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

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

Authors

  • Ebrahim SOORİ*, Ravi AGARWAL

Keywords:

Weak convergence, Strongly convergence, Hilbert space

Abstract

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.

References

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.

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.

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.

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.

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.

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.

K. Shimoji and W. Takahashi, Strong convergence to common fixed points of infinite nonexpansive mappings and applications, Taiwanese J. Math., 5 (2001),387-404.

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.

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Published

2023-08-01

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Section

Articles

How to Cite

A simple proof for Kazmi et al.’s iterative scheme . (2023). Advances in the Theory of Nonlinear Analysis and Its Application, 6(1), 28-32. https://atnaea.org/index.php/journal/article/view/98