Strong convergence and bounded perturbation resilience of modified forward-backward splitting methods for accretive operators in Banach spaces with application

In this paper, we introduce a new modified forward-backward splitting algorithm with perturbations for approximating a common solution of infinite families of inclusion problems and accretive variational inequality problems, which is also a common fixed point of infinite family of demicontractive mappings in Banach spaces. First, we establish some relationships between the set of fixed points of demicontractive mappings and variational inequality. Also, we prove the strong convergence of the sequence generated by our algorithm, its bounded perturbation resilience and further obtain some consequent results. Finally, we apply our result to approximate the solution of certain nonlinear intcgro-diffcrential equation with generalized p-Laplacian operator. Our results extend, improve and complement many recent results in the literature.