On the generalized proximal point algorithmwith applications to inclusion problems

Ram U. Verma

doi:10.3934/jimo.2009.5.381

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2009, Volume 5, Issue 2: 381-390. Doi: 10.3934/jimo.2009.5.381

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On the generalized proximal point algorithm with applications to inclusion problems

Ram U. Verma^1,

1.
International Publications (USA), 12085 Lake Cypress Circle, Suite I109, Orlando, Florida 32828

Received: July 31, 2008

Revised: September 30, 2008

Published: March 2009

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Abstract

A class of generalized proximal point algorithms based on the $A-$ maximal monotonicity is introduced, and then it is applied to the approximation solvability of a general class of nonlinear inclusion problems using the generalized resolvent operator technique. This seems to be of interest in the sense that it is application-oriented.

Keywords:

Variationalinclusions; Maximal monotone mapping; $A-$ maximal monotone mapping;Generalized resolvent operator; General proximal point algorithm.

Mathematics Subject Classification: Primary: 49J40; Secondary: 65B05.

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