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| An Inertial Tseng's Extragradient Method for Approximating Solution of Split Problems in Banach Spaces |
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| KeyWord:Variational inequality problem, inertial Tseng's extragradient method, fixed point, Banach spaces |
| Author Name | Affiliation | | Ajio Terlumun Jude | Department of Mathematical Sciences, Bayero University, PMB 3011, Gwarzo Road Kano, Nigeria | | Godwin Chidi Ugwunnadi | Department of Mathematics, University of Eswatini, Private Bag 4, Kwaluseni M201, Eswatini
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, P.O. Box 94, Pretoria 0204, South Africa | | Bashir Ali | Department of Mathematical Sciences, Bayero University, PMB 3011, Gwarzo Road Kano, Nigeria |
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| Abstract: |
| 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. |
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