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On Over-Relaxed Proximal Point Algorithms for Generalized Nonlinear Operator Equation with (A,η,m)-Monotonicity Framework
Department of Mathematics, Sichuan University of Science and Engineering, Zigong, China
- 1 Department of Mathematics, Sichuan University of Science and Engineering, Zigong, China
International Journal of Modern Nonlinear Theory and Application·Volume 01 (2012)·Pages 67–72·Published 28 September 2012·DOI10.4236/ijmnta.2012.13009
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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.
KeywordsNew Over-Relaxed Proximal Point AlgorithmNonlinear Operator Equation with (Aηm)-Monotonicity FrameworkGeneralized Resolvent Operator TechniqueSolvability and Convergence
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