## Charles E. Chidume, Abubakar Adamu, On split generalized mixed equality equilibrium and split equality fixed point problems

Full Text: PDF
DOI: 10.23952/asvao.2.2020.3.02
Volume 2, Issue 3, 31 December 2020, Pages 273-283

Abstract. For $p\geq 2$, a new iterative algorithm is introduced and used to approximate a common element of the set of solutions of a split generalized mixed equality equilibrium problem and the set of solutions of a split equality fixed point problem for quasi-$\phi$-nonexpansive mappings in $p$-uniformly convex and uniformly smooth real Banach spaces. A strong convergence theorem is proved without any compactness-type assumption on the mappings. Furthermore, our theorem, which is applicable, in particular, in $L_p$, $l_p$ and the Sobolev spaces $W_p^m(\Omega)$ for $2\leq p<\infty$, complements several important recent results that were established in $2$-uniformly convex and uniformly smooth real Banach spaces.