TY - JOUR AU - Chidume, C. E. AU - Nnakwe, M. O. AU - Adamu, A. PY - 2019 DA - 2019/06/17 TI - A strong convergence theorem for generalized-Φ-strongly monotone maps, with applications JO - Fixed Point Theory and Applications SP - 11 VL - 2019 IS - 1 AB - Let X be a uniformly convex and uniformly smooth real Banach space with dual space $X^{*}$. In this paper, a Mann-type iterative algorithm that approximates the zero of a generalized-Φ-strongly monotone map is constructed. A strong convergence theorem for a sequence generated by the algorithm is proved. Furthermore, the theorem is applied to approximate the solution of a convex optimization problem, a Hammerstein integral equation, and a variational inequality problem. This theorem generalizes, improves, and complements some recent results. Finally, examples of generalized-Φ-strongly monotone maps are constructed and numerical experiments which illustrate the convergence of the sequence generated by our algorithm are presented. SN - 1687-1812 UR - https://doi.org/10.1186/s13663-019-0660-9 DO - 10.1186/s13663-019-0660-9 ID - Chidume2019 ER -