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In the present paper, we give a new simple proof on the sharp bounds of coefficient functionals related to the Carathéodory functions and make a correction on the extremal functions. The result is further used to investigate some initial coefficient bounds on a subclass of bounded turning functions R ℘ associated with a cardioid domain. For functions in this class, we calculate the bounds of the Fekete–Szegö-type inequality and the second- and third-order Hankel determinants. All the results are proved to be sharp. [ABSTRACT FROM AUTHOR]

Abstract: Ever since 2012 when Srivastava et al. [22] introduced and initiated the study of many interesting fundamental properties and characteristics of a certain pair of potentially useful families of the so-called generalized incomplete hypergeometric functions, there have appeared many closely-related works dealing essentially with notable developments involving various classes of generalized hypergeometric functions and generalized hypergeometric polynomials, which are defined by means of the corresponding incomplete and other novel extensions of the familiar Pochhammer symbol. Here, in this sequel to some of these earlier works, we derive several general families of hypergeometric generating functions by applying (for example) some such combinatorial identities as Gould’s identity, which stem essentially from the Lagrange expansion theorem. We also indicate various (known or new) special cases and consequences of the results presented in this paper. [Copyright &y& Elsevier]

In this study, we consider different types of convex-exponent products of elements of a certain class of log-harmonic mapping and then find sufficient conditions for them to be starlike log-harmonic functions. For instance, we show that, if f is a spirallike function, then choosing a suitable value of γ , the log-harmonic mapping F (z) = f (z) | f (z) | 2 γ is α - s p i r a l i k e of order ρ. Our results generalize earlier work in the literature. [ABSTRACT FROM AUTHOR]

Abstract: In a recent paper, Srivastava et al. (2012) [23] introduced and studied some fundamental properties and characteristics of a family of potentially useful incomplete hypergeometric functions. The main object of this paper is to investigate several generating functions for a certain class of incomplete hypergeometric polynomials associated with them. Various (known or new) special cases and consequences of the results presented in this paper are also considered. [Copyright &y& Elsevier]

Abstract: In the present paper, we obtain the subordination- and superordination-preserving properties of a certain general family of nonlinear integral operators which are defined on the space of normalized analytic functions in the open unit disk. The sandwich-type results for these integral operators are also presented. [Copyright &y& Elsevier]