Convergence, data dependence and $T$-stability of  $AK$ iteration procedure for contractive like operators

G. V. R. Babu 1 and G. Satyanarayana 2 *

doi:10.26637/MJM0702/0023

Convergence, data dependence and $T$-stability of $AK$ iteration procedure for contractive like operators

Authors :

G. V. R. Babu ¹and G. Satyanarayana ^{2 *}

Author Address :

^1,2 Department of Mathematics, Andhra University, Visakhapatnam-530 003, India.
² Department of Mathematics, Dr. Lankapalli Bullayya college, Visakhapatnam-530 013, India.

*Corresponding author.

Abstract :

In this paper, we prove the strong convergence of $AK$ iteration procedure to a fixed point of a contractive like operator defined on an arbitrary nonempty closed convex subset of a normed linear space. Further, we study data dependence and $T$-stability of this procedure. Our results generalize the results that are available in the existing literature.

Keywords :

Fixed point, contractive like operator, $AK$ iteration procedure, Data dependence and $T-$stability.

DOI :

10.26637/MJM0702/0023

Article Info :

Received : November 28, 2018; Accepted : April 09, 2019.