Perturbed Iterative Algorithms for Generalized Nonlinear Set-Valued Quasivariational Inclusions Involving Generalized <inline-formula><graphic file="1029-242X-2007-029863-i1.gif"/></inline-formula>-Accretive Mappings

• Main Author: Jin Mao-Ming
• Format: Article
• Language: English
• Published: SpringerOpen 2007-01-01
• Series: Journal of Inequalities and Applications
• Online Access: http://www.journalofinequalitiesandapplications.com/content/2007/029863

<p/> <p>A new class of generalized nonlinear set-valued quasivariational inclusions involving generalized <inline-formula><graphic file="1029-242X-2007-029863-i2.gif"/></inline-formula>-accretive mappings in Banach spaces are studied, which included many variational inclusions studied by others in recent years. By using the properties of the resolvent operator associated with generalized <inline-formula><graphic file="1029-242X-2007-029863-i3.gif"/></inline-formula>-accretive mappings, we established the equivalence between the generalized nonlinear set-valued quasi-variational inclusions and the fixed point problems, and some new perturbed iterative algorithms, proved that its proximate solution converges strongly to its exact solution in real Banach spaces.</p>