The generalized contraction proximal point algorithm with square-summable errors

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Abstract

Let (xn) be a sequence generated by xn+1=αnu+γnxn+δnJβnxn+en for n≥ 0 , where Jβn is the resolvent of a maximal monotone operator A with βn∈ (0 , ∞) , u, x0∈ H, (en) is a sequence of errors and αn∈ (0 , 1) , γn∈ (- 1 , 1) , δn∈ (0 , 2) are real numbers such that αn+ γn+ δn= 1 for all n≥ 0. We present strong convergence results for the sequence generated by the generalized contraction proximal point algorithm defined above under weaker accuracy conditions and mild conditions on the parameters αn, βn and δn. Our results generalize and unify many known results in the literature.

Original languageEnglish
Pages (from-to)321-332
Number of pages12
JournalAfrika Matematika
Volume28
Issue number3-4
DOIs
Publication statusPublished - Jun 1 2017

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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