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

Document Type : Research Paper


1 Department of Mathematics, Tabas Branch, Islamic Azad University, Tabas, Iran.

2 Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.

3 Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, Uttar Pradesh, India

4 Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung, Taiwan

5 Department of Mathematics, Ferdows Branch, Islamic Azad University, Ferdows, 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.


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Articles in Press, Corrected Proof
Available Online from 28 November 2023
  • Receive Date: 10 February 2022
  • Revise Date: 28 September 2023
  • Accept Date: 20 October 2023