An Ishikawa-Hybrid Proximal Point Algorithm for Nonlinear Set-Valued Inclusions Problem Based on <inline-formula> <graphic file="1687-1812-2010-501293-i1.gif"/></inline-formula>-Accretive Framework

• Main Authors: Jin MaoMing, Li HongGang, Xu AnJian
• Format: Article
• Language: English
• Published: SpringerOpen 2010-01-01
• Series: Fixed Point Theory and Applications
• Online Access: http://www.fixedpointtheoryandapplications.com/content/2010/501293

<p/> <p>A general nonlinear framework for an Ishikawa-hybrid proximal point algorithm using the notion of <inline-formula> <graphic file="1687-1812-2010-501293-i2.gif"/></inline-formula>-accretive is developed. Convergence analysis for the algorithm of solving a nonlinear set-valued inclusions problem and existence analysis of solution for the nonlinear set-valued inclusions problem are explored along with some results on the resolvent operator corresponding to <inline-formula> <graphic file="1687-1812-2010-501293-i3.gif"/></inline-formula>-accretive mapping due to Lan-Cho-Verma in Banach space. The result that sequence <inline-formula> <graphic file="1687-1812-2010-501293-i4.gif"/></inline-formula> generated by the algorithm converges linearly to a solution of the nonlinear set-valued inclusions problem with the convergence rate <inline-formula> <graphic file="1687-1812-2010-501293-i5.gif"/></inline-formula> is proved.</p>