TY - JOUR
T1 - Inertial Self-Adaptive Method for Solving Fixed Point Constraint Split Common Null Point Problem
AU - Abass , Hammed Anuoluwapo
JO - Journal of Nonlinear Modeling and Analysis
VL - 4
SP - 1254
EP - 1273
PY - 2025
DA - 2025/07
SN - 7
DO - http://doi.org/10.12150/jnma.2025.1254
UR - https://global-sci.org/intro/article_detail/jnma/24234.html
KW - Fixed point problem, split common null point problem, demimetric mappings, iterative method.
AB - <p style="text-align: justify;">In this manuscript, we study the split null point problem in the
settings of real Hilbert spaces using two different iterative methods. In our
first method, we propose a self-adaptive algorithm with an inertial technique
for solving split common null point problem and fixed point of a finite family
of a demimetric mapping without the computation of the resolvent of a monotone operator. In our second method, we propose a self-adaptive algorithm
with a multi-step inertial technique to approximate a solution of the aforementioned problems and to accelerate the rate of convergence of our iterative
method. The selection of the stepsize employed in our iterative algorithms
does not require prior knowledge of the operator norm. Lastly, we present a
numerical example to show the performance of our iterative algorithms. The
result discussed in this article extends and complements many related results
in literature.</p>