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Keywords:
mean value; higher order divided difference; approximate Peano derivative; $n$-convex function
mean value; higher order divided difference; approximate Peano derivative; $n$-convex function
Summary:
Several mean value theorems for higher order divided differences and approximate Peano derivatives are proved.
References:
[1] Bruckner, A. M.: Differentiation of Real Functions. Lect. Notes Math., Springer, New York (1978). MR 0507448 | Zbl 0382.26002
[2] Bullen, P. S.: A criterion for $n$-convexity. Pacific J. Math. 36 (1971), 81-98. DOI 10.2140/pjm.1971.36.81 | MR 0274681 | Zbl 0194.08602
[3] Bullen, P. S., Mukhopadhyay, S. N.: Properties of Baire$^*$-1 Darboux functions and some mean value theorems for Peano derivatives. Math. Jap. 36 (1991), 309-316. MR 1095745 | Zbl 0726.26002
[4] Evans, M. J.: $L_p$ derivatives and approximate Peano derivatives. Trans. Amer. Math. Soc. 165 (1972), 381-388 . MR 0293030
[5] Mukhopadhyay, S. N.: On the approximate Peano derivatives. Fund. Math. 88 (1975), 133-143. MR 0376974 | Zbl 0307.26007
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