Document Zbl 1438.47110

Simultaneous iteration for variational inequalities over common solutions for finite families of nonlinear problems. (English) Zbl 1438.47110

J. Nonlinear Sci. Appl. 11, No. 3, 394-416 (2018).

Summary: In this paper, we apply Theorem 3.2 of [G. M. Lee and L.-J. Lin, J. Nonlinear Convex Anal. 18, No. 10, 1781–1800 (2017; Zbl 1505.47070)] to study the variational inequality over split equality fixed point problems for three finite families of strongly quasi-nonexpansive mappings. Then we use this result to study variational inequalities over split equality for three various finite families of nonlinear mappings. We give a unified method to study split equality for three various finite families of nonlinear problems. Our results contain many results on split equality fixed point problems and multiple sets split feasibility problems as special cases. Our results can treat large scale of nonlinear problems by grouping these problems into finite families of nonlinear problems, then use simultaneous iteration to find the solutions of these problems. Our results will give a simple and quick method to study large scale of nonlinear problems and will have many applications to study a large scale of nonlinear problems.

Cited in 1 Document

MSC:

47J25	Iterative procedures involving nonlinear operators
47H06	Nonlinear accretive operators, dissipative operators, etc.
47H09	Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
65K15	Numerical methods for variational inequalities and related problems

Keywords:

split equality fixed point problem; split fixed point problem; quasi-pseudocontractive mapping; demicontractive mapping; pseudo-contractive mapping; multiple sets split feasibility problems

Citations:

Zbl 1505.47070

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References:

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