Abstract
The primary objective of this paper is to present and investigate an inertial Krasnoselski-Mann (KM) type iterative method for approximating a common solution to a split monotone variational inclusion problem and a hierarchical fixed point problem for a finite family of $l$-strictly pseudocontractive non-self mappings. Additionally, we demonstrate that the iterative sequences provided by the proposed method converge weakly to a common solution to these problems. The methodology and conclusions described in this work extend and unify previously published findings in this domain. Finally, a numerical example is presented to demonstrate the suggested iterative method's convergence analysis of the sequences obtained. We also carried out a justification how the inertial term is useful.
Key words: Strictly pseudocontractive mapping, Split monotone variational inclusion problem, Hierarchical fixed point problem, Nonexpansive mapping, Weak convergence, Averaged mapping, Krasnoselski-Mann type iterative method.
Full Text
Article Information
| Title | Inertial KM-type algorithm for solving split monotone variational inclusion problem and hierarchical fixed point problem |
| Source | Methods Funct. Anal. Topology, Vol. 31 (2025), no. 3, 222-237 |
| DOI | 10.31392/MFAT-npu26_3.2025.06 |
| Milestones | Received 03/10/2024; Revised 30/08/2025 |
| Copyright | The Author(s) 2025 (CC BY-SA) |
Authors Information
Mubashshir U. Khairoowala
G.L. Bajaj Institute of Technology and Management, Greator Noida, India
Shamshad Husain
Department of Applied Mathematics, Faculty of Engineering and Technology, Aligarh Muslim University, Aligarh, India
Mohd Furkan
University Polytechnic, Faculty of Engineering and Technology, Aligarh Muslim University, Aligarh, India
Citation Example
Mubashshir U. Khairoowala, Shamshad Husain, and Mohd Furkan, Inertial KM-type algorithm for solving split monotone variational inclusion problem and hierarchical fixed point problem, Methods Funct. Anal. Topology 31
(2025), no. 3, 222-237.
BibTex
@article {MFAT2126,
AUTHOR = {Mubashshir U. Khairoowala and Shamshad Husain and Mohd Furkan},
TITLE = {Inertial KM-type algorithm for solving split monotone variational inclusion problem and hierarchical fixed point problem},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {31},
YEAR = {2025},
NUMBER = {3},
PAGES = {222-237},
ISSN = {1029-3531},
DOI = {10.31392/MFAT-npu26_3.2025.06},
URL = {https://mfat.imath.kiev.ua/article/?id=2126},
}
