Rational Approximation on the Positive Real Axis

Introduction Rational Chebyshev approximation to reciprocals of certain entire functions by reciprocals of polynomials on the positive real axis has recently attracted the attention of many mathematicians . By developing certain new methods of approach we successfully attacked ([3]-[6]) some of the related problems . This paper is a continuation of our earlier papers ([3]-[6] ) . The results of this paper improve and extend some of the earlier results with simplified proofs (cf . Theorem 3) . For a reader interested in this topic, this paper may serve as a guide by illustrating some of the techniques (old ones with refinements, as well as new) which we used to solve some of the very interesting and difficult problems of the field (cf. examples 1, 2, 3 of Theorem 5) .