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 and Ching-Feng Wen

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

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.

Date: 2013
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https://doi.org/10.1155/2013/854297

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:854297

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