Projection iterative approximations for a new class of general random implicit quasi-variational inequalities
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We introduce a class of projection-contraction methods for solving a class of general random implicit quasi-variational inequalities with random multivalued mappings in Hilbert spaces, construct some random iterative algorithms, and give some existence theorems of random solutions for this class of general random implicit quasi-variational inequalities. We also discuss the convergence and stability of a new perturbed Ishikawa iterative algorithm for solving a class of generalized random nonlinear implicit quasi-variational inequalities involving random single-valued mappings. The results presented in this paper improve and extend the earlier and recent results.
KeywordsHilbert Space Recent Result Iterative Algorithm Existence Theorem Multivalued Mapping
- 3.Chang SS: Fixed Point. Theory and Applications. Chongqing, Chongqing; 1984.Google Scholar
- 4.Chang SS: Variational Inequality and Complementarity Problem Theory with Applications. Shanghai Scientific and Technological Literature, Shanghai; 1991.Google Scholar
- 9.Cho YJ, Shim SH, Huang N-J, Kang SM: Generalized strongly nonlinear implicit quasi-variational inequalities for fuzzy mappings. In Set Valued Mappings with Applications in Nonlinear Analysis, Ser. Math. Anal. Appl.. Volume 4. Taylor & Francis, London; 2002:63–77.Google Scholar
- 21.Toskos CP, Padgett WJ: Random Integral Equation with Applications in Life Sciences and Engineering. Academic Press, New York; 1974.Google Scholar
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