We prove a Filippov type existence theorem for mild solutions of a nonconvex evolution inclusion by applying the contraction principle in the space of selections of the multifunction instead of the space of solutions.

We prove the Lipschitz dependence on the initial condition of the solution set of a nonconvex second-order differential inclusions by applying the contraction principle in the space of selections of the multifunction instead of the space of solutions.

In this paper a new type of fuzzy multifunction termed as δ-precontinuous fuzzy multifunction has been introduced and studied. Some characterizations and several properties of this multifunction are obtained. We also characterize this multifunction by newly define fuzzy neighbourhood of a fuzzy set in a fuzzy topological space. Finally, in the last section some applications of this fuzzy multif...

Intervals are related to the representation of uncertainty. In this sense, we introduce an integral of Gould type for an interval-valued multifunction relative to an interval-valued set multifunction, with respect to Guo and Zhang order relation. Classicaland specific properties of this new type of integral are established and several examples and applications from multicriteria decision making...

We introduce a new class of multifunctions called a slightly m-continuous multifunction which is a generalization of both slightly continuous functions [10] and m-continuous multifunctions [33]. In this paper we obtain several properties of such a multifunction.

The spaces for which each δ-continuous function can be extended to a 2δ-small point-open l.s.c. multifunction (resp. point-closed u.s.c. multifunction) are studied. Some sufficient conditions and counterexamples are given.

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...

We introduce a new class of multifunctions called a slightly m-continuous multifunction which is a generalization of both slightly continuous functions [10] andm-continuous multifunctions [33]. In this paper we obtain several properties of such a multifunction.

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...