A Split Common Fixed Point and Null Point Problem for Lipschitzian Quasi Pseudocontractive Mappings in Hilbert Spaces

Abstract

A split common fixed point and null point problem (SCFPNPP) which includes the splitcommon fixed point problem, the split common null point problem and other problems related to the fixed pointproblem and the null point problem is studied. We introduce a Halpern--Ishikawa type algorithm for studying the split common fixed point and null point problem for Lipschitzian quasi pseudocontractive operators and maximal monotone operators in real Hilbert spaces. Moreover, we establish a strong convergence results under some suitable conditions and reduce our main result to above-mentioned problems. We give numerical result to demonstrate the convergence of our algorithms and compare rate of convergence some iterative algorithms. Finally, we applied the study to split feasibility problem (FEP), split equilibrium problem (SEP), split variational inequality problem (SVIP) and split optimization problem (SOP).