- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 4 Issue: 2
- Iterative approximation of common fixed points of generalized nonexpansive maps in convex metric spa...
Iterative approximation of common fixed points of generalized nonexpansive maps in convex metric spaces
Authors : Gedala SATYANARAYANA, G. V. R. BABU
Pages : 112-120
Doi:10.31197/atnaa.649269
View : 6 | Download : 4
Publication Date : 2020-06-30
Article Type : Research
Abstract :We define SP-iteration procedure associated with three self maps T1; T2; T3 defined on a nonempty convex subset of a convex metric space X and prove -convergence of this iteration procedure to a common fixed point of T1; T2; T3 under the hypotheses that each Ti is either an -nonexpansive map or a Suzuki nonexpansive map in the setting of uniformly convex metric spaces. Also, we prove the strong convergence of this iteration procedure to a common fixed point of T1; T2; T3 under certain additional hypotheses namely either semicompact or condition (D).Keywords : SP-iteration procedure, alpha-nonexpansive map, Suzuki nonexpansive map, common fixed point, delta-convergence, strong convergence, uniformly convex metric space