Iterative algorithms for a class of implicit quasi variational inequalities
DOI:
https://doi.org/10.54153/sjpas.2026.v8i1.1055Abstract
It is known that one of the most paramount and complicated problems in variational inequality Theory (VIT) is the development of an efficacious and implementable approximation schemes for solving diverse categories of variational inequality. Thus, through this study we introduce a new iterative schemes with errors to solve generalized strongly nonlinear implicit quasivariational inequalities (GSNIQVI) by fixed point defined on for a set-valued mapping with closed convex values in Hilbert space . These iterative schemes are constructed for Lipschitz continuous mappings, -strongly monotone, and -strongly monotone mappings under some appropriate conditions. These iterative schemes is solving special case of GSNIQVI with errors and without errors. We proved an existence and uniqueness results for solution GNIQVIP and convergence of new iterative algorithms with errors, and without errors, for several mappings: the first is a Lipschitz continuous mapping, the second Â, Ĉ, Ê, Û are Lipschitz continuous mappings, the third Ň is a mapping such that Ň is a strongly monotone with respect to  in , -strongly monotone with respect to Ĉ in , -strongly monotone with respect to Ê in and Lipschitz continuous with respect to , and the fourth is the metric projection which is Lipschitz continuous. Our results is inspired and encouraged for several research works in the literature.
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