Maximum Modulus, Maximum Term and Interpolation Error of an Entire Function

Let f be analytic on the compact set E ⊂ C , of positive transfinite diameter and let Cr denote the largest equipotential curve of E such that f is analytic within Cr. Generally, the growth of an entire function is measured in terms of its order and type. Here we have established the relations between maximum modulus, maximum term and interpolation error of best uniform approximation to a function = ∈ ) (E C f { f holomorphic on int (E) and continuous on E } by algebraic polynomials and Lagrange polynomials, in the form of direct estimates. Key words/phrases: Equipotential curve, extremal polynomials , interpolation errors, Lagrange interpolation polynomial, transfinite diameter