear analysis is Banach contraction principle, which made clear a systematic rule to find the fixed point of a given mapping on a metric space
In 2014, Jleli and Samet [1] introduced the concept of a new contraction known as the θ-contraction, which generalizes the Banach contraction principle in a beautiful way
Design the Pompeiu–Hausdorff metric Hd induced by ð on CB(X) as
Summary
Introduction andPreliminaries e most publicized famous result in nonlinear analysis is Banach contraction principle, which made clear a systematic rule to find the fixed point of a given mapping on a metric space. Let (X, ð) be a metric space and Λ be a nonempty subset of X, and T: Λ ⟶ CB(X) is known as α-admissible, if there exists a mapping α: Λ × Λ ⟶ [0, ∞) such that α β1, β2 ≥ 1⇒α(μ, ]) ≥ 1, (10)
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