TY - JOUR
ID - 5508
TI - Comparison of Harder stability and Rus stability of Mann iteration procedure and their equivalence
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN - 2008-6822
AU - Babu, Gutti Venkata Ravindranadh
AU - Satyanarayana, Gedala
AD - Department of Mathematics, Andhra University, Visakhapatnam-530 003, India
AD - Department of Mathematics, Andhra University, Visakhapatnam-530 003, India.
Y1 - 2022
PY - 2022
VL - 13
IS - 1
SP - 409
EP - 420
KW - Fixed point
KW - Mann iteration procedure
KW - stability in the sense of Harder
KW - limit shadowing property
KW - stability in the sense of Rus
DO - 10.22075/ijnaa.2021.17495.1939
N2 - In this paper, we study the stability of Mann iteration procedure in two directions, namely one due to Harder and the second one due to Rus with respect to a map $T:K\to K$ where $K$ is a nonempty closed convex subset of a normed linear space $X$ and there exist $\delta\in(0,1)$ and $L\geq 0$ such that $||Tx-Ty||\leq\delta||x-y||+L||x-Tx||$ for $x,y\in K$. Also, we show that the Mann iteration procedure is stable in the sense of Rus may not imply that it is stable in the sense of Harder for weak contraction maps. Further, we compare and study the equivalence of these two stabilities and provide examples to illustrate our results.
UR - https://ijnaa.semnan.ac.ir/article_5508.html
L1 - https://ijnaa.semnan.ac.ir/article_5508_73c55573cbd9c4cd62f4df92bd2278b4.pdf
ER -