TY - JOUR
T1 - An Inertial Tseng’s Extragradient Method for Approximating Solution of Split Problems in Banach Spaces
AU - Jude , Ajio Terlumun
AU - Ugwunnadi , Godwin Chidi
AU - Ali , Bashir
JO - Journal of Nonlinear Modeling and Analysis
VL - 4
SP - 1383
EP - 1415
PY - 2025
DA - 2025/07
SN - 7
DO - http://doi.org/10.12150/jnma.2025.1383
UR - https://global-sci.org/intro/article_detail/jnma/24242.html
KW - Variational inequality problem, inertial Tseng’s extragradient method, fixed point, Banach spaces.
AB - <p style="text-align: justify;">In this paper, we introduce a new inertial type algorithm with a
self-adaptive step size for approximating a common element of the set of solutions of split common null point and pseudomonotone variational inequality
problem as well as the set of common fixed point of a finite family of quasi nonexpansive mappings in uniformly smooth and 2-uniformly convex real Banach
space. The proposed algorithm is constructed in such a way that its convergence analysis does not require a prior estimate of the operator norm. We also
give numerical examples to illustrate the performance of our algorithm. Our
results generalize and improve many existing results in the literature.</p>