in this paper we introduce a sequential block iterative method and its simultaneous version with op-timal combination of weights (instead of convex combination) for solving convex feasibility problems.when the intersection of the given family of convex sets is nonempty, it is shown that any sequencegenerated by the given algorithms converges to a feasible point. additionally for linear feasibil...

Convexity is one of the most important concepts in a study of analysis. Especially, it has been applied around the optimization problem widely. Our purpose is to define the concept of convexity of a set on Mizar, and to develop the generalities of convex analysis. The construction of this article is as follows: Convexity of the set is defined in the section 1. The section 2 gives the definition...

We first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a Banach space and next show that if the Banach space is having the Opial condition, then the fixed points set of such a mapping with the convex range is nonempty. In particular, we establish that if the Banach space is uniformly convex, and the range of such a mapping is bounded, closed and con...

We present a model of truthful elicitation which generalizes and extends mechanisms, scoring rules, number related settings that do not qualify as one or the other. Our main result is characterization theorem, yielding characterizations for all these settings. This includes new rules non-convex sets distributions. combine theorem with duality to give simple construction convert between randomiz...

The main aim of this short note is to show that the subdifferentiability and duality results established by Laghdir (2005), Laghdir and Benabbou (2007), and Alimohammady et al. (2011), stated in Fréchet spaces, are consequences of the corresponding known results using Moreau–Rockafellar type conditions.