Common fixed point theorems and applications.
Common fixed point theorems for compatible and weakly compatible mappings.
Common fixed point theorems in Menger spaces.
Common fixed points of generalized contractive hybrid pairs in symmetric spaces.
Common fixed points of set-valued mappings.
Compactness and convergence of set-valued measures
We prove criteria for relative compactness in the space of set-valued measures whose values are compact convex sets in a Banach space, and we generalize to set-valued measures the famous theorem of Dieudonné on convergence of real non-negative regular measures.
Completely -continuous multifunctions.
Computing homology.
Concave iteration semigroups of linear set-valued functions
We consider a concave iteration semigroup of linear continuous set-valued functions defined on a closed convex cone in a separable Banach space. We prove that such an iteration semigroup has a selection which is also an iteration semigroup of linear continuous functions. Moreover it is majorized by an "exponential" family of linear continuous set-valued functions.
Concerning a certain -algebra in compact Hausdorff spaces
Conley index for set-valued maps: from theory to computation
Recent results on the Conley index theory for discrete multi-valued dynamical systems with their consequences for the computation of the index for representable maps are recapitulated. The terminology is simplified with respect to previous presentations, some superfluous hypotheses are abandoned and some conclusions are proved in a simpler way.
Connection matrix pairs
We discuss the ideas of Morse decompositions and index filtrations for isolated invariant sets for both single-valued and multi-valued maps. We introduce the definition of connection matrix pairs and present the theorem of their existence. Connection matrix pair theory for multi-valued maps is used to show that connection matrix pairs obey the continuation property. We conclude by addressing applications to numerical analysis. This paper is primarily an overview of the papers [R1] and [R2].
Consonance and Cantor set-selectors
It is shown that every metrizable consonant space is a Cantor set-selector. Some applications are derived from this fact, also the relationship is discussed in the framework of hyperspaces and Prohorov spaces.
Constant selections and minimax inequalities
In this paper, we establish two constant selection theorems for a map whose dual is upper or lower semicontinuous. As applications, matching theorems, analytic alternatives, and minimax inequalities are obtained.
Continuity of multifunctions with respect to local sieves and quasi-uniform convergence
Continuity of the superposition of set-valued functions.
Continuity properties of convex-type set-valued maps.
Continuous extensions of multifunctions
Continuous selections and approximations in α-convex metric spaces
In the paper, the notion of a generalized convexity was defined and studied from the view-point of the selection and approximation theory of set-valued maps. We study the simultaneous existence of continuous relative selections and graph-approximations of lower semicontinuous and upper semicontinuous set-valued maps with α-convex values having nonempty intersection.
Continuous selections for a class of non-convex multivalued maps