Abstract
In this paper, we investigate the sufficient condition for the existence of best proximity points for non-self-multivalued mappings. Additionally, we discuss the stability theorem for such mappings. Our results improve and generalize some existing results on the topic in the literature, in particular, the results of Lim and of Abkar and Gabeleh.
Highlights
Introduction and preliminariesLet (X, d) be a metric space and A, B be subsets of X
Our results extend and generalize some results by Lim [ ], and Abkar and Gabeleh [ ]
Assume that A is nonempty and T : A → B is a mapping satisfying the following conditions: (i) for each x ∈ A, we have Tx ∈ B ; (ii) the pair (A, B) satisfies the weak P-property; (iii) there exists x ∈ A such that T is a proximal contraction on the closed ball B(x, r), that is, d(Tx, Ty) ≤ αd(x, y) for each x, y ∈ B(x, r) ∩ A
Summary
Introduction and preliminariesLet (X, d) be a metric space and A, B be subsets of X. We discuss sufficient conditions which ensure the existence of best proximity points for multivalued non-self-mappings satisfying contraction condition on the closed ball of a complete metric space.
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