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In this paper, we propose a modified implicit rule for the uniformly L-Lipschitzian and asymptotically pseudocontractive mapping in a Banach space.Related strong convergence theorems are established under the assumptions on certain parameters.Furthermore, it also provides solution to an appropriate variational inequality problem. Our main result improves and extends many known results of the recent literature.

malaya journal of matematik

A modified viscosity implicit rule for a variational inequality problem and a uniformly L-Lipschitzian asymptotically pseudocontractive mapping in a Banach space