@article{82e9a1445fc146a5911d6c6db4b8e8b7,
title = "A strong convergence halpern-type inertial algorithm for solving system of split variational inequalities and fixed point problems∗",
abstract = "In this paper, we propose a new Halpern-type inertial extrapola-tion method for approximating common solutions of the system of split varia-tional inequalities for two inverse-strongly monotone operators, the variational inequality problem for monotone operator, and the fixed point of composi-tion of two nonlinear mappings in real Hilbert spaces. We establish that the proposed method converges strongly to an element in the solution set of the aforementioned problems under certain mild conditions. In addition, we present some numerical experiments to show the efficiency and applicability of our method in comparison with some related methods in the literature. This result improves and generalizes many recent results in this direction in the literature.",
keywords = "Firmly nonexpansive, Fixed point problem, Generalized system of variational inequality problem, Inertial iterative scheme, Split feasibility problem",
author = "Mebawondu, {A. A.} and Jolaoso, {L. O.} and Abass, {H. A.} and Oyewole, {O. K.} and Aremu, {K. O.}",
note = "Funding Information: Funding. This paper is supported by the Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, South Africa. Funding Information: Acknowledgement. A.A. Mebawondu, H.A. Abass and O.K. Oyewole acknowledge with thanks the bursary and financial support from Department of Science and Technology and National Research Foundation, Republic of South Africa Center of Excellence in Mathematical and Statistical Sciences (DSI-NRF COE-MaSS) Doctoral Bursary. Funding Information: †The corresponding author. Email: jollatanu@yahoo.co.uk, lateef.jolaoso@smu.ac.za(L. O. Jolaoso) 1School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, 4001, South Africa 2DSI-NRF Center of Excellence in Mathematical and Statistical Sciences (CoE-MaSS) 3Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, P.O. Box 94 Medunsa 0204, Pretoria, South Africa 4Department of Mathematics, Usmanu Danfodiyo University Sokoto, Sokoto state, Nigeria 5Department of Mathematics, Mountain Top University, Prayer City, Ogun statee, Nigeria. ∗A. A. Mebawondu and H. A. Abass acknowledge with thanks the bursary and financial support from Department of Science and Technology and Na-tional Research Foundation, Republic of South Africa Center of Excellence in Mathematical and Statistical Sciences (DSI-NRF COE-MaSS) Post-Doctoral Bursary. Publisher Copyright: {\textcopyright} 2021, Wilmington Scientific Publisher. All rights reserved.",
year = "2021",
doi = "10.11948/20200411",
language = "English",
volume = "11",
pages = "2762--2791",
journal = "Journal of Applied Analysis and Computation",
issn = "2156-907X",
publisher = "Wilmington Scientific Publishers",
number = "6",
}