IJPAM: Volume 55, No. 2 (2009)

ROLE OF RELATIVELY RELAXED PROXIMAL POINT
ALGORITHMS TO THE APPROXIMATION SOLVABILITY
OF NONLINEAR VARIATIONAL INCLUSIONS

Ram U. Verma
Department of Mathematical Sciences
Florida Institute of Technology
Melbourne, FL 32901, USA
e-mail: verma99@msn.com


Abstract.Applying the notion of relatively maximal $(m)$-relaxed monotonicity to the approximation solvability of a general class of inclusion problems, a generalization to the investigation of Eckstein and Bertsekas (1992) on the weak convergence using the proximal point algorithm in a real Hilbert space setting is achieved. Further more, it can be used to generalize the Yosida approximation, which, in turn, can be applied to first-order evolution inclusions.

Received: August 1, 2009

AMS Subject Classification: 49J40, 47H10, 65B05

Key Words and Phrases: inclusion problems, maximal monotone mapping, relatively maximal $(m)$-relaxed monotone mapping, generalized resolvent operator

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 55
Issue: 2