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

Poonam Mishra 1 * and Shailesh Dhar Diwan 2 and Manoj Kumar 3

doi:10.26637/MJM0704/0008

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

Authors :

Poonam Mishra ^{1 *}and Shailesh Dhar Diwan ² and Manoj Kumar ³

Author Address :

^1,2,3 Department of Applied Mathematics, Amity University Chhattisgarh, Raipur-492001, India.

*Corresponding author.

Abstract :

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.

Keywords :

Variational inequality, asymptotically pseudocontractive mapping, viscosity implicit rule, Banach space.

DOI :

10.26637/MJM0704/0008

Article Info :

Received : February 12, 2019; Accepted : September 22, 2019.