The boundaries of the solutions of the linear Volterra integral equations with convolution kernel

Authors:
Ismet Özdemir and Ö. Faruk Temizer

Journal:
Math. Comp. **75** (2006), 1175-1199

MSC (2000):
Primary 45D05; Secondary 45E10

Published electronically:
March 3, 2006

MathSciNet review:
2219024

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Abstract | References | Similar Articles | Additional Information

Abstract: Some boundaries about the solution of the linear Volterra integral equations of the second type with unit source term and positive monotonically increasing convolution kernel were obtained in Ling, 1978 and 1982. A method enabling the expansion of the boundary of the solution function of an equation in this type was developed in I. Özdemir and Ö. F. Temizer, 2002.

In this paper, by using the method in Özdemir and Temizer, it is shown that the boundary of the solution function of an equation in the same form can also be expanded under different conditions than those that they used.

**1.**Richard Bellman and Kenneth L. Cooke,*Differential-difference equations*, Academic Press, New York-London, 1963. MR**0147745****2.**Rina Ling,*Integral equations of Volterra type*, J. Math. Anal. Appl.**64**(1978), no. 2, 381–397. MR**0487317****3.**Rina Ling,*Solutions of singular integral equations*, Internat. J. Math. Math. Sci.**5**(1982), no. 1, 123–131. MR**666499**, 10.1155/S016117128200012X**4.**İsmet Özdemir and Ö. Faruk Temizer,*Expansion of the boundaries of the solutions of the linear Volterra integral equations with convolution kernel*, Integral Equations Operator Theory**43**(2002), no. 4, 466–479. MR**1909376**, 10.1007/BF01212705**5.**F. G. Tricomi,*Integral equations*, Pure and Applied Mathematics. Vol. V, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1957. MR**0094665**

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Additional Information

**Ismet Özdemir**

Affiliation:
Inönü Üniversitesi, Eğitim Fakültesi, 44280-Malatya, Turkey

Email:
isozdemir@inonu.edu.tr

**Ö. Faruk Temizer**

Affiliation:
Inönü Üniversitesi, Eğitim Fakültesi, 44280-Malatya, Turkey

Email:
oftemizer@inonu.edu.tr

DOI:
http://dx.doi.org/10.1090/S0025-5718-06-01834-5

Keywords:
Linear Volterra integral equations with convolution kernel,
equivalence theorem,
convolution theorem.

Received by editor(s):
June 17, 2004

Published electronically:
March 3, 2006

Article copyright:
© Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.