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Mercerian Conditions for the Method (F, dn)

Published online by Cambridge University Press:  20 November 2018

H. B. Skerry
H. B. Skerry*
Affiliation:
Lehigh University, Bethlehem, Pennsylvania
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This paper sets forth conditions sufficient that the generalized Lototsky method (F, dn) be regular and Mercerian. If the dn's are real and of constant sign, then the conditions are also necessary. Moreover, it follows that if f is a polynomial, then under the same conditions the method (f,dn) is equivalent to the Sonnenschein method generated by f . Various related results are also given.

Definition 2.1. Let f be a nonconstant function holomorphic on the closed unit disk and let be a complex sequence with f (l) + dn ≠ 0. Suppose

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 23 , Issue 6 , December 1971 , pp. 1078 - 1085
Copyright
Copyright © Canadian Mathematical Society 1971

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