Role of Relative A-Maximal Monotonicity in Overrelaxed Proximal-Point Algorithms with Applications

  • R. P. Agarwal
  • R. U. Verma


A general framework for a class of overrelaxed proximal point algorithms based on the notion of relative A-maximal monotonicity is introduced; then, the convergence analysis for solving a general class of nonlinear variational inclusion problems is explored. The framework developed in this communication is quite suitable, unlike other existing notions of generalized maximal monotonicity, including A-maximal (m)-relaxed monotonicity in literature, to generalize first-order nonlinear evolution equations/evolution inclusions based on the generalized nonlinear Yosida approximations in Hilbert spaces as well as in Banach spaces.


Variational inclusions Maximal monotone mapping Relative A-maximal monotone mapping Generalized resolvent operator 


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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Mathematical SciencesFlorida Institute of TechnologyMelbourneUSA
  2. 2.International PublicationsOrlandoUSA

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