Solving Split Equality Fixed Point Problem for Quasi-Phi-Nonexpansive Mappings

Charles Ejike Chidume, Abubakar Adamu

Abstract

An iterative algorithm is constructed to approximate solutions of split equality fixed point problem (SEFPP) for quasi-$\phi$-nonexpansive mappings in real Banach spaces more general than Hilbert spaces. Weak convergence of the sequence generated by the algorithm is proved. The theorem proved complements recent important results to provide algorithms for approximating solutions of SEFPP.  Furthermore, strong convergence of the sequence generated by  the algorithm is proved under the assumption that the operators are semi-compact. Moreover, applications of the theorem to split equality problem and split variational inclusion problem are presented. Finally, numerical examples are presented to illustrate the strong convergence of the sequence generated by our algorithm.