Let X be a complex Banach space, a norming set for X , and D ⊂ X a bounded, closed, and convex domain such that its norm closure D is compact in σ(X , ). Let ∅ = C ⊂D lie strictly inside D. We study convergence properties of infinite products of those selfmappings of C which can be extended to holomorphic self-mappings of D. Endowing the space of sequences of such mappings with an appropriate m...

The infinite product Q1 n1⁄40ð1 aqnÞ, plays a part in the theory of basic functions, similar to that of the Gamma function in the theoryof ordinaryhy pergeometric functions, so it is pertinent to enquire how such products can be evaluated numerically. In this paper we will discuss the numerical evaluation of the infinite products using the method of gridded data interpolation. 2004 Elsevier Inc...