In this paper we develop and study some integral transforms of Caratheodory functions. We apply the transforms to study certain other classes of analytic and univalent functions both to obtain new results and provide new proofs of some known ones.
In this paper, the \(q\)-derivative operator and the principle of subordination were employed to define a subclass \(\mathcal{B}_q(\tau,\lambda,\phi)\) of analytic and bi-univalent functions in the open unit disk \(\mathcal{U}\). For functions \(f(z)\in\mathcal{B}_q(\tau,\lambda,\phi)\), we obtained early coefficient bounds and some Fekete-Szegö estimates for real and complex parameters.
We use the concept of q-differentiation to define a class Eq(β, δ) of analytic and univalent functions. The investigations thereafter includes coefficient estimates, inclusion property and some conditions for membership of some analytic functions to be in the class Eq(β, δ). Our results generalize some known and new ones.
Let S denote the class of functions that are analytic, normalized and univalent in the open unit disk { } : 1 E z z = <. Subclasses of S are the class of starlike and convex functions denoted by * S and C respectively. A new subclass of analytic functions that generalize some known subclasses of analytic functions was defined and investigated. We obtained coefficient bounds, upper estimates for the Fekete-Szegö functional and the Hankel determinant.
In this paper, we considered a family of analytic and univalent functions having positive real parts in the unit disk and defined by a q-difference operator. The coefficients, the Fekete-Szego estimates and the second Hankel determinants were established for the family of functions. Our family of functions generalized some earlier known ones and by varying some parameters, our results also generalized some known ones.
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