TY - JOUR
ID - 994
TI - Construction of measures of noncompactness of $C^k(\Omega)$ and $C^k_0$ and their application to functional integral-differential equations
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Arab, R.
AU - Allahyari, R.
AU - Shole Haghighi, A.
AD - Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran.
AD - Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.
Y1 - 2017
PY - 2017
VL - 43
IS - 1
SP - 53
EP - 67
KW - Measure of noncompactness
KW - Darbo's fixed point theorem
KW - Arzela-Ascoli theorem
KW - integral-differential equations
DO -
N2 - In this paper, first, we investigate the construction of compact sets of $ C^k$ and $ C_0^k$ by proving ``$C^k, C_0^k-version$" of Arzel\`{a}-Ascoli theorem, and then introduce new measures of noncompactness on these spaces. Finally, as an application, we study the existence of entire solutions for a class of the functional integral-differential equations by using Darbo's fixed point theorem associated with these new measures of noncompactness. Further, some examples are presented to show the efficiency of our results.
UR - http://bims.iranjournals.ir/article_994.html
L1 - http://bims.iranjournals.ir/article_994_cd6cfba8a4671e144751135c1b54b0c3.pdf
ER -