IJPAM: Volume 60, No. 1 (2010)

HYBRID PROXIMAL POINT ALGORITHMS ON
$(A,\eta)-$MAXIMAL MONOTONICITY FOR
NONLINEAR VARIATIONAL INCLUSIONS

Ram U. Verma
Department of Mathematics
Seminole State College of Florida
Sanford, FL 32773, USA
e-mail: verma99@msn.com


Abstract.A general framework for a hybrid proximal point algorithm using the notion of $(A,\eta)$-monotonicity is developed. Convergence analysis for this algorithm in the context of solving a class of nonlinear inclusion problems is explored along with some results on the resolvent operator corresponding to $(A,\eta)$-monotonicity.

Received: February 23, 2010

AMS Subject Classification: 49J40, 65B05

Key Words and Phrases: variational inclusions, maximal monotone mapping, $(A,\eta)$-maximal monotone mapping, generalized resolvent operator

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 60
Issue: 1