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On a language generated by smooth functions. (Russian) Zbl 1098.41012

Summary: We apply a new approach to the study of continuous functions \(\varphi:[a,b]\to{\mathbf R}\) with bounded second derivative and their discrete analogues. We describe minimal prohibited subsequences in sequences of finite second differences generated by discrete analogues of functions with second derivative bounded from below or from above. Analogous sequences for classes of functions with second derivative bounded from two sides are investigated.

MSC:

41A30 Approximation by other special function classes
26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems
26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
39A12 Discrete version of topics in analysis
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