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2013 Implicit Relaxed and Hybrid Methods with Regularization for Minimization Problems and Asymptotically Strict Pseudocontractive Mappings in the Intermediate Sense
Lu-Chuan Ceng, Qamrul Hasan Ansari, Ching-Feng Wen
Abstr. Appl. Anal. 2013(SI60): 1-14 (2013). DOI: 10.1155/2013/854297

Abstract

We first introduce an implicit relaxed method with regularization for finding a common element of the set of fixed points of an asymptotically strict pseudocontractive mapping S in the intermediate sense and the set of solutions of the minimization problem (MP) for a convex and continuously Frechet differentiable functional in the setting of Hilbert spaces. The implicit relaxed method with regularization is based on three well-known methods: the extragradient method, viscosity approximation method, and gradient projection algorithm with regularization. We derive a weak convergence theorem for two sequences generated by this method. On the other hand, we also prove a new strong convergence theorem by an implicit hybrid method with regularization for the MP and the mapping S . The implicit hybrid method with regularization is based on four well-known methods: the CQ method, extragradient method, viscosity approximation method, and gradient projection algorithm with regularization.

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Lu-Chuan Ceng. Qamrul Hasan Ansari. Ching-Feng Wen. "Implicit Relaxed and Hybrid Methods with Regularization for Minimization Problems and Asymptotically Strict Pseudocontractive Mappings in the Intermediate Sense." Abstr. Appl. Anal. 2013 (SI60) 1 - 14, 2013. https://doi.org/10.1155/2013/854297

Information

Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 1273.47107
MathSciNet: MR3045051
Digital Object Identifier: 10.1155/2013/854297

Rights: Copyright © 2013 Hindawi

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Vol.2013 • No. SI60 • 2013
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