Content uploaded by C. David Minda
Author content
All content in this area was uploaded by C. David Minda on Oct 09, 2014
Content may be subject to copyright.
A unified treatment of some special classes of functions
... Lemma 1.3. [15] If 1 ( ) = 1+ 1 + 2 2 + · · · is a function having positive real part in D and is a complex number, then we get ...
The fractional-differintegral operator defines two new subclasses of analytic functions in the open unit disc in this article. Fekete-Szegö inequalities are also derived for these newly defined subclasses.
... In this case, ω(0) = 0 and |ω| < 1 such that ( ) = ( ( )) as proven, ( ) ≺ ( ) and f( ) ⊂ g( ) Implied by (0) = (0). [13] used the idea of subordination to create various sub classes of radii of convexity and starlikeness. To achieve this goal, a univalent function ϕ(ξ) is taken into consideration. ...
Recent years have shown us how fascinating the univalent function is many new publications have been written in this field. Currently, operators of normalized analytic functions, differential and integral operators are highly sought after. Numerous researchers have examined and debated a great deal of material for the operators. This work introduces a new subclass of the function class for univalent functions defined by the Raducanu-Orhan differential operator connected with pascal distribution series. Our goal in this work is to further our understanding and make inferences regarding the functions that are a part of these new subclass. Furthermore, the convexity of the subclass, growth and distortion, radius of starlike, extreme points, and integral means of inequalities are obtained. All this research was performed inside an open unit disc.
In this paper, we acquaint universally prestarlike generalized functions of order with associated with generalized telephone numbers and we get coefficient bounds for and also for which has not been discussed earlier. Further we obtain the Fekete-Szegö functional for the class of universally prestarlike functions and applications to certain probability distribution based on convolution product for such functions.
Emphasising their connection with shell-like star-like curves, this work investigates a new subclass of star-like functions defined by q-Fibonacci numbers and q-polynomials. We study the geometric and analytic properties of this subclass, including the computation of intervals of univalence and nonunivalence for some functions. Moreover, we define a sufficient condition for functions in this subclass to satisfy the criteria of the famous class of analytic functions with positive real components. This work improves our understanding of the link between Fibonacci-type sequences and the geometric properties of analytic functions by using subordination ideas and the features of q-Fibonacci sequences. Emphasising the possibility for diverse research in combinatorial and analytical mathematics, the results offer fresh insights and support further study on the applications of calculus in geometric function theory.
We investigate sharp upper bounds for the third-order Hankel determinants for two important subclasses ℱ and 𝒲 of normalized analytic functions f defined in an open unit disk satisfying Re f′ > 0, defined analytically by the conditions and respectively.
A new class of Bazilevič functions of the type is defined involving differential characterizations inspired by the study of multiplicative calculus. The defined function class unifies the studies of well-known subclasses like convex, starlike and alpha-convex functions. To further make our study more versatile, we have studied the new function class involving a differential operator defined using the Mittag-Leffler function. Estimates of Taylor–Maclaurin coefficients and of the functions which belong to the defined function class are obtained. Further, the Fekete–Szeg˝o inequality of this new class which was computationally cumbersome is part of our main results in this paper.
In this paper, we make use of the concept of fractional q-calculus to introduce two new classes of biBazilevic functions involving q-Ruscheweyh differential operator that are subordinate to Gegenbauer polynomials and q-analogue of hyperbolic tangent functions. This study explores the characteristics and behaviors of these functions, offering estimates for the modulus of the initial Taylor series coefficients a2 and a3 within this specific class and their various subclasses. Additionally, this study delves into the classical Fekete-Szeg¨o functional problem concerning functions f that are part of our newly defined class and several of their subclasses.
The notion of Hankel determinant Hq in univalent functions theory is initiated by Noonan and Thomas while studying it for areally mean multivalent mappings. This determinant has significant role while dealing with singularities and particularly it’s important for analyzing integral coefficient. Fekete-Szeg¨o functional used in the study of the area theorem is a particular case of this determinant. We explore a known class of holomorphic mappings which is related with the various classes of functions with conjugate symmetric points We also study upper bounds in different settings of the coefficients of these mappings. We also relate our exploration with the existing literature of the subject.
This study focuses on deriving Fekete-Szegö inequalities for a specific subclass of univalent functions with complex order, related to quasi-subordination. It investigates the geometric properties of these functions and the conditions for subordination between analytic functions within the open unit disk. The research also discusses generalized starlikeness and convexity as examples of subordination and explores the role of analytic Schwarz functions in this context. New results are provided for superior functions of various orders, contributing to the field of geometric function theory. The findings offer insights into quasi-subordination and its practical applications in pure mathematics, advancing the understanding of function behavior under subordination constraints.
ResearchGate has not been able to resolve any references for this publication.