Strong convergence of the one step implicit iteration for $alpha$-demicontractive mappings

Apurva Kumar Das 1 * and Shailesh Dhar Diwan 2

doi:10.26637/MJM0604/0016

Strong convergence of the one step implicit iteration for $alpha$-demicontractive mappings

Authors :

Apurva Kumar Das ^{1 *} and Shailesh Dhar Diwan ²

Author Address :

¹Department of Mathematics, Government Polytechnic, Sukma, Chhattisgarh-494111, India.
² Department of Mathematics, Government Engineering College, Raipur, Chhattisgarh-492015, India.

*Corresponding author.

Abstract :

A new class of demicontractivity called $alpha$-demicontractivity is introduced by L. Maruster and S. Maruster[6] in which they proved strong convergence theorem using Mann iteration process in Hilbert space. In this paper, we have introduced one step implicit iteration process for $alpha$-demicontractive mapping and proved strong convergence theorem in Hilbert space.

Keywords :

Fixed point, $alpha$-Demicontractive mapping, Strong convergence, Hilbert space, One step implicit iteration.

DOI :

10.26637/MJM0604/0016

Article Info :

Received : July 03, 2018; Accepted : November 11, 2018.