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

Author(s): Ismet Özdemir; Ö. Faruk Temizer.
Journal: Math. Comp. 75 (2006), 1175-1199.
MSC (2000): Primary 45D05; Secondary 45E10
Posted: March 3, 2006
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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.

References:

1.: R. Bellman and K. L. Cooke, Differential - Difference Equations, Academic Press, New York, 1963. MR 0147745 (26:5259)
2.: R. Ling, Integral equations of Volterra type, J. Math. Anal. Appl. 64 (1978), 381-397. MR 0487317 (58:6964)
3.: R. Ling, Solutions of singular integral equations, Internat. J. Math. & Math. Sci. 5(1) (1982), 123-131. MR 0666499 (83j:45005)
4.: I. Özdemir and Ö. F. Temizer, Expansion of the boundaries of the solutions of the linear Volterra integral equations with convolution kernel, Integral Equations Operator Theory 43 (2002), 466-479.MR 1909376 (2003b:45001)
5.: F. G. Tricomi, Integral Equations, Interscience Publishers, Inc., New York, 1957.MR 0094665 (20:1177)

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Additional Information:

Ismet Özdemir
Affiliation: Inönü Üniversitesi, Egitim Fakültesi, 44280-Malatya, Turkey
Email: isozdemir@inonu.edu.tr

Ö. Faruk Temizer
Affiliation: Inönü Üniversitesi, Egitim Fakültesi, 44280-Malatya, Turkey
Email: oftemizer@inonu.edu.tr

DOI: 10.1090/S0025-5718-06-01834-5
PII: S 0025-5718(06)01834-5
Keywords: Linear Volterra integral equations with convolution kernel, equivalence theorem, convolution theorem.
Received by editor(s): June 17, 2004
Posted: March 3, 2006
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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The following works have cited this article

İsmet Özdemir, Ö. Faruk Temizer , On the solutions of the linear integral equations of Volterra type, Mathematical Methods in the Applied Sciences 30 (2007), 2329-2369.


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