Mathematics and Statistics Vol. 3(5), pp. 113 - 120
DOI: 10.13189/ms.2015.030501
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The Problem of Integral Geometry of Volterra Type with a Weight Function of a Special Type

Akram.H. Begmatov ^1,2,*, M.E. Muminov ³, Z.H. Ochilov ^2
1 Gwangyang Jecheol High School, South of Korea
² Samarkand State University, Uzbekistan
³ Faculty of Science, Malaysia Technology University, Malaysia

ABSTRACT

We study new problem of reconstruction of a function in a strip from their given integrals with known weight function along polygonal lines. We obtained two simply inversion formulas for the solution to the problem. We prove uniqueness and existence theorems for solutions and obtain stability estimates of a solution to the problem in Sobolev's spaces and thus show their weak ill-posedness. Then we consider integral geometry problems with perturbation. The uniqueness theorems are proved and stability estimates of solutions in Sobolev spaces are obtained.

KEYWORDS
Ill-posed Problems, Integral Geometry Problems, Integral Transforms, Inversion Formula, Uniqueness, Existence Theorem, Weak Instability, Perturbation

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Akram.H. Begmatov , M.E. Muminov , Z.H. Ochilov , "The Problem of Integral Geometry of Volterra Type with a Weight Function of a Special Type," Mathematics and Statistics, Vol. 3, No. 5, pp. 113 - 120, 2015. DOI: 10.13189/ms.2015.030501.

(b). APA Format:
Akram.H. Begmatov , M.E. Muminov , Z.H. Ochilov (2015). The Problem of Integral Geometry of Volterra Type with a Weight Function of a Special Type. Mathematics and Statistics, 3(5), 113 - 120. DOI: 10.13189/ms.2015.030501.