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The Hankel determinant, which plays a significant role in the theory of univalent functions, is investigated here in the context of bi-univalent analytic functions. Specifically, this paper is dedicated to deriving an upper-bound estimate for the second-order Hankel determinant for a general subclass of bi-univalent analytic functions that incorporate Gegenbauer polynomials within the unit disk. Through the careful specialization of parameters in our main result, we unveil several novel findings. [ABSTRACT FROM AUTHOR]

Radius constants for functions in three classes of analytic functions to be a starlike function of order ff, parabolic starlike function, starlike function associated with lemniscate of Bernoulli, exponential function, cardioid, sine function, lune, a particular rational function, and reverse lemniscate are obtained. One of these classes are characterized by the condition Re g=(zez) > 0. The other two classes are defined by using the function g and they consist respectively of functions f satisfying Re f=g > 0 and jf=g 􀀀 1j < 1. [ABSTRACT FROM AUTHOR]

In this work, we define three subclasses of analytic functions. We then obtain the radius estimates of these functions to belong to various subclasses of starlike functions. [ABSTRACT FROM AUTHOR]

In this paper, by applying the Hohlov linear operator, connections between the class SD(α), α ≥ 0, and two subclasses of the class A of normalized analytic functions are established. Also an integral operator related to hypergeometric function is considered. [ABSTRACT FROM AUTHOR]

An analytic function f is quasi-subordinate to an analytic function g, in the open unit disk if there exist analytic functions φ and w, with |φ(z)| ≤ 1, w(0) = 0 and |w(z)| < 1 such that f(z) = φ(z)g(w(z)). Certain subclasses of analytic univalent functions associated with quasi-subordination are defined and the bounds for the Fekete-Szego coefficient functional |a3 - μa22| for functions belonging to these subclasses are derived. [ABSTRACT FROM AUTHOR]

For complex constants A and B with |B| ≤ 1, A ≠ B, let S*[A,B] be the class consisting of normalized analytic functions f satisfying zf'(z)/f(z) ≺ 1+Az/1+Bz . The radius of starlikeness, the radius of strong-starlikeness, and the radius of parabolic-starlikeness are obtained for functions in S*[A,B]. Consequences of these results are also discussed. [ABSTRACT FROM AUTHOR]

Due to the well-known Srivastava-Attiya operator, we investigate here some results relating the p-valent of the operator with differential subordination and subordination. Further, we obtain some interesting results on sandwich-type theorem for the same. [ABSTRACT FROM AUTHOR]

Motivated by the success of the Janowski starlike function, we consider here closely related functions for log-harmonic mappings of the form f(z) = zh(z)g(z) defined on the open unit disc U. The functions are in the class of the generalized Janowski starlike log-harmonic mapping, S*lh(A, B, α), with the functional zh(z) in the class of the generalized Janowski starlike functions, S*(A, B, α). By means of these functions, we obtained results on the generalized Janowski close-tostarlike log-harmonic mappings, CSTlh(A, B, α). [ABSTRACT FROM AUTHOR]

Several subclasses of meromorphic functions in the unit disk are introduced by means of convolution with a given fixed meromorphic function. Subjecting each convoluted-derived function in the class to be subordinated to a given normalized convex function with positive real part, these subclasses extend the classical subclasses of meromorphic starlikeness, convexity, close-to- convexity, and quasi-convexity. Class relations, as well as inclusion and convolution properties of these subclasses, are investigated. [ABSTRACT FROM AUTHOR]