MODIFIED TWO STEPS IMPLICIT MIDPOINT ITERATION
METHOD TO APPROXIMATE FIXED POINTS FOR NONEXPANSIVE MAPPINGS
S. Ithaya Ezhil Manna
Department of Mathematics
St. Joseph's College (Autonomous)
Affiliated to Bharathidasan University
Tiruchirappalli - 620002, Tamilnadu, INDIA
In this paper, we establish the weak convergence of fixed points for nonexpansive mappings in the setting of uniformly convex Banach spaces using modified two steps implicit midpoint rule.
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References
[1] A.R. Khan, H. Fukhar-ud-din, Weak convergence of Ishikawa Iterates for
nonexpansive maps, Proc. Wo. Co. Engg. Com. Sci., 2 (2010), 20-22.
[2] H.K. Xu, Inequalities in Banach spaces with applications, Nonlinear Anal.,
16 (1991), 1127-1138.
[3] H.K. Xu, M.A. Alghamdi, N. Shahzad, The viscosity technique for the
implicit midpoint rule of nonexpansive mappings in Hilbert spaces, Fixed
Point Theo. Appl., 2015, No 41 (2015).
[4] H.Y. Zhou, G.T. Guo, H.J. Hwang, Y.J. Cho, On the iterative methods for
nonlinear operator equations in Banach spaces, PanAmer. Math. J., 14,
No 4 (2004), 61-68.
[5] K.K. Tan, H.K. Xu, Approximating fixed points of nonexpansive mappings
by Ishikawa iteration process, J. Math. Anal. Appl., 178 (1993), 301-308.
[6] M.O. Aibinu, J.K. Kim, On the rate of convergence of viscosity implicit iterative algorithms, Nonlinear Funct. Anal. Appl., 25, No 1 (2020), 135152.
[7] M.A. Alghamdi, M. Ali Alghamdi, N. Shahzad, H.K. Xu, The implicit
midpoint rule for nonexpansive mappings, Fixed Point Theo. Appl., 96
(2014), 1-9.
[8] Y. Song, Q. Li, Successive approximations for quasi firmly type nonexpansive mappings, Math. Commun., 16 (2011), 251-264.
[9] Y. Yao, N. Shahzad, Y.C. Liou, Modified semi-implicit midpoint rule for nonexpansive mappings, Fixed Point Theo. Appl., 2015, No 166 (2015).