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The present study aims at investigating some characterizations of a new subclass G α (μ , τ) and obtaining the bounds on the first two Taylor–Maclaurin coefficients for functions belonging to the newly introduced subclass. In order to achieve this, a compound function L x , n σ (z) is derived from the convolution of the analytic function f (z) and a modified exponential Pareto distribution G (x) in conjunction with the famous Libera integral operator L (ζ) . With the aid of the derived function, the aforementioned subclass G α (μ , τ) is introduced, while some properties of functions belonging to this subclass are considered in the open unit disk. [ABSTRACT FROM AUTHOR]

The research presented in this paper deals with analytic p-valent functions related to the generalized probability distribution in the open unit disk U. Using the Hadamard product or convolution, function f s (z) is defined as involving an analytic p-valent function and generalized distribution expressed in terms of analytic p-valent functions. Neighborhood properties for functions f s (z) are established. Further, by applying a previously introduced linear transformation to f s (z) and using an extended Libera integral operator, a new generalized Libera-type operator is defined. Moreover, using the same linear transformation, subclasses of starlike, convex, close-to-convex and spiralike functions are defined and investigated in order to obtain geometrical properties that characterize the new generalized Libera-type operator. Symmetry properties are due to the involvement of the Libera integral operator and convolution transform. [ABSTRACT FROM AUTHOR]