In this work, theorems of weak convergence of an implicit iterative algorithm with errors for treating a nonexpansive semigroup and a Lipschitzian pseudocontractive semigroup are estabilshed in the framework of real Banach spaces. 2010 Mathematics Subject Classification. Primary 60J05; Secondary 60J20.

This paper investigates the Lipschitz continuity of the solution map in the settings of horizontal, vertical, and mixed linear complementarity problems. In each of these cases, we show that the solution map is (globally) Lipschitzian if and only if the solution map is single-valued. These generalize a similar result of Murthy, Parthasarathy, and Sabatini proved in the LCP setting.

we study the convergence of the modified noor iterative scheme for the class of asymptotically pseudocontractive mappings in the intermediate sense which is not necessarily lipschitzian. our results improves, extends and unifies the results of schu [23] and qin {it et al.} [25].

Set-valued optimization which is an extension of vector to set-valued problems a growing branch applied mathematics. The application technics and the investigation optimality conditions has been enormous interest in research problems. In this paper we have considered Mayer type problem governed by discrete inclusion system with Lipschitzian mappings. A necessary condition for K-optimal solution...