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)