Nonlinear viscosity algorithm with perturbation for non-expansive multi-valued mappings

Nonlinear viscosity algorithm with perturbation for non-expansive multi-valued mappings

Автор: Sahebi Hamid Reza

Журнал: Владикавказский математический журнал @vmj-ru

Статья в выпуске: 1 т.23, 2021 года.

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The viscosity iterative algorithms for finding a common element of the set of fixed points for nonlinear operators and the set of solutions of variational inequality problems have been investigated by many authors. The viscosity technique allow us to apply this method to convex optimization, linear programming and monoton inclusions. In this paper, based on viscosity technique with perturbation, we introduce a new nonlinear viscosity algorithm for finding an element of the set of fixed points of nonexpansive multi-valued mappings in a Hilbert spaces. Furthermore, strong convergence theorems of this algorithm were established under suitable assumptions imposed on parameters. Our results can be viewed as a generalization and improvement of various existing results in the current literature. Moreover, some numerical examples that show the efficiency and implementation of our algorithm are presented.

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Fixed point problem, generalized equilibrium problem, nonexpansive multi-valued mapping, hilbert space

Короткий адрес: https://sciup.org/143175697

IDR: 143175697   |   DOI: 10.46698/e7204-1864-5097-s

Список литературы Nonlinear viscosity algorithm with perturbation for non-expansive multi-valued mappings

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