A Research Approximation to Generalized Riemann Derivatives by Integral Operator Families

Lutfi Akin

doi:doi:10.11648/j.mcs.20180301.12

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A Research Approximation to Generalized Riemann Derivatives by Integral Operator Families

Lutfi Akin

Published in Mathematics and Computer Science (Volume 3, Issue 1)

Received: 23 November 2017 Accepted: 4 December 2017 Published: 19 January 2018

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Abstract

Approximation theory has very important applications of polynomial approximation in various areas of functional analysis, Harmonic analysis, Fourier analysis, application mathematic, operator theory in the field generalized derivatives and numerical solutions of differential and integral equations, etc. Integral operators is very important in Harmonic and Fourier analysis. 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 L_n of positive linear operators. Generalized derivatives (Riemann, Peano and Taylor derivative) are more general than ordinary derivative. Approximation theory is very important for mathematical world. Nowadays, many mathematicians are working in this field.

Published in	Mathematics and Computer Science (Volume 3, Issue 1)
DOI	10.11648/j.mcs.20180301.12
Page(s)	7-12
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2018. Published by Science Publishing Group

Keywords

Riemann Derivative, Kernel Function, Diferantiable Function, Operator Theory

References

[1]	Altomare, F. and Campiti, M. 1994. Korovkin Type Approximation Theory and its Application, Walter de Gruyter, Berlin and NewYork.
[2]	Korovkin, P. P., 1960. Linear Positive Operators and Approximation Theory. Hindistan Publishing Corp., 222pp, Hindustan.
[3]	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.
[4]	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.
[5]	Butzer, P. L. and Nessel, R. J., 1971. Fourier Analysis and Approximation, Academic Pres, 555p, New York and London.
[6]	Akin, L., 2008. “Approximation to Generalized Derivatives by Integral Operator Families.”, Harran University, Institute of Science, Master Thesis, Sanliurfa, 55p.
[7]	Butzer, P. L., 1960. Representation and Approximation of Function By General Singular Integrals, Proceeding Konikel. Acad. Wet 63, Nederland.
[8]	Hacısalihoğlu, H. and Haciyev, A., 1995. “Convergence of Linear Positive Operator Sequences.”, Ankara, 100s, Ankara.
[9]	Stein, E. M., 1993. Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Pres., 289pp, The United States of America.
[10]	Zeren, Y., 2006. Approximation of Schwartz Differentiable Functions of Several Variables by the Sequence of Integral Operators. Khazar Journal of mathematics, 1:73-78.
[11]	Zeren, Y., 2002. “Asymptotic Value of Approximation of Derivatives Approximated by Integral Operator Family.”, Ankara University, Institute of Science, Ph. D. Tesis Ankara, 50p.
[12]	Mamedov I. F., Zeren Y., Akın L., 2017. “Compactification of Weighted Hardy Operator in Variable Exponent Lebesgue Spaces”, Asian Journal Mathematics and Computer Research, 17(1):38-47.
[13]	Akin L. and Zeren Y., 2017. “Approximation to generalized Taylor derivative by integral operator families”, MSU J. of Sci., Volume 5, Issue 2, p 421-423.

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APA Style

Lutfi Akin. (2018). A Research Approximation to Generalized Riemann Derivatives by Integral Operator Families. Mathematics and Computer Science, 3(1), 7-12. https://doi.org/10.11648/j.mcs.20180301.12

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Lutfi Akin. A Research Approximation to Generalized Riemann Derivatives by Integral Operator Families. Math. Comput. Sci. 2018, 3(1), 7-12. doi: 10.11648/j.mcs.20180301.12

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Lutfi Akin. A Research Approximation to Generalized Riemann Derivatives by Integral Operator Families. Math Comput Sci. 2018;3(1):7-12. doi: 10.11648/j.mcs.20180301.12

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@article{10.11648/j.mcs.20180301.12,
  author = {Lutfi Akin},
  title = {A Research Approximation to Generalized Riemann Derivatives by Integral Operator Families},
  journal = {Mathematics and Computer Science},
  volume = {3},
  number = {1},
  pages = {7-12},
  doi = {10.11648/j.mcs.20180301.12},
  url = {https://doi.org/10.11648/j.mcs.20180301.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20180301.12},
  abstract = {Approximation theory has very important applications of polynomial approximation in various areas of functional analysis, Harmonic analysis, Fourier analysis, application mathematic, operator theory in the field generalized derivatives and numerical solutions of differential and integral equations, etc. Integral operators is very important in Harmonic and Fourier analysis. 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 Ln of positive linear operators. Generalized derivatives (Riemann, Peano and Taylor derivative) are more general than ordinary derivative. Approximation theory is very important for mathematical world. Nowadays, many mathematicians are working in this field.},
 year = {2018}
}

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TY  - JOUR
T1  - A Research Approximation to Generalized Riemann Derivatives by Integral Operator Families
AU  - Lutfi Akin
Y1  - 2018/01/19
PY  - 2018
N1  - https://doi.org/10.11648/j.mcs.20180301.12
DO  - 10.11648/j.mcs.20180301.12
T2  - Mathematics and Computer Science
JF  - Mathematics and Computer Science
JO  - Mathematics and Computer Science
SP  - 7
EP  - 12
PB  - Science Publishing Group
SN  - 2575-6028
UR  - https://doi.org/10.11648/j.mcs.20180301.12
AB  - Approximation theory has very important applications of polynomial approximation in various areas of functional analysis, Harmonic analysis, Fourier analysis, application mathematic, operator theory in the field generalized derivatives and numerical solutions of differential and integral equations, etc. Integral operators is very important in Harmonic and Fourier analysis. 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 Ln of positive linear operators. Generalized derivatives (Riemann, Peano and Taylor derivative) are more general than ordinary derivative. Approximation theory is very important for mathematical world. Nowadays, many mathematicians are working in this field.
VL  - 3
IS  - 1
ER  -

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Author Information

Lutfi Akin

Department of Business Administration, Faculty of Economics and Administrative Sciences, Mardin Artuklu University, Mardin, Turkey

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APA Style

Lutfi Akin. (2018). A Research Approximation to Generalized Riemann Derivatives by Integral Operator Families. Mathematics and Computer Science, 3(1), 7-12. https://doi.org/10.11648/j.mcs.20180301.12

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ACS Style

Lutfi Akin. A Research Approximation to Generalized Riemann Derivatives by Integral Operator Families. Math. Comput. Sci. 2018, 3(1), 7-12. doi: 10.11648/j.mcs.20180301.12

Copy | Download

AMA Style

Lutfi Akin. A Research Approximation to Generalized Riemann Derivatives by Integral Operator Families. Math Comput Sci. 2018;3(1):7-12. doi: 10.11648/j.mcs.20180301.12

Copy | Download

@article{10.11648/j.mcs.20180301.12,
  author = {Lutfi Akin},
  title = {A Research Approximation to Generalized Riemann Derivatives by Integral Operator Families},
  journal = {Mathematics and Computer Science},
  volume = {3},
  number = {1},
  pages = {7-12},
  doi = {10.11648/j.mcs.20180301.12},
  url = {https://doi.org/10.11648/j.mcs.20180301.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20180301.12},
  abstract = {Approximation theory has very important applications of polynomial approximation in various areas of functional analysis, Harmonic analysis, Fourier analysis, application mathematic, operator theory in the field generalized derivatives and numerical solutions of differential and integral equations, etc. Integral operators is very important in Harmonic and Fourier analysis. 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 Ln of positive linear operators. Generalized derivatives (Riemann, Peano and Taylor derivative) are more general than ordinary derivative. Approximation theory is very important for mathematical world. Nowadays, many mathematicians are working in this field.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - A Research Approximation to Generalized Riemann Derivatives by Integral Operator Families
AU  - Lutfi Akin
Y1  - 2018/01/19
PY  - 2018
N1  - https://doi.org/10.11648/j.mcs.20180301.12
DO  - 10.11648/j.mcs.20180301.12
T2  - Mathematics and Computer Science
JF  - Mathematics and Computer Science
JO  - Mathematics and Computer Science
SP  - 7
EP  - 12
PB  - Science Publishing Group
SN  - 2575-6028
UR  - https://doi.org/10.11648/j.mcs.20180301.12
AB  - Approximation theory has very important applications of polynomial approximation in various areas of functional analysis, Harmonic analysis, Fourier analysis, application mathematic, operator theory in the field generalized derivatives and numerical solutions of differential and integral equations, etc. Integral operators is very important in Harmonic and Fourier analysis. 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 Ln of positive linear operators. Generalized derivatives (Riemann, Peano and Taylor derivative) are more general than ordinary derivative. Approximation theory is very important for mathematical world. Nowadays, many mathematicians are working in this field.
VL  - 3
IS  - 1
ER  -

Copy | Download