Search results for "Metric projection"
showing 4 items of 4 documents
Best approximation and variational inequality problems involving a simulation function
2016
We prove the existence of a g-best proximity point for a pair of mappings, by using suitable hypotheses on a metric space. Moreover, we establish some convergence results for a variational inequality problem, by using the variational characterization of metric projections in a real Hilbert space. Our results are applicable to classical problems of optimization theory.
Contribution to variational analysis : stability of tangent and normal cones and convexity of Chebyshev sets
2014
The aim of this thesis is to study the following three problems: 1) We are concerned with the behavior of normal cones and subdifferentials with respect to two types of convergence of sets and functions: Mosco and Attouch-Wets convergences. Our analysis is devoted to proximal, Fréchet, and Mordukhovich limiting normal cones and subdifferentials. The results obtained can be seen as extensions of Attouch theorem to the context of non-convex functions on locally uniformly convex Banach space. 2) For a given bornology β on a Banach space X we are interested in the validity of the following "lim inf" formula (…).Here Tβ(C; x) and Tc(C; x) denote the β-tangent cone and the Clarke tangent cone to …
phi-Best proximity point theorems and applications to variational inequality problems
2017
The main concern of this study is to introduce the notion of $$\varphi $$ -best proximity points and establish the existence and uniqueness of $$\varphi $$ -best proximity point for non-self mappings satisfying $$(F,\varphi )$$ -proximal and $$(F,\varphi )$$ -weak proximal contraction conditions in the context of complete metric spaces. Some examples are supplied to support the usability of our results. As applications of the obtained results, some new best proximity point results in partial metric spaces are presented. Furthermore, sufficient conditions to ensure the existence of a unique solution for a variational inequality problem are also discussed.
A Mission Impossible? Learning the Logic of Space with Impossible Figures in Experience-Based Mathematics Education
2016
Most visual effects based on mathematically and physically describable phenomena and formalizable processes. Creating visual illusions, paradox structures and ‘impossible’ figures through playful and artistic procedures, holds an exciting pedagogical opportunity for raising students’ interest towards mathematics and natural sciences and technical aspects of visual arts. The Experience Workshop Math-Art Movement has a number of pedagogical methods, which are connected to visual paradoxes and perspective illusions. In the first part of our article, we introduce classroom exercises connected to the Hungarian artist Tamás F. Farkas’s paradox structures and impossible figures. There are certain …