Strong convergence of split equality variational inequality, variational inclusion, and multiple sets fixed point problems in Hilbert spaces with application

C Batra, R Chugh, R Kumar, K Suwais… - Journal of Inequalities …, 2024 - Springer
Journal of Inequalities and Applications, 2024Springer
This paper introduces an innovative inertial simultaneous cyclic iterative algorithm designed
to address a range of mathematical problems within the realm of split equality variational
inequalities. Specifically, the algorithm accommodates finite families of split equality
variational inequality problems, infinite families of split equality variational inclusion
problems, and multiple-sets split equality fixed point problems involving demicontractive
operators in infinite-dimensional Hilbert spaces. The algorithm integrates well-established …
Abstract
This paper introduces an innovative inertial simultaneous cyclic iterative algorithm designed to address a range of mathematical problems within the realm of split equality variational inequalities. Specifically, the algorithm accommodates finite families of split equality variational inequality problems, infinite families of split equality variational inclusion problems, and multiple-sets split equality fixed point problems involving demicontractive operators in infinite-dimensional Hilbert spaces. The algorithm integrates well-established methods, including the cyclic method, the inertial method, the viscosity approximation method, and the projection method. We establish the strong convergence of this proposed algorithm, demonstrating its applicability in various scenarios and unifying disparate findings from existing literature. Additionally, a numerical example is presented to validate the primary convergence theorem.
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