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Existence and Algorithm of Solutions for Generalized Set-valued Strongly Nonlinear Mixed Variational-like Type Inequalities |
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| Authors: | HU Meng-yu ZENG Lu-chuan CHEN Shan-min |
| Affiliation: | 1. Department of Mathematics, Shanghai Normal University, Shanghai 200234, China;Department of Applied Mathematics, Donghua University, Shanghai 200051, China 2. Department of Mathematics, Shanghai Normal University, Shanghai 200234, China 3. Department of Applied Mathematics, Donghua University, Shanghai 200051, China |
| Abstract: | The auxiliary principle technique is extended to study a class of generalized set-valued strongly nonlinear mixed variational-like type inequalities. Firstly, the existence of solutions to the auxiliary problems for this class of generalized set-valued strongly nonlinear mixed variational-like type inequalities is shown. Secondly, the iterative algorithm for solving this class of generalized set-valued strongly nonlinear mixed variational-like type inequalities is given by using this existence result. Finally,the strong convergence of iterative sequences generated by the algorithm is proven. The present results improve,generalize and modify the earlier and recent ones obtained previously by some authors in the literature. |
| Keywords: | iterative algorithm set-valued mapping existence convergence Hilbert space |
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