Inertial viscosity type algorithm for solution of split null fixed point problem with applications

Muhammad Waseem Asghar; Mujahid Abbas; Muhammad Waseem Asghar; Mujahid Abbas

doi:10.3934/math.20261029

AIMS Mathematics

2026, Volume 11, Issue 8: 25672-25704. doi: 10.3934/math.20261029

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Inertial viscosity type algorithm for solution of split null fixed point problem with applications

Muhammad Waseem Asghar ^{1
,
,},
Mujahid Abbas ^1,2

1.
Department of Mechanical Engineering Science, University of Johannesburg, Johannesburg, 2092, South Africa
2.
Department of Medical Research, China Medical University, Taichung, 404328, Taiwan

Received: 01 June 2026 Revised: 12 July 2026 Accepted: 27 July 2026 Published: 19 August 2026
MSC : 47H09, 65K15, 47H10, 90C33

The purpose of this study is to introduce an inertial viscosity type iterative algorithm with a self-adaptive step size to approximate the solution of a split null fixed point problem involving nonexpansive mappings. Under suitable mild assumptions, we establish strong convergence of the iterative sequence generated by the proposed method. As a consequence, we also obtain approximation results for solutions of split feasibility fixed point and split minimization fixed point problems. In addition, we apply our algorithm to solve the signal processing problem. The applicability of the proposed algorithm is demonstrated through a numerical example. Furthermore, a graphical comparison with several existing methods in the literature is presented to illustrate its performance.
- split null fixed point,
- split feasibility fixed point,
- split minimization fixed point,
- inertial viscosity algorithm
Citation: Muhammad Waseem Asghar, Mujahid Abbas. Inertial viscosity type algorithm for solution of split null fixed point problem with applications[J]. AIMS Mathematics, 2026, 11(8): 25672-25704. doi: 10.3934/math.20261029

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Abstract

The purpose of this study is to introduce an inertial viscosity type iterative algorithm with a self-adaptive step size to approximate the solution of a split null fixed point problem involving nonexpansive mappings. Under suitable mild assumptions, we establish strong convergence of the iterative sequence generated by the proposed method. As a consequence, we also obtain approximation results for solutions of split feasibility fixed point and split minimization fixed point problems. In addition, we apply our algorithm to solve the signal processing problem. The applicability of the proposed algorithm is demonstrated through a numerical example. Furthermore, a graphical comparison with several existing methods in the literature is presented to illustrate its performance.

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