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

• 作者: Fang Li
• 来源期刊: 现代非线性理论与应用(英文)
• 学科: 数学
• 关键词: New Over-Relaxed Proximal Point Algorithm Nonlinear OPERATOR Equation with (A η m)-Monotonicity FRAMEWORK Generalized RESOLVENT OPERATOR Technique Solvability and Convergence
• 年，卷（期）: 2012,（3）
• 页码范围: 67-72
• 页数: 6页
• 分类号: O1

摘要

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.