Generalized relaxed proximal point algorithms involving relative maximal accretive models with applications in Banach spaces
Commun. Korean Math. Soc. 2010 Vol. 25, No. 2, 313-325
https://doi.org/10.4134/CKMS.2010.25.2.313
Published online June 1, 2010
Ram U. Verma
Florida Institute of Technology, International Publications (USA)
Abstract : General models for the relaxed proximal point algorithm using the notion of relative maximal accretiveness (RMA) are developed, and then the convergence analysis for these models in the context of solving a general class of nonlinear inclusion problems differs significantly than that of Rockafellar (1976), where the local Lipschitz continuity at zero is adopted instead. Moreover, our approach not only generalizes convergence results to real Banach space settings, but also provides a suitable alternative to other problems arising from other related fields.
Keywords : variational inclusions, maximal relaxed accretive mapping, relative maximal accretive mapping, generalized resolvent operator
MSC numbers : 49J40, 65B05
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