JOURNAL OF INDUSTRIAL AND doi:10.3934/jimo.2020063 MANAGEMENT OPTIMIZATION MULTI-STEP ITERATIVE ALGORITHM FOR MINIMIZATION AND FIXED POINT PROBLEMS IN P-UNIFORMLY CONVEX METRIC SPACES Kazeem Olalekan Aremu School of Mathematics, Statistics and Computer Science University of KwaZulu-Natal Durban, South Africa Chinedu Izuchukwu School of Mathematics, Statistics and Computer Science University of KwaZulu-Natal Durban, South Africa and DSI-NRF Center of Excellence in Mathematical and Statistical Sciences (CoE-MaSS) Johannesburg, South Africa Grace Nnenanya Ogwo and Oluwatosin Temitope Mewomo School of Mathematics, Statistics and Computer Science University of KwaZulu-Natal Durban, South Africa (Communicated by Nobuo Yamashita) Abstract. In this paper, we propose and study a multi-step iterative algo- rithm that comprises of a finite family of asymptotically k i -strictly pseudocon- tractive mappings with respect to p, and a p-resolvent operator associated with a proper convex and lower semicontinuous function in a p-uniformly convex metric space. Also, we establish the Δ-convergence of the proposed algorithm to a common fixed point of finite family of asymptotically k i -strictly pseudo- contractive mappings which is also a minimizer of a proper convex and lower semicontinuous function. Furthermore, nontrivial numerical examples of our algorithm are given to show its applicability. Our results complement a host of recent results in literature. 2010 Mathematics Subject Classification. Primary: 47H09; 47H10; 49J20; 49J40. Key words and phrases. p-uniformly convex metric spaces; asymptotically k-strictly pseudo- contractive mapping; p-resolvent operator; Δ-convergence. The second author is supported by the Department of Science and Innovation and National Re- search Foundation, Republic of South Africa, Center of Excellence in Mathematical and Statistical Sciences (DSI-NRF COE-MaSS), Doctoral Bursary. The third author is supported by the African Institute for Mathematical Sciences (AIMS), South Africa. The fourth author is supported by the National Research Foundation (NRF) of South Africa Incentive Funding for Rated Researchers (Grant Number 119903). * Corresponding author: O. T. Mewomo. 1