ON SPLIT FEASIBILITY AND FIXED POINT EQUALITY PROBLEMS

Abstract

This paper introduces a new mathematical problem, termed the split feasibilityand fixed point equality problem (SFFPEP), which generalizes several well-known problems,including the split feasibility problem (SFP), the split equality problem (SEP), the splitfeasibility and fixed point problem (SFFPP), and the split equality fixed point problem(SEFPP). To solve the SFFPEP, we propose a novel iterative algorithm within the frameworkof quasi-nonexpansive mappings in Hilbert spaces. We establish the convergence propertiesof the algorithm and provide a numerical example to demonstrate its effectiveness, thereby validating our theoretical findings. The proposed approach contributes to the broader studyof split problems and fixed point theory, offering new insights and practical tools for solvingcomplex optimization problems.