Sets In Normed Spaces Research Articles

On projected solutions for quasi equilibrium problems with non-self constraint map

In a normed space setting, this paper studies the conditions under which the projected solutions to a quasi equilibrium problem with non-self constraint map exist. Our approach is based on an iterative algorithm which gives rise to a sequence such that, under the assumption of asymptotic regularity, its limit points are projected solutions. Finally, as a particular case, we discuss the existence of projected solutions to a quasi variational inequality problem.

Piecewise Linear Vector Optimization Problems on Locally Convex Hausdorff Topological Vector Spaces

Piecewise linear vector optimization problems in the locally convex Hausdorff topological vector space setting are considered in this paper. The efficient solution set of these problems are shown to be the unions of finitely many semi-closed generalized polyhedral convex sets. If, in addition, the problem is convex, then the efficient solution set and the weakly efficient solution set are the unions of finitely many generalized polyhedral convex sets and they are connected by line segments. Our results develop the preceding ones of Zheng and Yang (Sci. China Ser. A. 51, 1243–1256 2008), and Yang and Yen (J. Optim. Theory Appl. 147, 113–124 2010), which were established in the normed space setting.

A Krasnosel’skii–Zincenko-type method in $$K\!$$ K -normed spaces for solving equations

We present a new semilocal convergence result for a Krasnosel’skii–Zincenko-type method (KZTM) to solve a nonlinear operator equation in a \(K\!\)-normed space setting. Using our new idea of restricted convergence domains, we show how to expand the convergence domain of KZTM under the same computational cost as in earlier studies. Numerical examples show how to solve an equation in cases not possible before.

Best proximity pairs and equilibrium pairs for Kakutani multimaps

Best proximity pairs and equilibrium pairs for Kakutani multimaps

On weak and strong solutions of [formula omitted]-implicit generalized variational inequalities with applications

On weak and strong solutions of [formula omitted]-implicit generalized variational inequalities with applications

Approachability and fixed points for non-convex set-valued maps

Approachability and fixed points for non-convex set-valued maps

On r-Separated Sets in Normed Spaces

On r-Separated Sets in Normed Spaces