Commun. Korean Math. Soc. 2010; 25(2): 313-325
Printed June 1, 2010
https://doi.org/10.4134/CKMS.2010.25.2.313
Copyright © The Korean Mathematical Society.
Ram U. Verma
Florida Institute of Technology, International Publications (USA)
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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