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

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Authors :

Apurva Kumar Das 1 * and Shailesh Dhar Diwan 2

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.



Article Info :

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



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