14 research outputs found
Some Properties of BazileviÄ Functions Involving SrivastavaâTomovski Operator
We introduce a new class of BazileviÄ functions involving the SrivastavaâTomovski generalization of the Mittag-Leffler function. The family of functions introduced here is superordinated by a conic domain, which is impacted by the Janowski function. We obtain coefficient estimates and subordination conditions for starlikeness and FeketeâSzegö functional for functions belonging to the class
Starlike Functions of Complex Order with Respect to Symmetric Points Defined Using Higher Order Derivatives
In this paper, we introduce and study a new subclass of multivalent functions with respect to symmetric points involving higher order derivatives. In order to unify and extend various well-known results, we have defined the class subordinate to a conic region impacted by Janowski functions. We focused on conic regions when it pertained to applications of our main results. Inclusion results, subordination property and coefficient inequality of the defined class are the main results of this paper. The applications of our results which are extensions of those given in earlier works are presented here as corollaries
Properties of Meromorphic Spiral-Like Functions Associated with Symmetric Functions
To consolidate or adapt to many studies on meromorphic functions, we define a new subclass of meromorphic functions of complex order involving a differential operator. The defined function class combines the concept of spiral-like functions with other studies pertaining to subclasses of multivalent meromorphic functions. Inclusion relations, integral representation, geometrical interpretation, coefficient estimates and solution to the Fekete-Szegö problem of the defined classes are the highlights of this present study. Further to keep up with the present direction of research, we extend the study using quantum calculus. Applications of our main results are given as corollaries
A study of sharp coefficient bounds for a new subfamily of starlike functions
AbstractIn this article, by employing the hyperbolic tangent function tanhz, a subfamilyStanhâof starlike functions in the open unit diskDâC:D={z:zâC and |z|<1}is introduced and investigated. The main contribution of this article includes derivations of sharp inequalities involving the TaylorâMaclaurin coefficients for functions belonging to the classStanhâof starlike functions inD. In particular, the bounds of the first three TaylorâMaclaurin coefficients, the estimates of the FeketeâSzegö type functionals, and the estimates of the second- and third-order Hankel determinants are the main problems that are proposed to be studied here
Inequalities
Inequalities appear in various fields of natural science and engineering. Classical inequalities are still being improved and/or generalized by many researchers. That is, inequalities have been actively studied by mathematicians. In this book, we selected the papers that were published as the Special Issue ââInequalitiesââ in the journal Mathematics (MDPI publisher). They were ordered by similar topics for readersâ convenience and to give new and interesting results in mathematical inequalities, such as the improvements in famous inequalities, the results of Frame theory, the coefficient inequalities of functions, and the kind of convex functions used for HermiteâHadamard inequalities. The editor believes that the contents of this book will be useful to study the latest results for researchers of this field
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Fractional calculus operator and its applications to certain classes of analytic functions. A study on fractional derivative operator in analytic and multivalent functions.
The main object of this thesis is to obtain numerous applications of fractional derivative operator concerning analytic and -valent (or multivalent) functions in the open unit disk by introducing new classes and deriving new properties. Our finding will provide interesting new results and indicate extensions of a number of known results. In this thesis we investigate a wide class of problems. First, by making use of certain fractional derivative operator, we define various new classes of -valent functions with negative coefficients in the open unit disk such as classes of -valent starlike functions involving results of (Owa, 1985a), classes of -valent starlike and convex functions involving the Hadamard product (or convolution) and classes of -uniformly -valent starlike and convex functions, in obtaining, coefficient estimates, distortion properties, extreme points, closure theorems, modified Hadmard products and inclusion properties. Also, we obtain radii of convexity, starlikeness and close-to-convexity for functions belonging to those classes. Moreover, we derive several new sufficient conditions for starlikeness and convexity of the fractional derivative operator by using certain results of (Owa, 1985a), convolution, JackÂżs lemma and NunokakawaÂż Lemma. In addition, we obtain coefficient bounds for the functional of functions belonging to certain classes of -valent functions of complex order which generalized the concepts of starlike, BazileviÂż and non-BazileviÂż functions. We use the method of differential subordination and superordination for analytic functions in the open unit disk in order to derive various new subordination, superordination and sandwich results involving the fractional derivative operator. Finally, we obtain some new strong differential subordination, superordination, sandwich results for -valent functions associated with the fractional derivative operator by investigating appropriate classes of admissible functions. First order linear strong differential subordination properties are studied. Further results including strong differential subordination and superordination based on the fact that the coefficients of the functions associated with the fractional derivative operator are not constants but complex-valued functions are also studied
Geometrical Theory of Analytic Functions
The book contains papers published in the Mathematics Special Issue, entitled "Geometrical Theory of Analytic Functions". Fifteen papers devoted to the study concerning complex-valued functions of one variable present new outcomes related to special classes of univalent functions, differential equations in view of geometric function theory, quantum calculus and its applications in geometric function theory, operators and special functions associated with differential subordination and superordination theories and starlikeness, and convexity criteria
Higher-order q-derivatives and their applications to subclasses of multivalent Janowski type q-starlike functions
In the present investigation, with the help of certain higher- order q-derivatives, some new subclasses of multivalent q-starlike functions which are associated with the Janowski functions are defined. Then, certain interesting results, for example, radius problems and the results related to distortion, are derived. We also derive a sufficient condition and certain coefficient inequalities for our defined function classes. Some known consequences related to this subject are also highlighted. Finally, the well-demonstrated fact about the (p, q)-variations is also given in the concluding section
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