Creating a novel algorithm for studying the strong convergence to a sequence with applications

This manuscript introduces a novel algorithm tailored to investigate the strong convergence of sequences under specific conditions. Notably, the framework incorporates a finite family of generalized demimetric operators within real Hilbert spaces, broadening existing operator theory. The proposed algorithm efficiently establishes strong convergence and demonstrates its versatility through successful applications, including proving the existence of solutions to split minimization and feasibility problems, thereby showcasing its potential in optimization and numerical analysis.