Research Article Iterative Scheme for Split Variational Inclusion and a Fixed-Point Problem of a Finite Collection of Nonexpansive Mappings M. Dilshad , 1 A. F. Aljohani, 1 and M. Akram 2 1 Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia 2 Department of Mathematics, Faculty of Science, Islamic University of Madinah, Saudi Arabia Correspondence should be addressed to M. Dilshad; mdilshaad@gmail.com Received 31 July 2020; Revised 22 August 2020; Accepted 31 August 2020; Published 9 October 2020 Academic Editor: Mohammad Mursaleen Copyright © 2020 M. Dilshad et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This article is aimed at introducing an iterative scheme to approximate the common solution of split variational inclusion and a fixed-point problem of a finite collection of nonexpansive mappings. It is proven that under some suitable assumptions, the sequences achieved by the proposed iterative scheme converge strongly to a common element of the solution sets of these problems. Some consequences of the main theorem are also given. Finally, the convergence analysis of the sequences achieved from the iterative scheme is illustrated with the help of a numerical example. 1. Introduction Let H 1 and H 2 be two real Hilbert spaces endowed with inner product h⋅ , ⋅i and induced norm k⋅k. A mapping T : H 1 ⟶ H 1 is called contraction, if ∃κ ∈ ð0, 1Þ such that kT ðφÞ − T ðψÞk ≤ κkφ − ψk, ∀φ, ψ ∈ H 1 . If κ =1, then T becomes nonexpansive. A mapping T is said to have a fixed point, if ∃φ ∈ ðH 1 Þ such that T ðφÞ = ðφÞ. Further, if T n : H 1 ⟶ H 1 , ðn = 1,⋯,MÞ is a finite collection of nonexpansive mappings. Then, the fixed-point problem (FPP) is defined as find φ ∈ H 1 such that \ M n=1 T n φ ðÞ = φ: ð1Þ It is easy to show that if T M n=1 FixðT n Þ ≠ 0, then T M n=1 FixðT n Þ is closed and convex. Many iterative methods have been adopted to examine the solution of a fixed- point problem for nonexpansive mappings and its variant forms, see [1–5] and references therein. We know that most of the techniques for solving the fixed-point problems can be acquired from Mann’s iterative technique [3], namely, for arbitrary x 0 ∈ C , compute x k+1 = α k x k +1 − α k ð ÞTx k , k ≥ 0, ð2Þ where T is a nonexpansive mapping from a nonempty closed convex subset C of Hilbert space H 1 to itself and α n is a control sequence, which force fx k g to converge (weak) to a fixed point of T . To obtain the strong convergence result, Moudafi [4] proposed the viscosity approximation method by combining the nonexpansive mapping T with a contrac- tion of given mapping f over C . For an arbitrary x 0 ∈ C , compute the sequence fx k g generated by x k+1 = α k fx k ð Þ +1 − α k ð ÞTx k , k ≥ 0, ð3Þ where α n ∈ ð0, 1Þ goes slowly to zero. The sequence fx k+1 g achieved from this iterative method converges strongly to a fixed point of T . On the other hand, let us recall some work about split variational inequality/inclusion problems. A multivalued Hindawi Journal of Function Spaces Volume 2020, Article ID 3567648, 10 pages https://doi.org/10.1155/2020/3567648