On the existence of solutions of a perturbed functional integral equation in the space of Lebesgue integrable functions on R+

Al Sayed, W.; Darwish, M. A.

doi:10.7862/rf.2018.2

Artykuł - szczegóły

Tytuł artykułu

On the existence of solutions of a perturbed functional integral equation in the space of Lebesgue integrable functions on R+

Autorzy

Al Sayed W. , Darwish M. A.

Treść / Zawartość

Pełne teksty: $C:\Users\chemia2\Desktop\18-20(1).pdf [zdalny]$

Identyfikatory

DOI

10.7862/rf.2018.2

Warianty tytułu

Języki publikacji

Abstrakty

In this paper, we investigate and study the existence of solutions for perturbed functional integral equations of convolution type using Darbo's fixed point theorem, which is associated with the measure of noncompactness in the space of Lebesgue integrable functions on R+. Finally, we offer an example to demonstrate that our abstract result is applicable.

Słowa kluczowe

existence convolution space of Lebesgue integrable functions measure of noncompactness

istnienie konwolucja splot przestrzeń funkcji całkowalnych Lebesgue'a miara braku zgodności

Wydawca

Oficyna Wydawnicza Politechniki Rzeszowskiej

Czasopismo

Journal of Mathematics and Applications

Rocznik

2018

Tom

Vol. 41

Strony

19--27

Opis fizyczny

Bibliogr. 24 poz.

Twórcy

autor

Al Sayed W.

wsaid@fbsu.edu.sa

College of Sciences and Humanities, Fahad Bin Sultan University, Tabuk, Saudi Arabia

autor

Darwish M. A.

madarwish@sci.dmu.edu.eg

Department of Mathematics, Faculty of Science, Damanhour University, Damanhour, Egypt

Bibliografia

[1] A. Aghajani, Y. Jalilian, K. Sadarangani, Existence of solutions for mixed Volterra-Fredholm integral equations, EJDE 2012 (137) (2012) 1-12.
[2] A. Aghajani, Y. Jalilian, Existence and global attractivity of solutions of a non-linear functional integral equation, Commun. Nonlinear Sci. Numer. Simul. 15 (11) (2010) 3306-3312.
[3] J. Banaś, A. Chlebowicz, On existence of integrable solutions of a functional integral equation under Carathéodory conditions, Nonlinear Anal. 70 (9) (2009) 3172-3179.
[4] J. Banaś, A. Chlebowicz, On integrable solutions of a nonlinear Volterra integral equation under Carathéodory conditions, Bull. Lond. Math. Soc. 41 (6) (2009) 1073-1084.
[5] J. Banaś, M. Pasławska-Południak, Monotonic solutions of Urysohn integral equation on unbounded interval, Comput. Math. Appl. 47 (1) (2004) 1947-1954.
[6] J. Banaś, Z. Knap, Integrable solutions of a functional-integral equation, Revista Mat. Univ. Complutense de Madrid 2 (1989) 31-38.
[7] J. Banaś, Z. Knap, Measures of weak noncompactness and nonlinear integral equations of convolution type, J. Math. Anal. Appl. 146 (2) (1990) 353-362.
[8] J. Banaś, J. Rivero, On measures of weak noncompactness, Ann. Mat. Pure Appl. 151 (1988) 213-224.
[9] J. Banaś, K. Goebel, Measures of Noncompactness in Banach Spaces, Lecture Notes in Pure and Applied Mathematics 60, Marcel Dekker, New York, 1980.
[10] H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer Science & Business Media, 2010.
[11] T.A. Burton, Volterra Integral and Differential Equations, Academic Press, New York, 1983.
[12] G. Darbo, Punti uniti in trasformazioni a codominio non compatto, Rend. Sem. Mat. Univ. Padova 24 (1995) 84-92.
[13] M.A. Darwish, On a perturbed functional integral equation of Urysohn type, Appl. Math. Comput. 218 (2012) 8800-8805.
[14] M.A. Darwish, J. Henderson, Solvability of a functional integral equation under Carathéodory conditions, Commun. Appl. Nonlinear Anal. 16 (1) (2009) 23-36.
[15] M.A. Darwish, On integral equations of Urysohn-Volterra type, Appl. Math. Comput. 136 (2003) 93-98.
[16] M.A. Darwish, Monotonic solutions of a functional integral equation of Urysohn type, PanAm. Math. J. 18 (4) (2008) 17-28.
[17] K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, Berlin, 1985.
[18] J. Dugundji, A. Granas, Fixed Point Theory, Monografie Matematyczne, PWN, Warsaw, 1982.
[19] G. Emmanuele, Measure of weak noncompactness and fixed point theorems, Bull. Math. Soc. Sci. Math. R. S. Roum. 25 (4) (1981) 353-358.
[20] G. Emmanuele, Integrable solutions of a functional-integral equation, J. Integral Equations Appl. 4 (1) (1992) 89-94.
[21] H. Hanche-Olsen, H. Holden, The Kolmogorov-Riese compactness theorem, arXiv:0906.4883 [math.CA] 2010.
[22] H. Khosravi, R. Allahyari, A.S. Haghighi, Existence of solutions of functional integral equations of convolution type using a new construction of a measure of noncompactness on Lp(R+), Appl. Math. Comput. 260 (2015) 140-147.
[23] D. O'Regan, M. Meehan, Existence Theory for Nonlinear Integral and Integro-differential Equations, Kluwer Academic Publishers, Dordrecht, 1998.
[24] P.P. Zabrejko et al., Integral Equations, Noordhoff International Publishing, The Netherlands, 1975 (Russian edition: Nauka, Moscow, 1968).

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).

Typ dokumentu

Bibliografia

Identyfikator YADDA

bwmeta1.element.baztech-f3fc1492-303d-4669-b666-342a435b962d