[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.2011.26.4.685

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

Verma, Ram U. (Department of Mathematics Seminole State College oF Florida)

Publication Information

Communications of the Korean Mathematical Society / v.26, no.4, 2011 , pp. 685-693 More about this Journal

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;

Citations & Related Records

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