In this paper, we introduce the concept of contractive pair maps and give some necessary sufficient conditions for existence uniqueness best proximity points such pairs. our approach, have been weakened. An application has presented to demonstrate usability results. Also, cyclic ?-contraction asymptotic convergence theorems on point mappings. The results extend, generalize improve known from th...

In this article we survey the existence of best proximity points for a class of non-self mappings which‎ satisfy a particular nonexpansiveness condition. In this way, we improve and extend a main result of Abkar and Gabeleh [‎A‎. ‎Abkar‎, ‎M‎. ‎Gabeleh‎, Best proximity points of non-self mappings‎, ‎Top‎, ‎21, (2013)‎, ‎287-295]‎ which guarantees the existence of best proximity points for nonex...

In this article, we introduce a new class of non-self mappings, called weak proximal contractions, which contains the proximal contractions as a subclass. Existence and uniqueness results of a best proximity point for weak proximal contractions are obtained. Also, we provide sufficient conditions for the existence of common best proximity points for two non-self mappings in metric spaces having...

Given A and B two subsets of a metric space, a mapping T : A∪B → A∪B is said to be cyclic if T (A) ⊆ B and T (B) ⊆ A. It is known that, if A and B are nonempty and complete and the cyclic map verifies for some k ∈ (0, 1) that d(Tx, Ty) ≤ kd(x, y) ∀ x ∈ A and y ∈ B, then A∩B 6= ∅ and the mapping T has a unique fixed point. A generalization of this situation was studied under the assumption of A ...

Let us consider two nonempty subsets A, B of a normed linear space X , and let us denote by 2B the set of all subsets of B. We introduce a new class of multivalued mappings {T : A → 2B}, called R-KKM mappings, which extends the notion of KKM mappings. First, we discuss some sufficient conditions for which the set ∩{T (x) : x ∈ A} is nonempty. Using this nonempty intersection theorem, we attempt...