TY - JOUR
T1 - CONVEX CONTRACTIONS OF ORDER n IN CAT(0) SPACES
AU - Yildirim, Isa
AU - Tekmanli, Yücel
AU - Khan, Safeer Hussain
PY - 2022/3/1
Y1 - 2022/3/1
N2 - In this paper, we work on convex contraction of order n. Our first result in general metric spaces shows that each convex contraction of order n is a Bessaga mapping. We then turn our attention to CAT (0) spaces. We prove a demiclosedness principle for such mappings in this setting. Next, we consider modified Mann iteration process and prove some convergence theorems for fixed points of such mappings in CAT (0) spaces. Our results are new in CAT (0) setting. Our results remain true in linear spaces like Hilbert and Banach spaces. Finally, we give an example in order to support our main results and to demonstrate the efficiency of modified Mann iteration process.
AB - In this paper, we work on convex contraction of order n. Our first result in general metric spaces shows that each convex contraction of order n is a Bessaga mapping. We then turn our attention to CAT (0) spaces. We prove a demiclosedness principle for such mappings in this setting. Next, we consider modified Mann iteration process and prove some convergence theorems for fixed points of such mappings in CAT (0) spaces. Our results are new in CAT (0) setting. Our results remain true in linear spaces like Hilbert and Banach spaces. Finally, we give an example in order to support our main results and to demonstrate the efficiency of modified Mann iteration process.
KW - CAT (0) space
KW - convergence
KW - Convex contraction of order n
KW - fixed point
KW - modified Mann iteration scheme
UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85129344777&origin=inward
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U2 - 10.47013/15.1.9
DO - 10.47013/15.1.9
M3 - Article
SN - 2075-7905
VL - 15
SP - 123
EP - 137
JO - Jordan Journal of Mathematics and Statistics
JF - Jordan Journal of Mathematics and Statistics
IS - 1
ER -