A simple proof for Kazmi et al.'s iterative scheme

Öz

In this paper, a simple proof for the existence iterative scheme using two Hilbert spaces due to Kazmi et al.
[K.R. Kazmi, R. Ali, M. Furkan, Hybrid iterative method for split monotone variational inclusion problem
and hierarchical fixed point problem for a finite family of nonexpansive mappings, Numer. Algor., 2017] is
provided.

Anahtar Kelimeler

• Weak convergence
• Strongly convergence
• Hilbert space

Kaynakça

1. [1] R.P. Agarwal, D. O'Regan and D.R. Sahu, Fixed point theory for Lipschitzian-type mappings with applications, in: Topological Fixed Point Theory and its Applications, vol. 6, Springer, New York, 2009.
2. [2] C.E. Chidume, O.M. Romanus and U.V. Nnyaba, An iterative algorithm for solving split equality fixed point problems for a class of nonexpansive-type mappings in Banach spaces, Numer Algor, 82 (2019), 987-1007.
3. [3] Z. Jouymandi, F. Moradlou, Extragradient Methods for Solving Equilibrium Problems, Variational Inequalities, and Fixed Point Problems, Numer. Funct .Anal. Optim., 38:11, (2017), 1391-1409.
4. [4] Z. Jouymandi and F. Moradlou, Extragradient methods for split feasibility problems and generalized equilibrium problems in Banach spaces, Math. Methods Appl. Sci., (2017), DOI: 10.1002/mma.4647.
5. [5] K.R. Kazmi, R. Ali, M. Furkan, Hybrid iterative method for split monotone variational inclusion problem and hierarchical fixed point problem for a finite family of nonexpansive mappings, Numer Algor, (2017), https://doi.org/10.1007/s11075- 017-0448-0.
6. [6] A.E. Ofem and D.I. Igbokwe, A New Faster Four step Iterative Algorithm for Suzuki Generalized Nonexpansive Mappings with an Application, Adv. Theory Nonlinear Anal. Appl. 5 (2021), 482-506.
7. [7] K. Shimoji and W. Takahashi, Strong convergence to common fixed points of infinite nonexpansive mappings and applications, Taiwanese J. Math., 5 (2001),387-404.
8. [8] L. Wangwe and S. Kumara, Some common fixed-point theorems for a pair of p-hybrid mappings via common limit range property in G-metric space, Results in Nonlinear Anal. 4 (2021), 87-104.