On The Generalized Divided Differences

September 5, 2016

Abstract:

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 f_m (x, V). The properties of f_m(x,V) are studied.

Author(s):

Subhasis Ray and Subhankar Ghosh, Department of Mathematics, Siksha Bhavan, Visva-Bharati, Shantiniketan, West Bengal, India

DOI:

https://doi.org/10.15415/mjis.2016.51005

Keywords:

Peano derivative, Divided difference, Riemann* derivative, n-convex function

References:

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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