Let (X, d) be a nonempty metric space, and let (2X , Hd) be the hyperspace of all nonempty compact subsets of X with the Hausdorff metric. Let F :X → 2X be an ε-contractive map. A general condition is given that guarantees the existence of a periodic point of F (the theorem extends a result of Edelstein to multi-valued maps). The condition holds when X is compact; hence, F has a periodic point ...

Continuous set-valued functions with convex images can be approximated by known positive operators of approximation, such as the Bernstein polynomial operators and the Schoenberg spline operators, with the usual sum between numbers replaced by the Minkowski sum of sets. Yet these operators fail to approximate set-valued functions with general sets as images. The Bernstein operators with growing...

This paper contains the equivalence between tvs-G cone metric and G-metric using a scalarization function $\zeta_p$, defined over locally convex Hausdorff topological vector space. ensures that most studies on existence uniqueness of fixed-point theorems space spaces are equivalent. We prove vector-valued version scalar-valued those spaces. Moreover, we present if real Banach is considered inst...

In this paper, we construct several types of multi-valued solutions to the Monge–Ampère equation in higher dimensions. Recently, there has been considerable interest in understanding the behavior of a metric generated by a solution of the Monge–Ampère equation at a singularity. See, for instance Loftin, Yau and Zaslow [14] and Leung [12]. To explain our results let us refer first to the theory ...