Comparison of Harder stability and Rus stability of Mann iteration procedure and their equivalence | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 31، دوره 13، شماره 1، خرداد 2022، صفحه 409-420 اصل مقاله (408.37 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.17495.1939 | ||
| نویسندگان | ||
| Gutti Venkata Ravindranadh Babu1؛ Gedala Satyanarayana* 2 | ||
| 1Department of Mathematics, Andhra University, Visakhapatnam-530 003, India | ||
| 2Department of Mathematics, Andhra University, Visakhapatnam-530 003, India. | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Fixed point؛ Mann iteration procedure؛ stability in the sense of Harder؛ limit shadowing property؛ stability in the sense of Rus | ||
| مراجع | ||
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