Log-Convex Polynomial Approximation in Log. of Twice Differentiable Functions

 Halgwrd Mohammed Darwesh

College of Science, University of Sulaimani

In this paper, we introduce a new concept of constrained approximation, which we call Log-convex
polynomial approximation in log. We obtained a direct theorem of log-convex polynomial approximation in
log for twice differentiable functions on [-1, 1], in term of the ordinary moduli of continuity.

Keywords: Shape preserving approximation, convex and log-convex functions, Splines,
moduli of continuity and smoothness.


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