Measures of noncompactness in a Banach algebra and their applications

• Autorzy: Dudek S.

Identyfikatory

DOI

10.7862/rf.2017.5

• Języki publikacji: EN

Abstrakty

EN

In this paper we study the existence of solutions of a nonlinear quadratic integral equation of fractional order. This equation is considered in the Banach space of real functions defined, continuous and bounded on the real half axis. Additionally, using the technique of measures of noncompactness we obtain some characterization of considered integral equation. We provide also an example illustrating the applicability of our approach.

Słowa kluczowe

EN

Banach algebra; integral equation of fractional order; fixed point theorem; asymptotic stability; ultimate monotonicity; measure of noncompactness

PL

algebra Banacha; przestrzeń Banacha; równanie całkowite rzędu ułamkowego; twierdzenie o punkcie stałym; stabilność asymptotyczna; monotoniczność

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2017
• Tom: Vol. 40
• Strony: 69--84
• Opis fizyczny: Bibliogr. 21 poz.

Twórcy

autor

Dudek S.

• Department of Nonlinear Analysis, Rzeszów University of Technology, al. Powstańców Warszawy 8, 35-959 Rzeszów

Bibliografia

• [1] J. Appell, J. Banaś and N. Merentes, Measures of noncompactnes in the study of asymptotically stable and ultimately nondecreasing solutions of integral equations, Zeit. Anal. Anwend. 29 (2010) 251-273.
• [2] J. Appell, P.P. Zabrejko, Nonlinear Superposition Operators, Cambridge Univ. Press, Cambridge 1990.
• [3] I.K. Argyros, Quadratic equations and applications to Chandrasekhar's and related equations, Bull. Austral. Math. Soc. 32 (1985) 275-282.
• [4] J. Banaś, S. Dudek, The technique of measures of noncompactness in Banach algebras and its applications to integral equations. Abstr. Appl. Anal., Volume 2013 (2013), Article ID 537897, 15 pages.
• [5] J. Banaś, K. Goebel, Measures of Noncompactness in Banach Spaces, Lect. Notes Pure and Appl. Math. 60, Marcel Dekker, New York 1980.
• [6] J. Banaś, M. Lecko, Fixed points of the product of operators in Banach algebra, Panamer. Math. J. 12 (2002) 101-109.
• [7] J. Banaś, L. Olszowy, On a class of measures of noncompactnes in Banach algebras and their application to nonlinear integral equations, Zeit. Anal. Anwend. 28 (2009) 475-498.
• [8] J. Banaś, D. O'Regan, On existence and local attractivity of solutions of aquadratic Volterra integral equation of fractional order, J. Math. Anal. Appl. 345 (2008) 573-582.
• [9] J. Banaś, B. Rzepka, On existence and asymptotic stability of solutions of a nonlinear integral equation, J. Math. Anal. Appl. 284 (2003) 165-173.
• [10] J. Banaś, B. Rzepka, Monotonic solutions of a quadratic integral equation of fractional order, J. Math. Anal. Appl. 322 (2007) 1371-1379.
• [11] J. Banaś, K. Sadarangani, Solutions of some functional-integral equations in Banach algebra, Math. Comput. Modelling 38 (2003) 245-250.
• [12] A. Ben Amar, S. Chouayekh and A. Jeribi, New fixed point theorems in Banach algebras under weak topology features and applications to nonlinear integral equations, J. Func. Anal. 259 (2010) 2215-2237.
• [13] 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.
• [14] S. Chandrasekhar, Radiative Transfer, Oxford Univ. Press, London 1950.
• [15] C. Corduneanu, Integral Equations and Applications, Cambridge Univ. Press,Cambridge 1991.
• [16] M. Darwish, On quadratic integral equation of fractional orders, J. Math. Anal. Appl. 311 (2005) 112-119.
• [17] K. Deimling, Nonlinear Functional Analysis, Springer Verlag, Berlin 1985.
• [18] B.C. Dhage, On α-condensing mappings in Banach algebras, The Math. Student. 63 (1994) 146-152.
• [19] B.C. Dhage, On a fixed point theorem in Banach algebras with applications, Appl. Math. Letters 18 (2005) 273-280.
• [20] G. Gripenberg, On some epidemic models, Q. Appl. Math. 39 (1981) 317-327.
• [21] S. Hu, M. Kharani and W. Zhuang, Integral equations arising in the kinetic theory of gases, Appl. Analysis 34 (1989) 261-266.

Uwagi

PL

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