Abstract
binayak12@yahoo.co.in, subhajit.math@gmail.comABSTRACTIn this paper we have defined a new iteration in order to solve an equilibrium problemin Hilbert spaces. The iteration we have introduced is a viscosity type iteration andinvolvesa semigroup of nonexpansiveoperators. We have established that depending onsome control conditions, our iteration stronglyconvergesto a solution of the equilibriumproblem.RESUMENEn este art´iculo hemos definido una iteraci´on nueva para resolver un problema de equi-librioen espaciosde Hilbert. Laiteraci´onqueintroducimoses detipo viscosoeinvolucraun semigrupo de operadores no expansivos. Hemos establecido que dependiendo de lascondiciones de control, nuestra iteraci´on converge fuertemente a una soluci´on de unproblema de equilibrio.Keywords and Phrases: Equilibrium problem, Nonexpansive semigroup, Viscosity iteration,Fixed point, Weak convergence, Hilbert space.2010 AMS Mathematics Subject Classification: 46C05, 47H10, 91B50.
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