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System of General Variational Inequalities Involving Different Nonlinear Operators Related to Fixed Point Problems and Its Applications

Abstract

By using the projection methods, we suggest and analyze the iterative schemes for finding the approximation solvability of a system of general variational inequalities involving different nonlinear operators in the framework of Hilbert spaces. Moreover, such solutions are also fixed points of a Lipschitz mapping. Some interesting cases and examples of applying the main results are discussed and showed. The results presented in this paper are more general and include many previously known results as special cases.

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Correspondence to Narin Petrot.

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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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Inchan, I., Petrot, N. System of General Variational Inequalities Involving Different Nonlinear Operators Related to Fixed Point Problems and Its Applications. Fixed Point Theory Appl 2011, 689478 (2011). https://doi.org/10.1155/2011/689478

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Keywords

  • Hilbert Space
  • Variational Inequality
  • Differential Geometry
  • Operator Relate
  • Interesting Case