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Perturbed Iterative Algorithms for Generalized Nonlinear Set-Valued Quasivariational Inclusions Involving Generalized-Accretive Mappings

Abstract

A new class of generalized nonlinear set-valued quasivariational inclusions involving generalized-accretive mappings in Banach spaces are studied, which included many variational inclusions studied by others in recent years. By using the properties of the resolvent operator associated with generalized-accretive mappings, we established the equivalence between the generalized nonlinear set-valued quasi-variational inclusions and the fixed point problems, and some new perturbed iterative algorithms, proved that its proximate solution converges strongly to its exact solution in real Banach spaces.

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Correspondence to Mao-Ming Jin.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Jin, MM. Perturbed Iterative Algorithms for Generalized Nonlinear Set-Valued Quasivariational Inclusions Involving Generalized-Accretive Mappings. J Inequal Appl 2007, 029863 (2007). https://doi.org/10.1155/2007/29863

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Keywords

  • Banach Space
  • Exact Solution
  • Iterative Algorithm
  • Point Problem
  • Real Banach Space
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