J. Nonl. Mod. Anal., 7 (2025), pp. 1383-1415.
Published online: 2025-07
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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.
}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2025.1383}, url = {http://global-sci.org/intro/article_detail/jnma/24242.html} }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.