\documentclass[10pt]{article}

 \usepackage{amsmath}
 \usepackage{amsfonts,amssymb}
 \usepackage{amsthm}
 \usepackage[active]{srcltx}

\usepackage[cp1251]{inputenc}

\usepackage[final]{graphicx}



\newenvironment{ltrtr}{
 \vspace{0.5\baselineskip} \noindent {\footnotesize{REFERENCES}} \vspace{-0.5\baselineskip}
 \begin{enumerate}
 \partopsep=0pt\topsep=0pt\itemsep=1pt\parsep=0pt\parskip=0pt}{\end{enumerate}}


\textwidth          13cm \textheight         18cm \topmargin   0mm
\oddsidemargin       5mm

\begin{document}


\setcounter{figure}{0} \setcounter{equation}{0}
\setcounter{table}{0} \setcounter{footnote}{0}

\begin{center}
 \title{}{\bf Investigation of discrete analogs of integral geometry problem with a weight function}

\author{}{Bakanov G.B., Meldebekova S.K.}

{\it Khoja Akhmet Yassawi International Kazakh-Turkish University, Turkestan, Kazakhstan}

{\it galitdin.bakanov@ayu.edu.kz, saule.meldebekova@ayu.edu.kz}

\end{center}

The interest in reconstruction problems has grown tremendously in the last four decades, stimulated by the spectrum of new modalities of image reconstruction. These are X-ray, MRI, gamma and positron radiography, ultrasound, seismic tomography, electron microscopy, synthetic radar imaging and others. The physical principles of these methods are very different; however their mathematical models and solution methods have very much in common. The umbrella name reconstructive integral geometry is used to specify the variety of these problems and methods \cite{1}-\cite{3}.

With fairly general assumptions about the family of curves and the weight function, the problem of integral geometry is reduced to a boundary value problem for a second-order partial differential equation. Estimates of the conditional stability of discrete analogs of a two-dimensional integral geometry problem with a weight function on the space of sufficiently smooth functions are obtained.

The results of studying the problem under consideration contribute to the development of the theory and practical implementation of integral geometry problems in various fields of science and technology.

The work has been supported by grant funding from the Committee of Science of the Ministry of Science and Higher Education of the Republic of Kazakhstan within the framework of the scientific project AP 19678469.

\begin{ltrtr}

\bibitem{1}
 {\it Kabanikhin S., Bakanov G. } On the stability of a finite-difference analogue of a two dimensional problem of integral geometry // Soviet Mathematics Doklady. - American Mathematical Society., 1987,  Vol. 35., No. 1., p. 16.

\bibitem{2}
{\it Kabanikhin S., Bakanov G. } On the stability estimation of finite-difference and differential-difference analogues of a two-dimensional integral geometry problem // Computerized Tomography. Proc. of the 4th Intern. simposium., Utrecht: VSP, 1995, p. 395.

\bibitem{3}
{\it Bakanov G.} Investigation of Finite-Difference Analogue of the Integral Geometry Problem with a Weight Function.//In Functional Analysis in Interdisciplinary Applications-II: ICAAM, Lefkosa, Cyprus, September 6-9, 2018 (pp. 29-38). Cham: Springer International Publishing.

\end{ltrtr}


\end{document}
