On determination of best-possible constants in integral inequalities involving derivatives

Author:
Beny Neta

Journal:
Math. Comp. **35** (1980), 1191-1193

MSC:
Primary 26D15; Secondary 46E30, 65J99

DOI:
https://doi.org/10.1090/S0025-5718-1980-0583496-X

MathSciNet review:
583496

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Abstract: This paper is concerned with the numerical approximation of the best possible constants in the inequality

**[1]**N. P. Kupcov,*Kolmogorov estimates for derivatives in 𝐿₂[0,∞)*, Trudy Mat. Inst. Steklov.**138**(1975), 94–117, 199 (Russian). Approximation of functions and operators. MR**0393388****[2]**S. B. Stečkin,*Inequalities between norms of derivatives of arbitrary functions*, Acta Sci. Math. (Szeged)**26**(1965), 225–230 (Russian). MR**0185064****[3]**S. B. Stečkin,*Best approximation of linear operators*, Mat. Zametki**1**(1967), 137–148 (Russian). MR**0211169****[4]**V. V. Arestov,*Precise inequalities between the norms of functions and their derivatives*, Acta Sci. Math. (Szeged)**33**(1972), 243–267 (Russian). MR**0320729****[5]**V. V. Arestov,*Some extremal problems for differentiable functions of one variable*, Trudy Mat. Inst. Steklov.**138**(1975), 3–28, 199 (Russian). Approximation of functions and operators. MR**0415165****[6]**Ju. N. Subbotin and L. V. Taĭkov,*Best approximation of a differentiation operator in the space 𝐿₂*, Mat. Zametki**3**(1968), 157–164 (Russian). MR**0228892****[7]**J. S. Bradley and W. N. Everitt,*On the inequality \parallel𝑓′′\parallel²≤𝐾\parallel𝑓\parallel\parallel𝑓⁽⁴⁾\parallel*, Quart. J. Math. Oxford Ser. (2)**25**(1974), 241–252. MR**0349930**, https://doi.org/10.1093/qmath/25.1.241**[8]**S. D. Conte,*Elementary numerical analysis: An algorithmic approach*, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1965. MR**0202267****[9]**William N. Everitt and Brian D. Sleeman (eds.),*Ordinary and partial differential equations*, Lecture Notes in Mathematics, Vol. 564, Springer-Verlag, Berlin-New York, 1976. MR**0477213**

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DOI:
https://doi.org/10.1090/S0025-5718-1980-0583496-X

Article copyright:
© Copyright 1980
American Mathematical Society