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- Title
Convex Minimization with Constraints of Systems of Variational Inequalities, Mixed Equilibrium, Variational Inequality, and Fixed Point Problems.
- Authors
Lu-Chuan Ceng; Cheng-Wen Liao; Chin-Tzong Pang; Ching-Feng Wen
- Abstract
We introduce and analyze one iterative algorithm by hybrid shrinking projection method for finding a solution of the minimization problem for a convex and continuously Fréchet differentiable functional, with constraints of several problems: finitely many generalized mixed equilibrium problems, finitely many variational inequalities, the general system of variational inequalities and the fixed point problem of an asymptotically strict pseudocontractive mapping in the intermediate sense in a real Hilbert space. We prove strong convergence theorem for the iterative algorithmunder suitable conditions. On the other hand, we also propose another iterative algorithm by hybrid shrinking projection method for finding a fixed point of infinitely many nonexpansive mappings with the same constraints, and derive its strong convergence under mild assumptions.
- Subjects
CONVEX functions; VARIATIONAL inequalities (Mathematics); FIXED point theory; ITERATIVE methods (Mathematics); CONTRACTIONS (Topology); HILBERT space
- Publication
Journal of Applied Mathematics, 2014, p1
- ISSN
1110-757X
- Publication type
Article
- DOI
10.1155/2014/105928