J. Nonlinear Sci. Appl., 14 (2021), 359–371 ISSN: 2008-1898 Journal Homepage: www.isr-publications.com/jnsa Iterative solution of split equilibrium and fixed point prob- lems in real Hilbert spaces J. N. Ezeora * , P. C. Jackreece Department of Mathematics and Statistics, University of Port Harcpourt, Nigeria. Abstract In this article, we introduce a hybrid iteration involving inertial-term for split equilibrium problem and fixed point for a finite family of asymptotically strictly pseudocontractive mappings. We prove that the sequence converges strongly to a solution of split equilibrium problem and a common fixed point of a finite family of asymptotically strictly pseudocontractive mappings. The results proved extend and improve recent results of Chang et al. [S. S. Chang, H. W. J. Lee, C. K. Chan, L. Wang, L. J. Qin, Appl. Math. Comput., 219 (2013), 10416–10424], Dewangan et al. [R. Dewangan, B. S. Thakur, M. Postolache, J. Inequal. Appl., 2014 (2014), 11 pages], and many others. Keywords: Total asymptotically strict pseudocontractive mapping, split equilibrium problem, fixed point problem, inertial-step, bounded linear operator. 2020 MSC: 47H09, 47H10, 49M05, 54H25. c 2021 All rights reserved. 1. Introduction Fixed point theory of nonexpansive mappings has valuable applications in different fields such as; convex feasibility problems, convex optimization problems, approximation theory, game theory, signal and image processing, partial differential equations and so on (see for example [16, 33] and the references therein). Existence of solutions associated with the above-mentioned problems depends on the existence of fixed points of certain noinlinear mappings. In 1994, Censor and Elfving [11] introduced in finite dimensional real Hilbert spaces, the split feasibility problems (SFP) for modeling inverse problems which arise from phase retrievals and in medical image reconstruction. It is now known that SFP can be applied in many disciplines such as; image restoration, computer tomograph and radiation therapy treatment planning (see [8, 9, 12, 13]). Consequently, the study of SFP has received the attention of many researchers (see [4, 27, 34, 36] and the references therein). Let H 1 and H 2 be two real Hilbert spaces and C and Q be nonempty closed convex subsets of H 1 and H 2 , respectively. The SFP is formulated as follows; find a point q ∈ H 1 such that q ∈ C and Aq ∈ Q, (1.1) * Corresponding author Email addresses: jeremiah.ezeora@uniport.edu.ng (J. N. Ezeora), prebo.jackreece@uniport.edu.ng (P. C. Jackreece) doi: 10.22436/jnsa.014.05.06 Received: 2021-01-22 Revised: 2021-02-27 Accepted: 2021-03-18