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Sufficiency for Gaussian hypergeometric functions to be uniformly convex

International Journal of Mathematics and Mathematical Sciences
Publication Date
  • Mathematics


Let F(a,b;c;z) be the classical hypergeometric function and f be a normalized analytic functions defined on the unit disk 𝒰. Let an operator Ia,b;c(f) be defined by [Ia,b;c(f)](z)=zF(a,b;c;z)*f(z). In this paper the authors identify two subfamilies of analytic functions ℱ1 and ℱ2 and obtain conditions on the parameters a,b,c such that f∈ℱ1 implies Ia,b;c(f)∈ℱ2.

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