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The Viscosity Approximation Forward-Backward Splitting Method for Zeros of the Sum of Monotone Operators

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  • Oganeditse Aaron Boikanyo

Abstract

We investigate the convergence analysis of the following general inexact algorithm for approximating a zero of the sum of a cocoercive operator and maximal monotone operators with : , for for given in a real Hilbert space , where , , and are sequences in with for all , denotes the error sequence, and is a contraction. The algorithm is known to converge under the following assumptions on and : (i) is bounded below away from 0 and above away from 1 and (ii) is summable in norm. In this paper, we show that these conditions can further be relaxed to, respectively, the following: (i) is bounded below away from 0 and above away from 3/2 and (ii) is square summable in norm; and we still obtain strong convergence results.

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  • Oganeditse Aaron Boikanyo, 2016. "The Viscosity Approximation Forward-Backward Splitting Method for Zeros of the Sum of Monotone Operators," Abstract and Applied Analysis, Hindawi, vol. 2016, pages 1-10, March.
    • Handle: RePEc:hin:jnlaaa:2371857
    DOI: 10.1155/2016/2371857
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    Cited by:

    1. Suthep Suantai & Narin Petrot & Montira Suwannaprapa, 2019. "Iterative Methods for Finding Solutions of a Class of Split Feasibility Problems over Fixed Point Sets in Hilbert Spaces," Mathematics, MDPI, vol. 7(11), pages 1-21, October.

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