바로가기메뉴

본문 바로가기 주메뉴 바로가기

logo

  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

Article Contents

Prev Next
e-Submission

Vol.17 No.2

Citation Share

AN APPLICATION OF DARBO'S FIXED POINT THEOREM TO A NONLINEAR QUADRATIC INTEGRAL EQUATION OF VOLTERRA TYPE

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2010, v.17 no.2, pp.175-183
Liu, Zeqing
Ume, Jeong-Sheok
Kang, Shin-Min
Liu,, Z. , Ume,, J. , & Kang,, S. (2010). AN APPLICATION OF DARBO'S FIXED POINT THEOREM TO A NONLINEAR QUADRATIC INTEGRAL EQUATION OF VOLTERRA TYPE. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 17(2), 175-183.

Abstract

Using Darbo's fixed point theorem, we establish the existence of monotone solutions for a nonlinear quadratic integral equation of Volterra type in the Banach space of real functions defined and continuous on a bounded and closed interval.

keywords
Darbo's fixed point theorem, measure of noncompactness, nonlinear quadratic integral equation, monotonic solution

Reference

1.

Cahlon, Baruch;Eskin, Michael. (1981). EXISTENCE THEOREMS FOR AN INTEGRAL EQUATION OF THE CHANDRASEKHAR H-EQUATION WITH PERTURBATION. Journal of Mathematical Analysis and Applications, 83(1), 159-171. 10.1016/0022-247X(81)90254-7.

2.

3.

(1955). . Rend. Sem. Mat. Univ. Padova, 24, 84-92.

4.

Hu, Shouchuan;Khavanin, Mohammad;Zhuang, WAN. (1989). Integral equations arising in the kinetic theory of gases. Applicable Analysis, 34(3), 261-266. 10.1080/00036818908839899.

5.

6.

Banas, J.;Rocha, J.;Sadarangani, K.B.. (2003). Solvability of a nonlinear integral equation of Volterra type. Journal of Computational and Applied Mathematics, 157(1), 31-48. 10.1016/S0377-0427(03)00373-X.

7.

Banas, J.;Rzepka, B.. (2003). On existence and asymptotic stability of solutions of a nonlinear integral equation. Journal of Mathematical Analysis and Applications, 284(1), 165-173. 10.1016/S0022-247X(03)00300-7.

8.

Banas, J.;Rodriquez, J.R.;Sadarangani, K.. (2001). On a nonlinear quadratic integral equation of Urysohn-Stieltjes type and its applications. Nonlinear Analysis, 47(2), 1175-1186. 10.1016/S0362-546X(01)00256-5.

9.

Banas, J.;Martinon, A.. (2004). Monotonic solutions of a quadratic integral equation of Volterra type. Computers & Mathematics with Applications, 47(2), 271-279. 10.1016/S0898-1221(04)90024-7.

10.

(2001). . Comment. Math., 41, 13-23.

11.

Banas, J.;Lecko, M.;El-Sayed, W.G.. (1998). Existence Theorems for Some Quadratic Integral Equations. Journal of Mathematical Analysis and Applications, 222(1), 276-285. 10.1006/jmaa.1998.5941.

12.

Banas, J.;Sadarangani, K.. (2001). Solvability of Volterra-Stieltjes operator-integral equations and their applications. Computers & Mathematics with Applications, 41(12), 1535-1544. 10.1016/S0898-1221(01)00118-3.

13.

Bana��. (2000). . Journal of Computational and Applied Mathematics, 113(1-2), 35-50. 10.1016/S0377-0427(99)00242-3.

14.

Agarwal, R.P.;O'Regan, D.. (1999). Global Existence for Nonlinear Operator Inclusions. Computers & Mathematics with Applications, 38(11), 131-139. 10.1016/S0898-1221(99)00292-8.

15.

Banas, J.;Rzepka, B.. (2003). An application of a measure of noncompactness in the study of asymptotic stability. Applied Mathematics Letters, 16(1), 1-6. 10.1016/S0893-9659(02)00136-2.

16.

17.

(1980). .

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

e-Submission OA Policy