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Relation between Lp-Riemann Derivative, Approximate Riemann Derivative and Riemann Derivative
T. K. Garai1
Section:Research Paper, Product Type: Isroset-Journal
Vol.6 ,
Issue.1 , pp.167-172, Feb-2019
CrossRef-DOI: https://doi.org/10.26438/ijsrmss/v6i1.167172
Online published on Feb 28, 2019
Copyright © T. K. Garai . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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IEEE Style Citation: T. K. Garai, “Relation between Lp-Riemann Derivative, Approximate Riemann Derivative and Riemann Derivative,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.1, pp.167-172, 2019.
MLA Style Citation: T. K. Garai "Relation between Lp-Riemann Derivative, Approximate Riemann Derivative and Riemann Derivative." International Journal of Scientific Research in Mathematical and Statistical Sciences 6.1 (2019): 167-172.
APA Style Citation: T. K. Garai, (2019). Relation between Lp-Riemann Derivative, Approximate Riemann Derivative and Riemann Derivative. International Journal of Scientific Research in Mathematical and Statistical Sciences, 6(1), 167-172.
BibTex Style Citation:
@article{Garai_2019,
author = {T. K. Garai},
title = {Relation between Lp-Riemann Derivative, Approximate Riemann Derivative and Riemann Derivative},
journal = {International Journal of Scientific Research in Mathematical and Statistical Sciences},
issue_date = {2 2019},
volume = {6},
Issue = {1},
month = {2},
year = {2019},
issn = {2347-2693},
pages = {167-172},
url = {https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=1154},
doi = {https://doi.org/10.26438/ijcse/v6i1.167172}
publisher = {IJCSE, Indore, INDIA},
}
RIS Style Citation:
TY - JOUR
DO = {https://doi.org/10.26438/ijcse/v6i1.167172}
UR - https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=1154
TI - Relation between Lp-Riemann Derivative, Approximate Riemann Derivative and Riemann Derivative
T2 - International Journal of Scientific Research in Mathematical and Statistical Sciences
AU - T. K. Garai
PY - 2019
DA - 2019/02/28
PB - IJCSE, Indore, INDIA
SP - 167-172
IS - 1
VL - 6
SN - 2347-2693
ER -
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Abstract :
As the Definition of Lp-derivative is such that which contains only the absolute value of the function and therefore it is not possible to define the Lp-derivates from the definition of Lp-derivative. So to remove this difficulty S.N. Mukhopadyay and S.Ray uses a special technique to define them in their paper [2]. In this article we define the Lp-Riemann Derivative using the same technique as it is used to define the Lp-derivates in [2] and relation between approximate Riemann Derivative and Riemann derivative are studied.
Key-Words / Index Term :
Riemann derivative, Approximate Riemann derivative Lp-Riemann derivative Holder`s inequality
References :
[1] S. N. Mukhopadhyay, Higher order derivatives, Chapman and Hall/CRC, Monographs and surveys in Pure and Applied Methematics, 144 (2012).
[2] S.N.Mukhopadhyay and S.Ray, "Relation between Lp-derivates and Peano, approximate Peano and Borel derivates of higher order". Real Analysis Exchange, 41(1)(2015/2016) 1-22.
[3] J.M.Ash, Generalisations of Riemman derivetive, Trans. American Math. Soc., 126 (1967), 181-199.
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