Strong convergence theorem for semigroup of asymptotically nonexpansive mappings using viscosity approximation

Balwant Singh Thakur

Viscosity method also called elliptic regularization, provide an efficient approach to a large number of problems coming from different branches of mathematical and physical sciences. One of the recent trend in the iterative construction of fixed point of nonlinear mappings is to use viscosity approximation method. In this paper we propose implicit and explicit viscosity method (VAM) for strongly continuous semigroup of asymptotically nonexpansive mappings and prove strong convergence of proposed VAM which converges strongly to a solution of a variational inequality.