The credal set operator is studied as a set-valued mapping that assigns the set of dominating probabilities to a coherent lower prevision on some set of gambles. It is shown that this mapping is affine on certain classes of coherent lower previsions, which enables to find a decomposition of credal sets. Continuity of the credal set operator is investigated on finite universes with the aim of ap...

If F is a set-valued mapping from IRn into IRm with closed graph, then y ∈ IRm is a critical value of F if for some x with y ∈ F (x), F is not metrically regular at (x, y). We prove that the set of critical values of a set-valued mapping whose graph is a definable (tame) set in an o-minimal structure containing additions and multiplications is a set of dimension not greater than m − 1 (resp. a ...

A general nonlinear framework for an Ishikawa-hybrid proximal point algorithm using the notion of A, η -accretive is developed. Convergence analysis for the algorithm of solving a nonlinear set-valued inclusions problem and existence analysis of solution for the nonlinear set-valued inclusions problem are explored along with some results on the resolvent operator corresponding to A, η -accretiv...

Let M be a set–valued mapping defined between two Banach spaces E and F . Several important aspects of behavior of M can be characterized in terms of the distance function to images ∆M defined by ∆M (x, y) := d ( y, M(x) ) for all (x, y) ∈ E × F . In this paper, we use this function to scalarize the Fréchet normal regularity of set–valued mappings. The Fréchet subdifferential regularity of ∆M i...

We introduce an iterative scheme by the viscosity approximate method for finding a common element of the set of solutions of a variational inclusion with set-valued maximal monotone mapping and inverse stronglymonotonemappings, the set of solutions of an equilibrium problem, and the set of fixed points of a nonexpansive mapping. We obtain a strong convergence theorem for the sequences generated...

For an upper semi-continuous set-valued mapping from one topological space to another and for a lower semi-continuous function defined on the product of these spaces, Berge’s theorem states lower semi-continuity of the minimum of this function taken over the image sets. It assumes that the image sets are compact. For Hausdorff topological spaces, this paper extends Berge’s theorem to set-valued...