Construction of compact-integral operators on C^\infty(\Bbb{R}_+) and C^n(\Bbb{R}_+) with application in the study of functional integro-differential equations

In this brief note, we present a fixed point theorem in the Fr\acute{e}chet space. Also we study a new family of measures of noncompactness on C^\infty(\Bbb{R}_+) and C^n(\Bbb{R}_+) and we investigate the construction of compact-integral operators on C^\infty(\Bbb{R}_+) and C^n(\Bbb{R}_+). Finally, we provide various examples which illustrate the existence of solutions for a wide variety of functional integral-differential equations.

Keywords:

Family of measures of noncompactness , condensing operators , integral-differential equations