Application of a Measure of Noncompactness in cs-Solvability and bs-Solvability of an Infinite System of Differential Equations

Abstract

The theory of measure of noncompactness has been a very helpful tool in non-linear functional analysis over the years. In this paper we have examined the solvability of an infinite system of third order differential equations in the sequence space of convergent series and sequence space of bounded series using the Hausdorff measure of noncompactness. We have also used the concept of Meir-Keeler condensing operator to utilize the fixed point theory in our approach and have analysed the approach for each sequence space with suitable examples.