Abstract
Let f be an analytic function on the unit disc \({\mathbb{D}}\) and F(a, b; c; z) be the Gaussian hypergeometric function. We consider the operator Ta,b,c on H(p, q, α) defined as Ta, b, cf(z) = f(z) * F(a, b; c; z), where * denotes the usual Hadamard/convolution product. We prove that the Taylor coefficients of F(a, b; c; z) are a multiplier from H(p, q, α) to H(p, q, α + a + b − c − 1) under certain conditions on a, b and c. As a consequence, we generalize some well-known results on fractional derivatives and integrals. Furthermore, we supply some conditions on a, b and c under which F(a, b; c; z) lies in H(p, q, α).
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