Meir-Keeler condensing operator to prove existence of solution for infinite systems of differential equations in the Banach space and numerical method to ‎find the ‎solution

Abstract

‎In this paper‎, ‎we establish the existence of solution for infinite systems of differential equations in the Banana sequence space n(ϕ), ℓp(1 ≤ p < ∞) and $c$ by using Meier-Keeler condensing operators‎. ‎With the help of examples we illustrate our results in the sequence spaces‎. ‎Also for validity of the results‎, ‎we find an approximation of solution by using a suitable method with high accuracy‎.