On the solutions of a class of nonlinear functional integral quations in space C [0,a]

• Autorzy: Özdemir İ. , Çakan Ü.

Identyfikatory

DOI

10.7862/rf.2015.9

• Języki publikacji: EN

Abstrakty

EN

The principal aim of this paper is to give sufficient conditions for solvability of a class of some nonlinear functional integral equations in the space of continuous functions defined on interval [0,a]. The main tool used in our study is associated with the technique of measures of noncompactness. We give also some examples satisfying the conditions of our main theorem but not satisfying the conditions in [8].

Słowa kluczowe

EN

nonlinear integral equation; measure of noncompactness; Darbo fixed point theorem; Darbo condition

PL

równanie całkowe; teoria punktu stałego; miara niezwartości; twierdzenie Darboux'a; własność Darboux

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2015
• Tom: Vol. 38
• Strony: 105--114
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Özdemir İ.

• Inönü Üniversitesi, Eğitim Fakültesi, A-Blok, Malatya, 44280, Turkey

autor

Çakan Ü.

• Nevşehir Hacı Bektaş Veli Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölumü, Nevsehir, 50300, Turkey

Bibliografia

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• [3] J. Banaś and K. Sadarangani, Solutions of some functional-integral equations in Banach algebra, Math. Comput. Modelling, 38 (2003), 245-250.
• [4] J. Banaś, J. Rocha and K. B. Sadarangani, Solvability of a nonlinear integral equation of Volterra type, J. Comput. Appl. Math., 157 (2003), 31-48.
• [5] J. Banaś, J. Caballero, J. Rocha and K. Sadarangani, Monotonic solutions of a class of quadratic integral equations of Volterra type, Comput. Math. Appl., 49 (2005), 943-952.
• [6] K. Deimling, Nonlinear functional analysis, Berlin, Springer, 1985.
• [7] K. Maleknejad, K. Nouri and R. Mollapourasl, Investigation on the existence of solutions for some nonlinear functional-integral equations, Nonlinear Anal., 71 (2009), 1575-1578.
• [8] K. Maleknejad, K. Nour and R. Mollapourasl, Existence of solutions for some nonlinear integral equations, Commun. Nonlinear Sci. Numer. Simul., 14 (2009), 2559-2564.
• [9] İ. Özdemir, Ü. Çakan and B. İlhan, On the existence of the solutions for some nonlinear Volterra integral equations, Abstr. Appl. Anal., 2013 (2013), Article ID 698234, 5 pages.
• [10] Ü. Çakan and İ. Özdemir, An application of the measure of noncompactness to some nonlinear functional integral equations in C [0,a], Adv. Math. Sci. Appl., 23-2 (2013), 575-584.
• [11] Z. Liu, S. M. Kang and J. S. Ume, Solvability and asymptotic stability of a nonlinear functional-integral equation, Appl. Math. Lett., 24 (2011), 911-917.