Page 45 - programme book

AN-005
An Accelerated Projection-based Parallel Hybrid Algorithm for Fixed
Point and Split Null Point Problems in Hilbert Spaces

Yasir Arfat 1, 2, a) , Poom Kumam 1,2, b) and Muhammad Aqeel Ahmad Khan 3, c)

1 KMUTT Fixed Point Research Laboratory, KMUTT-Fixed Point Theory and Applications Research Group,
Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT),
126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand. .
2 Center of Excellence in Theoretical and Computational Science (TaCS-CoE), SCL 802 Fixed Point Laboratory,
Science Laboratory Building, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit
Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand.
3 Full Department of Mathematics, COMSATS University Islamabad, Lahore, Campus, Lahore 54000, Pakistan.

a) Corresponding author: yasir.arfat@mail.kmutt.ac.th
b) poom.kum@kmutt.ac.th
c) itsakb@hotmail.com

Abstract. In this paper, we posit a framework for the investigation of the fixed-point problems (FPP)
involving an finite family of k-demicontractive operators and the split common null point problems
(SCNPP) in Hilbert spaces. We employ an accelerated variant of the parallel hybrid shrinking
projection algorithm for the construction of a common solution associated with the FPP and SNPP.
Theoretical results comprise strong convergence characteristics under suitable sets of constraints as
well as numerical results are established for the underlying algorithm. Applications to signal
processing as well as various abstract problems are also incorporated.

Keywords: Parallel Hybrid Algorithm, Inertial Extrapolation, Strong Convergence, Fixed Point
Problem, Demicontractive Operator, Null Point Problem