İntegral Operatör Aileleri ile Genelleştirilmiş Taylor Türevlerine Yaklaşım

Year 2017, Volume: 5 Issue: 2, 421 - 423, 01.12.2017

Lütfi Akın , Yusuf Zeren

Abstract

Yaklaşımlar teorisi, diferansiyel ve integral denklemlerin nümerik çözümlerinde, fonksiyonel analizin çeşitli bölgelerindeki uygulamalarda, Fourier analizde, uygulamalı matematik alanında, operatör teoride, genelleştirilmiş türevler alanında ve polinomsal yaklaşımın uygulamalarında vs. çok önemli bir yere sahiptir. Bu çalışma n L pozitif lineer operatör dizileri vasıtası ile bir f fonksiyonuna yaklaşımın araştırılması problemidir. Yaklaşımlar teorisi, çalışma alanı için iyi kurulmuş bir teoridir. Bu teori matematik dünyası için çok önemli bir yere sahiptir. Günümüzde birçok matematikçi yaklaşımlar teorisi alanında çalışmaktadır.  

Keywords

Taylor türev, Çekirdek fonksiyonu, Türevlenebilir fonksiyon

Approximation To Generalized Taylor Derivatives By Integral Operator Families

Abstract

This theory has important applications of polynomial approximation in various areas of functional analysis, Fourier analysis, application mathematic, operator theory, in the field generalized derivatives and numerical solutions of differential and integral equations, etc. The study of approximation theory is a well-established area of research which deals with the problem of approximating a function f by means of a sequence n L of positive linear operators. This theory is very important for mathematical world. Nowadays, many mathematicians are working in this field.

Keywords

Taylor derivative, Kernel function, Differentiable function

References

• Referans1. Korovkin, P.P., 1960. Linear Positive Operators and Approximation
• Theory. Hindustan Publishing Corp., 222pp, Hindustan.
• Referans2. Gadjiev, A. D., Djifarov, A.S. and Labsker, L.G., 1962. On Asymtotic Value of
• Approximation of Functions By Certain Families of Integral Operators, Izvestiya
• Acad. Sci. of The Azerbaijan., 3: 19-28. In Russian.
• Referans3. Gadjiev, A.D., 1962. On Asymptotic Values of Approximation of Derivatives of
• functions By Derivatives of Families of Linear Operators.Izvestiya Acad. of Sci. of
• Azebaijan , 6:15-24.
• Referans4. Butzer, P.L. and Nessel, R.J., 1971. Fourier Analysis and Approximation, Academic Pres, 555p, New York and London.
• Referans5. Akin, L., 2008. “Approximation to Generalized Derivatives by Integral Operator
• Families.”, Harran University, Institute of Science, Master Thesis, Sanliurfa, 55p.
• Referans6. Altomare, F. and Campiti, M. 1994. Korovkin Type Approximation Theory and its Application, Walter de Gruyter, Berlin and New York.
• Referans7. Butzer, P.L., 1960. Representation and Approximation of Function By General Singular Integrals, Proceeding Konikel. Acad. Wet 63,
• Nederland.
• Referans8. Hacısalihoğlu, H. and Haciyev, A., 1995. “Convergence of Linear Positive Operator
• Sequences.”, Ankara, 100s, Ankara.
• Referans9. Stein, E. M., 1993. Singular Integrals and Differentiability Properties of
• Functions, Princeton Univ. Pres., 289pp, The United States of America.
• Referans10. Zeren, Y., 2006. Approximation of Schwartz Differentiable Functions of
• Several Variables By The Sequence of Integral Operators. Khazar Journal of mathematics, 1: 73-78.
• Referans11. Zeren, Y., 2002. “Asymptotic Value of Approximation of Derivatives Approximated
• by Integral Operator Family.”, Ankara University, Institute of Science, Ph.D. Tesis
• Ankara, 50p.