Journal of Applied Mathematics and Computing https://doi.org/10.1007/s12190-020-01457-x ORIGINAL RESEARCH A common solution of generalized equilibrium problems and fixed points of pseudo-contractive-type maps Monday Ogudu Nnakwe 1 · Chibueze Christian Okeke 2 Received: 12 May 2020 / Revised: 20 October 2020 / Accepted: 26 October 2020 © Korean Society for Informatics and Computational Applied Mathematics 2020 Abstract In this paper, a new iterative algorithm of a Halpern-type is constructed. The sequence generated by the algorithm is proved to converge strongly to a common solution of two generalized equilibrium problems and a common J -fixed point of two continuous J -pseudo-contractive maps in a uniformly smooth and uniformly convex real Banach space. Furthermore, a numerical example is given to illustrate the implementability of our algorithm. Finally, the theorem complements, improves and unifies some related recent results in the literature. Keywords Pseudo-contractive maps · Fixed points · Equilibrium problems · Variational inequalities Mathematics Subject Classification 47H09 · 47H10 · 47J25 · 47J05 · 37C25 1 Introduction Let X ∗ be the dual space of a uniformly convex and uniformly smooth real Banach space X and M be a nonempty, closed and convex subset of X . Let  : M × M → R be a bi-functional and B : M → X ∗ be a nonlinear map. The generalized equilibrium problem is a problem of finding an element u ∈ M such that (u , z ) +〈z − u , Bu 〉≥ 0, ∀ z ∈ M . (1.1) The solution set of generalized equilibrium problem will be denoted by GEP (, B ). B Monday Ogudu Nnakwe mondaynnakwe@gmail.com Chibueze Christian Okeke chibueze.okeke87@yahoo.com 1 African University of Science and Technology, Abuja, Nigeria 2 Department of Mathematics, University of Eswatini, Kwaluseni, Eswatini 123