Nonincreasing solutions for quadratic integral equations of Convolution type

• Autorzy: El-Sayed W. G. , Abd El-Mowla A. A. H.

Identyfikatory

DOI

10.7862/rf.2019.6

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

quadratic integral equation; measure of noncompactness; fixed-point theorem; monotonic solutions

PL

równanie całkowe; miara braku zgodności; twierdzenie o punkcie stałym; rozwiązania monotoniczne

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2019
• Tom: Vol. 42
• Strony: 95--107
• Opis fizyczny: Bibliogr. 23 poz.

Twórcy

autor

El-Sayed W. G.

• Faculty of Science, Alexandria University, Alexandria EGYPT

autor

Abd El-Mowla A. A. H.

• Faculty of Science, Omar Al-Mukhtar University, Derna LIBYA

Bibliografia

• [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 Integrodifferential Equations, Kluwer Academic, Dordrecht, 1998.

Uwagi

PL

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