Nasze serwisy używają informacji zapisanych w plikach cookies. Korzystając z serwisu wyrażasz zgodę na używanie plików cookies zgodnie z aktualnymi ustawieniami przeglądarki, które możesz zmienić w dowolnej chwili. Więcej informacji odnośnie plików cookies.

Obowiązek informacyjny wynikający z Ustawy z dnia 16 listopada 2012 r. o zmianie ustawy – Prawo telekomunikacyjne oraz niektórych innych ustaw.

Wyłącz komunikat

 
 

Logowanie

Logowanie za pomocą Centralnej Usługi Uwierzytelniania PRz. Po zakończeniu pracy nie zapomnij zamknąć przeglądarki.

Journal of Mathematics and Applications

Journal of Mathematics and Applications
06/42, DOI: 10.7862/rf.2019.6

Nonincreasing Solutions for Quadratic Integral Equations of Convolution Type

Wagdy G. El-Sayed, A.A.H. Abd El-Mowla

DOI: 10.7862/rf.2019.6

Abstract

We study a nonlinear quadratic integral equation of Convolution type in the Banach space of real functions defined and continuous on a bounded and closed interval. By using a suitable measure of noncompactness, we show that the integral equation has monotonic solutions.

Full text (pdf)

References

  1. R.P. Agarwal, D. O'Regan, Global existence for nonlinear operator inclusion, Comput. Math. Appl. 38 (11-12) (1999) 131-139.
  2. R.P. Agarwal, D. O'Regan, P.J.Y. Wong, Positive Solutions of Differential, Difference and Integral Equations, Kluwer Academic, Dordecht, 1999.
  3. J. Banaś, Measures of noncompactness in the space of continuous tempered functions, Demonstratio Math. 14 (1981) 127-133.
  4. J. Banaś, K. Goebel, Measures of Noncompactness in Banach Spaces, Lecture Notes in Pure and Applied Mathematics, Vol. 60, Marcel Dekker, New York, 1980.
  5. J. Banaś, L. Olszowy, Measures of noncompactness related to monotonicity, Comment. Math. 41 (2001) 13-23.
  6. J. Banaś, A. Martinon, Monotonic solutions of a quadratic integral equation of Volterra type, Comput. Math. Appl. 47 (2004) 271-279.
  7. J. Banaś, M. Lecko, W.G. El-Sayed, Existence theorems for some quadratic integral equations, J. Math. Anal. Appl. 222 (1998) 276-285.
  8. J. Banaś, K. Sadarangani, Solvability of Volterra-Stieltjes operator-integral equations and their applications, Comput. Math. Appl. 41 (2001) 1535-1544.
  9. J. Banaś, J.R. Rodriguez, K. Sadarangani, On a class of Urysohn-Stieltjes quadratic integral equations and their applications, J. Comput. Appl. Math. 113 (2000) 35-50.
  10. J. Banaś, J. Rocha, K.B. Sadarangani, Solvability of a nonlinear integral equation of Volterra type, J. Comput. Appl. Math. 157 (2003) 31-48.
  11. J. Banaś, B. Rzepka, On existence and asymptotic stability of solutions of a nonlinear integral equation, J. Math. Anal. Appl. 284 (2003) 165-173.
  12. J. Banaś, J.R. Rodriguez, K. Sadarangani, On a nonlinear quadratic integral equation of Urysohn-Stieltjes type and its applications, Nonlinear Anal. 47 (2001) 1175-1186.
  13. J. Banaś, B. Rzepka, An applications of a measure of noncompactness in the study of asymptotic stability, Appl. Math. Lett. 16 (2003) 1-6.
  14. B. Cahlon, M. Eskin, Existence theorems for an integral equation of the Chandrasekhar H-equation with perturbation, J. Math. Anal. Appl. 83 (1981) 159-171.
  15. C. Corduneanu, Integral Equations and Applications, Cambridge University Press, Cambridge, MA, 1991.
  16. G. Darbo, Punti uniti in trasformazioni a codominio non compatto, Rend. Sem. Mat. Univ. Padova 24 (1955) 84-92.
  17. A.M.A. EL-Sayed, H.H.G. Hashem, Existence results for nonlinear quadratic functional integral equations of fractional orders, Miskolc Mathematical Notes 1 (2013) 79-88.
  18. A.M.A. EL-Sayed, H.H.G. Hashem, Integrable and continuous solutions of a nonlinear quadratic integral equation, Electron. J. Qual. Theory Differ. Equ. 25 (2008) 1-10.
  19. A.M.A. EL-Sayed, H.H.G. Hashem, Monotonic solutions of functional integral and differential equations of fractional order, Electron. J. Qual. Theory Differ. Equ. (2009) 1-8.
  20. A.M.A. EL-Sayed, H.H.G. Hashem, Monotonic positive solution of a nonlinear quadratic functional integral equation, Appl. Math. Comput. vol. 216 (2010) 2576-2580.
  21. W.G. EL-Sayed, B. Rzepka, Nondecreasing solutions of a quadratic integral equation of Urysohn type, Comput. Math. Appl. 51 (2006) 1065-1074.
  22. S. Hu, M. Khavani, W. Zhuang, Integral equations arising in the kinetic theory of gases, Appl. Anal. 34 (1989) 261-266.
  23. D. O'Regan, M. Meehan, Existence Theory for Nonlinear Integral and Integro-differential Equations, Kluwer Academic, Dordrecht, 1998.

About this Article

TITLE:
Nonincreasing Solutions for Quadratic Integral Equations of Convolution Type

AUTHORS:
Wagdy G. El-Sayed (1)
A.A.H. Abd El-Mowla (2)

AUTHORS AFFILIATIONS:
(1) Alexandria University, EGYPT
(2) Omar Al-Mukhtar University, LIBYA

JOURNAL:
Journal of Mathematics and Applications
06/42

KEY WORDS AND PHRASES:
Quadratic integral equation; Measure of noncompactness; Fixed-point theorem; Monotonic solutions.

FULL TEXT:
http://doi.prz.edu.pl/pl/pdf/jma/83

DOI:
10.7862/rf.2019.6

URL:
http://dx.doi.org/10.7862/rf.2019.6

RECEIVED:
2019-02-21

ACCEPTED:
2019-06-15

COPYRIGHT:
Oficyna Wydawnicza Politechniki Rzeszowskiej, al. Powstańców Warszawy 12, 35-959 Rzeszów

POLITECHNIKA RZESZOWSKA im. Ignacego Łukasiewicza; al. Powstańców Warszawy 12, 35-959 Rzeszów
tel.: +48 17 865 11 00, fax.: +48 17 854 12 60
Administrator serwisu:

Deklaracja dostępności | Polityka prywatności