Numer Algor https://doi.org/10.1007/s11075-017-0448-0 ORIGINAL PAPER Hybrid iterative method for split monotone variational inclusion problem and hierarchical fixed point problem for a finite family of nonexpansive mappings K. R. Kazmi 1 · Rehan Ali 1,2 · Mohd Furkan 1,3 Received: 20 June 2017 / Accepted: 16 November 2017 © Springer Science+Business Media, LLC, part of Springer Nature 2017 Abstract In this paper, we propose a hybrid iterative method to approximate a com- mon solution of split monotone variational inclusion problem and hierarchical fixed point problem for a finite family of nonexpansive mappings in real Hilbert spaces. We prove that sequences generated by the proposed hybrid iterative method converge strongly to a common solution of these problems. Further, we discuss some appli- cations of the main result. We also discuss a numerical example to demonstrate the applicability of the iterative method. The method and results presented in this paper extend and unify the corresponding known results in this area. Keywords Split monotone variational inclusion problem · Hierarchical fixed point problem · Hybrid iterative method · Maximal monotone operators · Nonexpansive mapping · Strong convergence Mathematics Subject Classifications (2010) 47H09 · 47J25 · 49J40 · 90C99  K. R. Kazmi krkazmi@gmail.com Rehan Ali rehan08amu@gmail.com Mohd Furkan mohdfurkan786@gmail.com 1 Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India 2 Present address: Department of Mathematics, Jamia Millia Islamia, New Delhi 110025, India 3 Present address: University Polytechnic, Aligarh Muslim University, Aligarh 202002, India