Abstract
AbstractIn this paper, we focus on some split inverse problems, namely the split equality variational inequalities and common fixed point problems, and combine various operator theory techniques to establish minimum-norm strong convergence for our proposed method. We present two strong convergent results with (and without) reference to the monotonicity property of the cost operators. Our convergence analyses assume very mild conditions and thus generalize and extend recent related results in the literature. Furthermore, several numerical examples illustrate the practical potentials and advantages of our proposed algorithm.
Funder
National Research Foundation of South Africa
DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), South Africa
International Mathematical Union
University of KwaZulu-Natal
Publisher
Springer Science and Business Media LLC
Reference48 articles.
1. Alakoya TO, Mewomo OT, Shehu Y (2022) Strong convergence results for quasimonotone variational inequalities. Math Methods Oper Res 95:249–279
2. Alakoya TO, Uzor VA, Mewomo OT, Yao J-C (2022) On a system of monotone variational inclusion problems with fixed-point constraint. J Inequ Appl 2022(47):33
3. Bauschke HH, Combettes PL (2001) A weak-to-strong convergence principle for Féjer. Math Oper Res 26(2):248–264
4. Boikano OA, Zegeye H (2020) The split equality fixed point problem of quasi-pseudo-contractive mapping without knowledge of norms. Numer Funct Anal Optim 41(7):759–777
5. Censor Y, Borteld T, Martin B, Trofimov A (2006) A unified approach for inversion problems in intensity-modulated radiation therapy. Phys Med Biol 51:2353–2365