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
نویسندگان
1 Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.
2 Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, Uttar Pradesh, India
3 Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung, Taiwan
4 Department of Mathematics, Tabas Branch, Islamic Azad University, Tabas, Iran.
5 Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.
6 Department of Mathematics, Ferdows Branch, Islamic Azad University, Ferdows, Iran.
doi
10.22075/ijnaa.2023.26265.3280چکیده
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.
