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Journals and Conferences
In this paper we give some results on single-valuedness of setvalued maps satisfying linear inclusions.
K–convex, K–midconvex and (K,λ)–convex set–valued maps are considered. Several conditions implying the continuity of such maps are collected.
We introduce the notion of strongly h-convex functions (defined on a normed space) and present some properties and representations of such functions. We obtain a characterization of inner product… (More)
We introduce the notion of strongly t-convex set-valued maps and present some properties of it. In particular, a Bernstein–Doetsch and Sierpiński-type theorems for strongly midconvex set-valued maps,… (More)
In this paper, we study the Baker’s superstability for the following functional equation (E (K)) ∑ φ∈Φ ∫ K f(xkφ(y)k)dωK(k) = |Φ|f(x)f(y), x, y ∈ G where G is a locally compact group, K is a compact… (More)
In this paper, strongly (α ,T ) -convex functions, i.e., functions f : D → R satisfying the functional inequality f (tx+(1− t)y) t f (x)+(1− t) f (y)− tα(1− t)(x− y)− (1− t)αt(y− x) for x,y ∈ D and t… (More)
Motivated by results on strongly convex and strongly Jensen-convex functions by R. Ger and K. Nikodem in [Strongly convex functions of higher order, Nonlinear Anal. 74 (2011), 661–665] we investigate… (More)
We prove that a set-valued map F : X → P0(Y ) satisfying the functional inclusion F(x)♦F(y) ⊆ F(x∗ y) admits, in appropriate conditions, a unique selection f : X → Y satisfying the functional… (More)
We establish connections between invariant means and set ideals. As an application, we obtain a necessary and sufficient condition for the separation almost everywhere of two functions by an additive… (More)