17 research outputs found
Certain classes of multivalent functions with negative coefficients associated with a convolution structure
Making use of a convolution structure, we introduce a new class of
analytic functions
defined in the open unit disc and investigate its various
characteristics. Further we obtained distortion bounds, extreme
points and radii of close-to-convexity, starlikeness and convexity
for functions belonging to the class
$mathbb{T}^{p}_{g}(lambda,alpha, beta).
Differential Subordination And Superordination For Analytic And Meromorphic Functions Defined By Linear Operators [QA331. N219 2007 f rb].
Suatu fungsi f yang tertakrif pada cakera unit terbuka U dalam satah kompleks C disebut univalen jika fungsi tersebut memetakan titik berlainan dalam U ke titik berlainan dalam C.
A function f defined on the open unit disk U of the complex plane C is univalent if it maps different points of U to different points of C
PROPERTIES OF A NEW SUBCLASS OF ANALYTIC FUNCTIONS ASSOCIATED TO RAFID - OPERATOR AND q-DERIVATIVE
In this article, we introduce a new subclass of analytic functions, using the exponent operators of Rafid and -derivative. The coefficient estimates, extreme points, convex linear combination, radii of starlikeness, convexity, and finally integral are investigated
Ruscheweyh-Goyal Derivative of Fractional Order, its Properties Pertaining to Pre-starlike Type Functions and Applications
The study of the operators possessing convolution form and their properties is considered advantageous in geometric function theory. In 1975 Ruscheweyh defined operator for analytic functions using the technique of convolution. In 2005, Goyal and Goyal generalized the Ruscheweyh operator to fractional order (which we call here Ruscheweyh-Goyal differential operator) using Srivastava-Saigo fractional differential operator involving hypergeometric function. Inspired by these earlier efforts, we discuss the properties of the Ruscheweyh-Goyal derivative of arbitrary order. We define a class of pre-starlike type functions involving the Ruscheweyh-Goyal fractional derivative and obtain the inclusion relation. Further, we prove that Ruscheweyh-Goyal derivative operator preserve the convexity and starlikeness for an analytic function. The majorization results for fractional Ruscheweyh-Goyal derivative has been discussed using a newly defined subclass
Classes of meromorphic multivalent functions with Montel’s normalization
In the paper we define classes of meromorphic multivalent functions with Montel’s normalization. We investigate the coefficients estimates, distortion properties, the radius of starlikeness, subordination theorems and partial sums for the defined classes of functions. Some remarks depicting consequences of the main results are also mentioned
Certain subclasses of multivalent functions defined by new multiplier transformations
In the present paper the new multiplier transformations
\mathrm{{\mathcal{J}% }}_{p}^{\delta }(\lambda ,\mu ,l) (\delta ,l\geq
0,\;\lambda \geq \mu \geq 0;\;p\in \mathrm{% }%\mathbb{N} )} of multivalent
functions is defined. Making use of the operator two new subclasses and \textbf{\ }of multivalent analytic
functions are introduced and investigated in the open unit disk. Some
interesting relations and characteristics such as inclusion relationships,
neighborhoods, partial sums, some applications of fractional calculus and
quasi-convolution properties of functions belonging to each of these subclasses
and
are
investigated. Relevant connections of the definitions and results presented in
this paper with those obtained in several earlier works on the subject are also
pointed out
New Developments in Geometric Function Theory
The book contains papers published in a Special Issue of Axioms, entitled "New Developments in Geometric Function Theory". An Editorial describes the 14 papers devoted to the study of complex-valued functions which present new outcomes related to special classes of univalent and bi-univalent functions, new operators and special functions associated with differential subordination and superordination theories, fractional calculus, and certain applications in geometric function theory
A subclass of meromorphic Janowski-type multivalent q-starlike functions involving a q-differential operator
Keeping in view the latest trends toward quantum calculus, due to its various applications in physics and applied mathematics, we introduce a new subclass of meromorphic multivalent functions in Janowski domain with the help of the q-differential operator. Furthermore, we investigate some useful geometric and algebraic properties of these functions. We discuss sufficiency criteria, distortion bounds, coefficient estimates, radius of starlikeness, radius of convexity, inclusion property, and convex combinations via some examples and, for some particular cases of the parameters defined, show the credibility of these results. © 2022, The Author(s)