@article{7286aa8e911a4431b572449b3d824dc2,

title = "On inertial type algorithms with generalized contraction mapping for solving monotone variational inclusion problems",

abstract = "In this article, we introduced two iterative processes consisting of an inertial term, forward-backward algorithm and generalized contraction for approximating the solution of monotone variational inclusion problem. The motivation for this work is to prove the strong convergence of inertial-type algorithms under some relaxed conditions because many of the existing results in this direction have only achieved weak convergence. We note that when the space is finite dimension, there is no disparity between weak and strong convergence, however this is not the case in infinite dimension. We provide some numerical examples to justify that inertial algorithms converge faster than non-inertial algorithms in terms of number of iterations and cpu time taken for the computation.",

keywords = "Accelerated algorithm, Fixed point problem, Inertial term, Inverse strongly monotone, Maximal monotone operators, Zero problem",

author = "Jolaoso, {L. O.} and Khamsi, {M. A.} and Mewomo, {O. T.} and Okeke, {C. C.}",

note = "Funding Information: Acknowledgement. The authors sincerely thank the anonymous reviewer for his careful reading, constructive comments and fruitful suggestions that substantially improved the manuscript. The first and fourth authors acknowledge with thanks the bursary and financial support from Department of Science and Innovation and National Research Foundation, Republic of South Africa Center of Excellence in Mathematical and Statistical Sciences (DSI-NRF COE-MaSS) Doctoral Bursary. The second author would like to acknowledge the support provided by the Deanship of Scientific Research at King Fahd University of Petroleum and Minerals for funding this work through Project No. IN171032. The third author is supported by the National Research Foundation (NRF) of South Africa Incentive Funding for Rated Researchers (Grant Number 119903). Opinions expressed and conclusions arrived are those of the authors and are not necessarily to be attributed to the CoE-MaSS and NRF. Publisher Copyright: {\textcopyright} 2021, House of the Book of Science. All rights reserved.",

year = "2021",

month = jul,

day = "1",

doi = "10.24193/fpt-ro.2021.2.45",

language = "English",

volume = "22",

pages = "685--712",

journal = "Fixed Point Theory",

issn = "1583-5022",

publisher = "House of the Book of Science",

number = "2",

}