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Let X = (X, +) be an arbitrary topological group. The set-valued function F : X → n(Y ) is called K-superquadratic iff F(x + y) + F(x − y) ⊂ 2F(x) + 2F(y) + K, for all x, y ∈ X, where Y denotes a topological vector space and K is a cone. In this paper the K-continuity problem of multifunctions of this kind will be considered with respect to K-boundedness. The case where Y = RN will be considered separately.
In this paper we study K-superquadratic set-valued functions.We will present here some connections between K-boundedness of K-superquadratic set-valued functions and K-semicontinuity of multifunctions of this kind.
Content available K-continuity of K-subquadratic set-valued functions
Let X = (X, +) be an arbitrary topological group. A set-valued function F : X → n(Y) is called K-subquadratic if 2F(s) + 2F(t) ⊂ F(s + t) + F(s - t) + K, for all s, t ϵ X, where Y denotes a topological vector space and where K is a cone in this space. In this paper the K-continuity problem of multifunctions of this kind will be considered with respect to weakly K-boundedness. The case where Y = R N will be considered separately.
Content available remote On rare s-precontinuity for multifunctions
In this paper, we introduce and study the notions of upper and lower rarely s-precontinuous multifunctions which are a generalization of weakly s-precontinuous multifunctions due to Ekici and Park [3].
Content available remote On meromorphic multivalent functions defined with the use of linear operator
In the present paper we introduce two classes of meromorphically multivalent functions and application of linear operators on these classes. We study various properties and coefficients bounds, the concept of neighbourhood also investigated.
Content available remote On E-continuity and E-minimality of multifunctions of two variables
In this article we formulate and prove some sufficient conditions for the l-Ex xy-continuity and the Ex x y- minimality of multifunctions of two variables.
Content available remote Cluster sets and related properties of multifunctions
In this paper we present some types of cluster sets of multifunction. Using these concepts we relate properties of cluster sets to some generalized continuity properties, minimality of multifunctions and closedness of its graphs.
In this paper we continue the study of the concept of graph continuity. We extend to multifunctions some results on the relationships between the graphs of functions. In addition, we introduce some generalized forms of continuity for multifunctions.
Content available remote On Frigon-Granas type multifunctions satisfying an implicit relation
The purpose of this paper is to prove two general fixed point theorems for two multifunctions T1,T2 : B(xo,r) - > Pcl(X) satisfying an implicit relation, which generalize Theorem 3.1 [2], Theorem 3.1 [3], Theorem 3.1 [1] and Theorem 3.1 [6]. In the last part we extend the results for a sequence of multifunctions.
The problem of existence of adjoint functions to boundary solutions is considered – it depends on the geometry of the attained set at the end point. This is applied to prove the smoothness of boundary solutions in the case of strictly convex right-hand side of di.erential inclusion which in turn permitts to show the smoothness of barrier solutions on semipermeable surfaces.
Content available remote Some properties of upper and lower θ-quasicontinuous multifunctions
In this paper we obtain new characterizations of upper and lower θ-quasicontinuous muitifunctions and investigate several properties of such multifunctions.
Content available remote Slightly beta-continuous multifunctions
In this paper, we introduce and study upper and lower slightly beta-continuous multifunctions as a generalization of upper (lower) semicontinuous, upper (lower) alfa-continuous, upper (lower) precontinuous, upper (lower) quasi-continuous, upper (lower) gamma-continuous, upper (lower) beta-continuous multifunctions and slightly beta-continuous functions. Some characterizations and several properties concerning upper (lower) slightly beta-continuous multifunctions are obtained. Furthermore, the relationships between upper (lower) slightly beta-continuous multifunctions and other related multifunctions are also discussed.
Content available remote On the Sincov functional equation
The Riemarm integral, the Hukuhara differences and derivatives will be applied to obtain solutions of the Sincov functional equation.
Content available remote On some approximation problems in Musielak-Orlicz spaces of multifunctions
We introduce the Musielak-Orlicz spaces of multifunctions Xmphi and Xc,m,phi. We prove that these spaces are complete. Also, we get some convergence and approximation theorems in these spaces.
Content available remote Fixed point theorems for weakly commuting and compatible multi-valued mappings
In this paper some common fixed point theorems for single- and multivalued contractive mappings with weak commutativity and compatibility conditions are given. Assumed that single-valued T and S are self-mappings on a generalized (in the sense of Jung [8]) metric space (X,d). Multi-valued mappings F,G : -Cl(X) have values in a space (Cl(X),H) of all nonempty and closed subsets of X, where H is a generalized Hausdorff metric in Cl(X).
The aim of this paper is to study uniform and topological structures on spaces of multifunctions. Uniform structures on hyperspaces compatible with the Fell, the Wijsman and the Hausdorff metric topology respectively are studied and the links between them are explored. Topologies induced by the above uniformities on spaces of multifunctions are considered and compared. Also connections between uniform convergence of multifunctions and their equi-semicontinuity are investigated.
Content available remote Integrodifferential iclusions in non separable Banach spaces
We consider a Cauchy problem for a nonlinear integrodifferential inclusion in non separable Banach spaces under Filippov type assumptions and we prove the existence of solutions. This result allows to obtain a relaxation theorem for the problem considered.
Content available remote On multidifferentials of multifunctions
In this article some properties of multidiffereiitials of set-valued maps (multifunctions) are studied. The functions considered here are mostly those that are not differentiable in a classical sense. Existence of minimal multidifferentials has been proved.
W artykule tym badane są pewne własności multiróżniczek funkcji wielo wartościowych (multifunkcji). Rozpatrywane funkcje nie są, zwykle różniczkowalne w klasycznym sensie. Pokazano istnienie minimalnych multiróżniczek.
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