Some integral operators and their properties

Authors

  • Nizami Mustafa Dept. of Mathematics, Faculty of Science and Letters, Kafkas University, 36100 Kars, Turkey

Keywords:

integral operator, Cauchy integral operator.

Abstract

In this study, some integral operators, which have broad applications in the theory of elementary particles and scattering, have been investigated in Holder space. We show that some important inequalities for the norm of these operators are also satisfied in Holder space.

Author Biography

Nizami Mustafa, Dept. of Mathematics, Faculty of Science and Letters, Kafkas University, 36100 Kars, Turkey

Mathematics, Prof. Dr.

References

Colton, D.L. & Kress, R. (1983). Integral equation methods in

scattering theory. John Willey & Sons, Inc., New York.

Daugavet, I.K. (1977). Introduction to approximation theory of

functions. Leningrad (in Russian).

Duduchava, R. (1982). An application of singular integral equations

to some problems of elasticity. Integral Equations and Operator Theory,

(1):475-489.

Ivanov, V.V. (1968). The theory of approximate methods and its

application to the numerical solution of singular integral equations.

Naukova Dumka, Kiev.

Kalandia, A.I. (1973).Mathematical methods of the two-dimensional

elastics. Nauka, Moscow.

Kreyszig, E. (1978). Introductory functional analysis with applications.

New York-Chichester-Brisbanc-Toronto-Singapore.

Lu, Jian-Ke. (1993). Boundary value problems for analytic functions.

World Scientific, Singapore-New-Jersey-London-Hong-Kong.

Mustafa, N. (2008). Fixed point theory and approximate solutions of

non-linear singular integral equations. Complex Variables and Elliptic

Equations, 53(11):1047-1058.

Mustafa, N. & Khalilov, E.H. (2009). The collocation method for

the solution of boundary integral equations. Applicable Analysis,

(12):1665-1675.

Mustafa, N. & a?lar, M. (2010). Approximate solution of singular

integral equations with negative index. Gazi University Journal of

Science, 23(4):449-455.

Mustafa, N. (2013). On the existence solution of a class boundary

integral equations. Gazi University Journal of Science, 26(2):165-171.

Panasyuk, V.V., Savruk, M.P. & Nazarchuk, Z.T. (1984). Singular

integral equations methods in two-dimensional diffraction problem.

Naukova Dumka, Kiev.

Parton, V.Z. & Perlin, P.I. (1977). Integral equations of elasticity

theory. Nauka, Moscow.

Re?ido?lu, H. (Kh. Mamedov) (2001). On the planar problem of the

theory elasticity. Works SSU 1:27-32.

Downloads

Published

17-11-2016