Frum-ketkov type multivalued operators

Abstract

Let (M, d) be a metric space, X ⊂ M be a nonempty closed subset and K ⊂ M be a nonempty compact subset. By definition, an upper semi-continuous multivalued operator F: X → P (X) is said to be a strong Frum-Ketkov type operator if there exists α ∈]0, 1[ such that ed (F (x), K) ≤ αDd (x, K), for every x ∈ X, where ed is the excess functional generated by d and Dd is the distance from a point to a set. In this paper, we will study the fixed points of strong Frum-Ketkov type multivalued operators. © 2021, SINUS Association. All rights reserved.