In this article, the notion of rational interpolative Meir-Keeler type contraction is discussed. The existence and uniqueness a fixed point for Das-Gupta are investigated. obtained results improve generalize existing on topic in recent literature.

In this paper, we introduce the new notion of contravariant (α−ψ) Meir–Keeler contractive mappings by defining α-orbital admissible and covariant contraction in bipolar metric spaces. We prove fixed point theorems for these contractions also provide some corollaries main results. An example is be given support our result. end, solve an integral equation using

Abstract We use methods from nonstandard analysis to unify and extend results the theory of asymptotic fixed points on metric spaces. Among topics we consider are Kirk’s point theorem with extensions, Boyd Wong’s theorem, Suzuki’s for contractions Meier–Keeler type. also show how final type can be modified yield uniform convergence compact bounded sets.

Throughout this paper, by R we denote the set of all nonnegative numbers, while N is the set of all natural numbers. Let A and B be nonempty subsets of a metric space X, d . Consider a mapping f : A ∪ B → A ∪ B, f is called a cyclic map if f A ⊆ B and f B ⊆ A. A point x in A is called a best proximity point of f in A if d x, fx d A,B is satisfied, where d A,B inf{d x, y : x ∈ A,y ∈ B}, and x ∈ ...