We establish uniform continuity of the value for zero-sum games with differential information, when the distance between changing information fields of each player is measured by the Boylan pseudometric. We also show that the optimal strategy correspondence is upper semicontinuous when the information fields of players change (even with the weak topology on players’ strategy sets), and is appro...

We consider the problem of approximating via ?-convergence a class of functionals depending on curvatures of smooth compact boundaries. We investigate the connections between the approximation problem and the lower semicontinuous envelope of the original functional. We provide some examples of lower semicontinuous functionals and their variational approximation.

In the paper, the notion of a generalized convexity was defined and studied from the view-point of the selection and approximation theory of set-valued maps. We study the simultaneous existence of continuous relative selections and graph-approximations of lower semicontinuous and upper semicontinuous set-valued maps with α-convex values having nonempty intersection.

We prove the existence of viable solutions for an autonomous second-order functional differential inclusions in the case when the multifunction that define the inclusion is upper semicontinuous compact valued and contained in the subdifferential of a proper lower semicontinuous convex function.

We introduce the concepts of IVF m-semiopen sets, IVF m-preopen sets, IVF m-semicontinuous mappings and IVF mprecontinuous mappings on interval-valued fuzzy minimal spaces. We investigate characterizations of IVF m-semicontinuous mappings and IVF m-precontinuous mappings and study properties of IVF m-semiopen sets and IVF m-preopen sets.

In this paper we present a topology on the space of real-valued functions defined on a functionally Hausdorff space X that is finer than the topology of pointwise convergence and for which (1) the closure of the set of continuous functions C(X) is the set of upper semicontinuous functions on X , and (2) the pointwise convergence of a net in C(X) to an upper semicontinuous limit automatically en...

In this paper we consider a splitting proximal algorithm with penalization for minimizing a finite sum of proper, convex and lower semicontinuous functions subject to the set of minimizers of another proper, convex and lower semicontinuous function. We show convergences of the generated sequence of iterates to an optimal solution of the considered hierarchical minimization problem. As an illust...

A number of semicontinuity concepts and the relations between them are discussed. Characterizations are given for when the (set-valued) metric projection P M onto a proximinal subspace M of a normed linear space X is approximate lower semicontinuous or 2-lower semicontinuous. A geometric characterization is given of those normed linear spaces X such that the metric projection onto every one-dim...