A new viscosity-type iteration for a finite family of split variational inclusion and fixed point problems between Hilbert and Banach spaces

In this paper, we introduce a new viscosity-type iteration process for approximating a common solution of a finite family of split variational inclusion problem and fixed point problem. We prove that the proposed algorithm converges strongly to a common solution of a finite family of split variational inclusion problems and fixed point problem for a finite family of type-one demicontractive mappings between a Hilbert space and a Banach space. Furthermore, we applied our results to study a finite family of split convex minimization problems, and also considered a numerical experiment of our results to further illustrate its applicability. Our results extend and improve the results of Byrne et al. (J. Nonlinear Convex Anal. 13:759–775, 2012), Kazmi and Rizvi (Optim. Lett. 8(3):1113–1124, 2014), Moudafi (J. Optim. Theory Appl. 150:275–283, 2011), Shehu and Ogbuisi (Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 110(2):503–518, 2016), Takahashi and Yao (Fixed Point Theory Appl. 2015:87, 2015), Chidume and Ezeora (Fixed Point Theory Appl. 2014:111, 2014), and a host of other important results in this direction.