Approximate Solution of a Nonlinear Volterra–Fredholm Integral Equations Via New 𝒵‐Iterative Algorithm

ABSTRACT In this paper, we pay attention to explore the existence of common fixed points of a pair of ‐ nonexpansive mappings. To execute the objective, firstly, we propose a novel three step iterative algorithm, namely ‐iteration, for a pair of mappings. Furthermore, we enquire for a few weak and strong convergence results and endorse the existence of common fixed points for two ‐ nonexpansive mappings. Our results are validated by constructive numerical examples. Lastly, the newly proposed iterative algorithm is employed to approximate the solution of a certain type of nonlinear Volterra–Fredholm integral equations on Banach spaces. Furthermore, an example on integral equations is constructed to authenticate our finding.