Strong convergence theorems for multivalued $alpha$-demicontractive and $alpha$-hemicontractive mappings

Apurva Kumar Das 1 * and Shailesh Dhar Diwan 2

doi:10.26637/MJM0701/0001

Strong convergence theorems for multivalued $alpha$-demicontractive and $alpha$-hemicontractive mappings

Authors :

Apurva Kumar Das ^{1 *} and Shailesh Dhar Diwan²

Author Address :

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

*Corresponding author.

Abstract :

In this paper, we introduce multivalued $alpha$-demicontractive and $alpha$-hemicontractive mappings and prove strong convergence theorems using Mann and Ishikawa iteration process in Hilbert spaces. We present some numerical examples which emphasize the results proved in the paper. Our theorem and corollaries extend the results of Isiogugu et al. cite{isiogugu2014} and Chidume et al. cite{chidume2014} in the setting of more general class of multivalued mappings.

Keywords :

Multivalued $alpha$-demicontractive, Multivalued $alpha$-hemicontractive, Fixed point, Mann iteration, Ishikawa iteration, Strong convergence, Hilbert space.

DOI :

10.26637/MJM0701/0001

Article Info :

Received : August 14, 2018; Accepted : November 19, 2018.