On Over-Relaxed Proximal Point Algorithms for Generalized Nonlinear Operator Equation with (A,η,m)-Monotonicity Framework

Fang Li

Department of Mathematics, Sichuan University of Science and Engineering, Zigong, China.

DOI: 10.4236/ijmnta.2012.13009                

Abstract

In this paper, a new class of over-relaxed proximal point algorithms for solving nonlinear operator equations with (A,η,m)-monotonicity framework in Hilbert spaces is introduced and studied. Further, by using the generalized resolvent operator technique associated with the (A,η,m)-monotone operators, the approximation solvability of the operator equation problems and the convergence of iterative sequences generated by the algorithm are discussed. Our results improve and generalize the corresponding results in the literature.

Keywords

New Over-Relaxed Proximal Point Algorithm; Nonlinear Operator Equation with (A, η, m)-Monotonicity Framework; Generalized Resolvent Operator Technique; Solvability and Convergence

Conflicts of Interest

The authors declare no conflicts of interest.

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