An Inertial Tseng’s Extragradient Method for Approximating Solution of Split Problems in Banach Spaces (Journal of Nonlinear Modeling and Analysis, 2025)
In this paper, we introduce a new inertial type algorithm with aself-adaptive step size for approximating a common element of the set of solutions of split common null point and pseudomonotone variational inequalityproblem 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 Banachspace. The proposed algorithm is constructed in such a way that its convergence analysis does not require a prior estimate of the operator norm. We alsogive numerical examples to illustrate the performance of our algorithm. Ourresults generalize and improve many existing results in the literature.
Keywords: Variational inequality problem; inertial Tseng’s extragradient method; fixed point; Banach spaces.