Open AccessАлгоритм нелинейной вязкости с возмущением для нерасширяющих многозначных отображений
Author(s) -
Hamid Reza Sahebi
Publication year - 2021
Publication title -
vladikavkazskij matematičeskij žurnal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.126
H-Index - 2
eISSN - 1814-0807
pISSN - 1683-3414
DOI - 10.46698/e7204-1864-5097-s
Subject(s) - variational inequality , mathematics , hilbert space , fixed point , convergence (economics) , generalization , nonlinear system , viscosity , perturbation (astronomy) , set (abstract data type) , regular polygon , mathematical optimization , nonlinear programming , algorithm , computer science , mathematical analysis , geometry , materials science , physics , quantum mechanics , economics , programming language , economic growth , composite material
The viscosity iterative algorithms for finding a commonelement of the set of fixed points for nonlinear operators and the setof solutions of variational inequality problems have been investigatedby many authors. The viscosity technique allowus to apply this method to convex optimization, linear programming andmonoton inclusions. In this paper, based on viscosity technique withperturbation, we introduce a new nonlinear viscosity algorithm forfinding an element of~the set of~fixed points of nonexpansivemulti-valued mappings in a Hilbert spaces. Furthermore, strongconvergence theorems of~this algorithm were established under suitableassumptions imposed on~parameters. Our results can be viewed as ageneralization and improvement of various existing results in thecurrent literature. Moreover, some numerical examples that show theefficiency and implementation of our algorithm are presented.