An inertially constructed projection based hybrid algorithm for fixed point and split null point problems

Abstract

In this paper, we posit a framework for the investigation of the fixed point problems (FPP) involving an infinite family of k-demicontractive operators and the split common null point problems (SCNPP) in Hilbert spaces. We employ an accelerated variant of the hybrid shrinking projection algorithm for the construction of a common solution associated with the FPP and SCNPP. 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

• hybrid algorithm
• inertial extrapolation
• strong convergence
• fixed point problem
• demicontractive operator
• null point problem