Iterative algorithms of generalized nonexpansive mappings and monotone operators with application to convex minimization problem

In this paper, we present some convergence results for various iterative algorithms built from Hardy-Rogers type generalized nonexpansive mappings and monotone operators in Hilbert spaces. We obtain some comparison results for the rates of convergence of these algorithms to the solution of variational inequality problem including Hardy–Rogers type generalized nonexpansive mappings and monotone operators. A numerical example is given to validate these results. We apply the iterative algorithms handled herein to solve convex minimization problem and illustrate this result by providing a non-trivial numerical example. The presented results considerably improve the corresponding results in Ali et al. (Comput Appl Math 39:74, 2020. https://doi.org/10.1007/s40314-020-1101-4).