Journal of Applied Mathematics & Bioinformatics

Convergence of Proximal Point Algorithms of Mann and Halpern Hybrid Types to a Zero of Monotone Operators in CAT(0) Spaces

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  • Abstract

    In this paper, by the classic Mann-type and Halpern-type algorithms, on the basis of monotone operators with firmly nonexpansive property, we build Mann-Halpern type and Halpern-Mann type proximal point algorithms about a zero of monotone operators in Hadamard space, and prove strong convergence and ? - convergence to a zero of monotone operators, respectively.

    Mathematics Subject Classification: 47H09; 47H10
    Keywords: Monotone operators; Mann-Halpern type; Halpern-Mann type; Proximal point algorithms; Hadamard space; ?-convergence; Strong convergence.