TY - JOUR
T1 - INERTIAL PROXIMAL AND CONTRACTION METHODS FOR SOLVING MONOTONE VARIATIONAL INCLUSION AND FIXED POINT PROBLEMS
AU - Abuchu, Jacob Ashiwere
AU - Ugwunnadi, Godwin Chidi
AU - Narain, Ojen Kumar
N1 - Publisher Copyright:
© 2023 Kyungnam University Press
PY - 2023
Y1 - 2023
N2 - In this paper, we study an iterative algorithm that is based on inertial proximal and contraction methods embellished with relaxation technique, for finding common solution of monotone variational inclusion, and fixed point problems of pseudocontractive mapping in real Hilbert spaces. We establish a strong convergence result of the proposed iterative method based on prediction stepsize conditions, and under some standard assumptions on the algorithm parameters. Finally, some special cases of general problem are given as applications. Our results improve and generalized some well-known and related results in literature.
AB - In this paper, we study an iterative algorithm that is based on inertial proximal and contraction methods embellished with relaxation technique, for finding common solution of monotone variational inclusion, and fixed point problems of pseudocontractive mapping in real Hilbert spaces. We establish a strong convergence result of the proposed iterative method based on prediction stepsize conditions, and under some standard assumptions on the algorithm parameters. Finally, some special cases of general problem are given as applications. Our results improve and generalized some well-known and related results in literature.
KW - Monotone variational inclusion problem
KW - inertial iterative method
KW - nonexpansive operator
KW - pseudocontractive operator
KW - resolvent operator
KW - strong convergence
UR - http://www.scopus.com/inward/record.url?scp=85149666956&partnerID=8YFLogxK
U2 - 10.22771/nfaa.2023.28.01.10
DO - 10.22771/nfaa.2023.28.01.10
M3 - Article
AN - SCOPUS:85149666956
SN - 1229-1595
VL - 28
SP - 175
EP - 203
JO - Nonlinear Functional Analysis and Applications
JF - Nonlinear Functional Analysis and Applications
IS - 1
ER -