A New Comprehensive Class of Analytic Functions Using Multiplier Transformations

作者：Lupas Alina Alb^*; Catas Adriana

来源：Journal of Computational Analysis and Applications, 2014, 17(4): 743-745.

• Analytic function
• p-valent starlike function
• p-valent convex function
• multiplier transformations

Let A (p, n) denote the class of normalized analytic functions f(z) in the open unit disc f(z) = z(p) + Sigma(infinity)(k=p+n) unit a(k)z(k), p, n is an element of N : = {1,2,3,...}. We consider in this paper multiplier transformations, namely I-p(m,lambda,iota) f(z) := z(p) + Sigma(infinity)(k=p+n) [p+lambda(k-p)+iota/p+l](m) a(k)z(k) where m is an element of N-0, N-0 = N boolean OR {0}, lambda is an element of R, lambda >= 0, l >= 0. By making use of the multiplier transformations, a new subclass of p-valent functions in the open unit disc is introduced. The new subclass is denoted by BIp (m, n, mu, alpha, lambda, l). Parallel results, for some related classes including the class of starlike and convex functions respectively, are also obtained.

• 出版日期2014-12