Asghar Allahyari - Department of Mathematics, Tabas Branch, Islamic Azad University, Tabas, Iran.
Hojjatollah Amiri Kayvanloo - Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.
Mohammad Mursaleen - Department of Mathematics, Aligarh Muslim University, Aligarh, ۲۰۲۰۰۲, Uttar Pradesh, India
Ali Shole Haghighi - Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.
Mohammad Davarpanah - Department of Mathematics, Ferdows Branch, Islamic Azad University, Ferdows, Iran.
Reza Allahyari - Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.

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.

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