The cognate of multiplicative Kannan contraction is inherited to substantiate the fixed point theorem in Rectangular multiplicative b metric spaces. Rectangular multiplicative b metric space is introduced by the generalization of multiplicative metric space and rectangular b metric space.
In this paper, we introduce the concept of (α z , ψ x , ξ y)-rational type I contractive mappings and provide sufficient conditions for the existence and uniqueness of a fixed point theorems.
This article presents best proximity point theorems for new classes of non-self mappings, known as generalized JSC-proximal contractions in metric spaces.Presented results and theorems are generalizations of [8] and [9] Mathematical Subject Classification:41A65; 46B20; 47H10.Let A and B be the non-empty subsets of a metric space. We know that the following notations and notions are used in the sequel. d(A, B) = inf{d(x, y) : x ∈ A and y ∈ B} A 0 = {x ∈ A : d(x, y) = d(A, B) for some y ∈ B} B 0 = {y ∈ B : d(x, y) = d(A, B) for some x ∈ A} If A and B are closed subsets of a normed linear space such that d(A, B) > 0, then A 0 and B 0 are contained in the boundaries of A and B respectively [7].Definition 2.1. [9] The Set B is said to be approximately compact with respect to A if every sequence {y n } of B satisfying the condition that d(x, y n ) → 3 Main Results Definition 3.1. A mapping T : A → B is said to be generalized JSCproximal contraction of the first kind if there exists ψ ∈ Ψ and non-negative numbers q, r, s, t with q + r + s + 2t < 1 such that the conditions d(u 1 , T x 1 ) = d(A, B) and d(u 2 , T x 2 ) = d(A, B)
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.