TY - JOUR
T1 - An Adapted Proximal Point Algorithm Utilizing the Golden Ratio Technique for Solving Equilibrium Problems in Banach Spaces
AU - Abass, Hammed Anuoluwapo
AU - Oyewole, Olawale Kazeem
AU - Moshokoa, Seithuti Philemon
AU - Adamu, Abubakar
N1 - Publisher Copyright:
© 2024 by the authors.
PY - 2024/12
Y1 - 2024/12
N2 - This paper explores the iterative approximation of solutions to equilibrium problems and proposes a simple proximal point method for addressing them. We incorporate the golden ratio technique as an extrapolation method, resulting in a two-step iterative process. This method is self-adaptive and does not require any Lipschitz-type conditions for implementation. We present and prove a weak convergence theorem along with a sublinear convergence rate for our method. The results extend some previously published findings from Hilbert spaces to 2-uniformly convex Banach spaces. To demonstrate the effectiveness of the method, we provide several numerical illustrations and compare the results with those from other methods available in the literature.
AB - This paper explores the iterative approximation of solutions to equilibrium problems and proposes a simple proximal point method for addressing them. We incorporate the golden ratio technique as an extrapolation method, resulting in a two-step iterative process. This method is self-adaptive and does not require any Lipschitz-type conditions for implementation. We present and prove a weak convergence theorem along with a sublinear convergence rate for our method. The results extend some previously published findings from Hilbert spaces to 2-uniformly convex Banach spaces. To demonstrate the effectiveness of the method, we provide several numerical illustrations and compare the results with those from other methods available in the literature.
KW - Lyapunov function
KW - banach space
KW - golden ration technique
KW - self-adaptive stepsize
KW - variational inequalities
UR - http://www.scopus.com/inward/record.url?scp=85212698742&partnerID=8YFLogxK
U2 - 10.3390/math12233773
DO - 10.3390/math12233773
M3 - Article
AN - SCOPUS:85212698742
SN - 2227-7390
VL - 12
JO - Mathematics
JF - Mathematics
IS - 23
M1 - 3773
ER -