On The Generalized Divided Differences
DOI:
https://doi.org/10.15415/mjis.2016.51005Keywords:
Peano derivative, Divided difference, Riemann* derivative, n-convex functionAbstract
Let V ⊂ℜ be a finite set and f :ℜ→ℜ. f(V) is divided the difference of f at the points of V. The m-th order Peano derivative of f({x}∪V)with respect to x is called generalized divided difference and is denoted by fm (x, V). The properties of fm(x,V) are studied.
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Fejzic H, Svetic R E and Weil C E, Differentiation of n-convex functions. Fund. Math 209 Vol-1 9–25 (2010) zbl 1202.26008.
S. N. Mukhopadhayay and S. Ray, Mean value Theorems for divided differences and approximate Peano derivatives. Mathematica Bohemica 134 Vol-2 (2009), 165–171, zbl 1212.26075.
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Articles in Mathematical Journal of Interdisciplinary Sciences (Math. J. Interdiscip. Sci.) by Chitkara University Publications are Open Access articles that are published with licensed under a Creative Commons Attribution- CC-BY 4.0 International License. Based on a work at https://mjis.chitkara.edu.in. This license permits one to use, remix, tweak and reproduction in any medium, even commercially provided one give credit for the original creation.
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Mathematical Journal of Interdisciplinary Sciences by Chitkara University Publications is licensed under a Creative Commons Attribution 4.0 International License. Based on a work at https://mjis.chitkara.edu.in |
