It is well known that a microperiodic function mapping a topological group into reals, which is continuous at some point is constant. We introduce the notion of a microperiodic multifunction, defined on a topological group with values in a metric space, and study regularity conditions implying an analogous result. We deal with Vietoris and Hausdorff continuity concepts.Stability of microperiodi...

it is well known that a microperiodic function mapping a topological group into reals, which is continuous at some point is constant. we introduce the notion of a microperiodic multifunction, defined on a topological group with values in a metric space, and study regularity conditions implying an analogous result. we deal with vietoris and hausdorff continuity concepts.stability of microperiodi...

The paper deals with affine selections of affine (both convex and concave) multifunctions acting between finite-dimensional real normed spaces. It is proved that each affine multifunction with compact values possesses an exhaustive family of affine selections and, consequently, can be represented by its affine selections. Moreover, a convex multifunction with compact values possesses an exhaust...

In this paper, we study a class of fractional q-differential inclusion order 0 < q 1 under L1-Caratheodory with convex-compact valued properties on multifunctions. By the use existence fixed point for closed contractive multifunction complete metric space which has been proved by Covitz and Nadler, provide solutions problem via some conditions. Also, give couple examples to elaborate our resul...

We introduce one-sided Lipschitz (OSL) conditions of set-valued maps with respect to given set differences. The existence of selections of such maps that pass through any point of their graphs and inherit uniformly their OSL constants is studied. We show that the OSL property of a convex-valued set-valued map with respect to the Demyanov difference with a given constant is characterized by the ...

We will always consider a Carathéodory set-valued map F : R×RN RN with nonempty, compact, and convex values. We recall that F is said to be a Carathéodory multifunction if F(·,x) is measurable for each x ∈ RN , and F(t,·) is upper semicontinuous for almost all (a.a.) t ∈ R. For the definitions of these standard notions, see, for example, [30]. Our main result is Theorem 4.2. It states the exist...

We quantify the sensitivity of KKT pairs associated with a parameterized family of nonlinear programming problems. Our approach involves proto-derivatives, which are generalized derivatives appropriate even in cases when the KKT pairs are not unique; we investigate what the theory of such derivatives yields in the special case when the KKT pairs are unique (locally). We demonstrate that the gra...

Gwinner (1981) proved an existence theorem for a variational inequality problem involving an upper semicontinuous multifunction with compact convex values. The aim of this paper is to solve this problem for a multifunction with open inverse values.

We characterize compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions on metric spaces, not necessarily compact, with Lipschitz involutions and determine their spectra.