Novi Sad J. Math. Vol. 49, No. 1, 2019, 117-136 https://doi.org/10.30755/NSJOM.07925 AN ITERATIVE METHOD FOR SOLUTION OF FINITE FAMILIES OF SPLIT MINIMIZATION PROBLEMS AND FIXED POINT PROBLEMS Hammed Anuoluwapo Abass 1 , Chinedu Izuchukwu 2 , Oluwatosin Temitope Mewomo 34 and Ferdinard Udochukwu Ogbuisi 56 Abstract The purpose of this paper is to introduce a proximal iterative algo- rithm for the approximation of a common solution of finite families of split minimization problem and a fixed point problem in the framework of Hilbert space. Using our iterative algorithm, we prove a strong con- vergence theorem for approximating a common solution of finite families of split minimization problem and a fixed point problem of nonexpansive mapping. Moreover, our result complements and extends some related results in literature. AMS Mathematics Subject Classification (2010): 47H09; 47H10 Key words and phrases: split minimization problem; nonexpansive map- ping; proximal iterative algorithm; Hilbert spaces. 1 Introduction Let H be a real Hilbert space with inner product and norm as 〈., .〉 and ||.|| respectively. Let C be a nonempty, closed and convex subset of H. A mapping T : C → C is said to be (i) a contraction, if there exists a constant k ∈ (0, 1) such that ||Tx − Ty|| ≤ k||x − y||, ∀ x, y ∈ C ; (ii) nonexpansive, if ||Tx − Ty|| ≤ ||x − y||, ∀ x, y ∈ C. A point p ∈ C is called a fixed point of T if Tp = p. We denote by F (T ) the set of all fixed points of T . 1 School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa. e-mail: 216075727@stu.ukzn.ac.za, hammedabass548@gmail.com 2 School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa. e-mail: izuchukwu c@yahoo.com, izuchukwuc@ukzn.ac.za 3 School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa. e-mail: mewomoo@ukzn.ac.za. 4 Corresponding author 5 School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa . e-mail: 215082189@stu.ukzn.ac.za, fudochukwu@yahoo.com 6 Department of Mathematics, University of Nigeria, Nsukka, Nigeria