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GENERAL FRAMEWORK FOR PROXIMAL POINT ALGORITHMS ON (A, η)-MAXIMAL MONOTONICIT FOR NONLINEAR VARIATIONAL INCLUSIONS

  • Verma, Ram U.
  • Received : 2011.05.01
  • Published : 2011.10.31

Abstract

General framework for proximal point algorithms based on the notion of (A, ${\eta}$)-maximal monotonicity (also referred to as (A, ${\eta}$)-monotonicity in literature) is developed. Linear convergence analysis for this class of algorithms to the context of solving a general class of nonlinear variational inclusion problems is successfully achieved along with some results on the generalized resolvent corresponding to (A, ${\eta}$)-monotonicity. The obtained results generalize and unify a wide range of investigations readily available in literature.

Keywords

variational inclusions;maximal monotone mapping;(A, $\eta$) maximal monotone mapping;generalized resolvent operator

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  1. General Class of Implicit Variational Inclusions and Graph Convergence on A-Maximal Relaxed Monotonicity vol.155, pp.1, 2012, https://doi.org/10.1007/s10957-012-0030-9