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Cubo (Temuco)

versión On-line ISSN 0719-0646

Cubo vol.15 no.3 Temuco  2013

http://dx.doi.org/10.4067/S0719-06462013000300002 

 

Approximating a solution of an equilibrium problem by Viscosity iteration involving a nonexpansive semigroup


Binayak S. Choudhury & Subhajit Kundu

Bengal Engineering and Science University, Shibpur Department of Mathematics, P.O.: B. Garden, Shibpur, Howrah - 711103, West Bengal, India. binayak12@yahoo.co.in, subhajit.math@gmail.com


ABSTRACT

In this paper we have defined a new iteration in order to solve an equilibrium problem in Hilbert spaces. The iteration we have introduced is a viscosity type iteration and involves a semigroup of nonexpansive operators. We have established that depending on some control conditions, our iteration strongly converges to a solution of the equilibrium problem.

Keywords and Phrases: Equilibrium problem, Nonexpansive semigroup, Viscosity iteration, Fixed point, Weak convergence, Hilbert space.


RESUMEN

En este artículo hemos definido una iteración nueva para resolver un problema de equilibrio en espacios de Hilbert. La iteración que introducimos es de tipo viscoso e involucra un semigrupo de operadores no expansivos. Hemos establecido que dependiendo de las condiciones de control, nuestra iteración converge fuertemente a una solución de un problema de equilibrio.

2010 AMS Mathematics Subject Classification: 46C05, 47H10, 91B50.


 

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Received: November 2012 / Accepted: September 2013.

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