On an integral operator

AbstractIn this paper we derive some criteria for univalence of a general integral operator for analytic functions in the open unit disk

Subclasses of Multivalent Meromorphic Functions with a Pole of Order p at the Origin

In this paper, we carry out a systematic study to discover the properties of a subclass of meromorphic starlike functions defined using the Mittag–Leffler three-parameter function. Differential operators involving special functions have been very useful in extracting information about the various properties of functions belonging to geometrically defined function classes. Here, we choose the Prabhakar function (or a three parameter Mittag–Leffler function) for our study, since it has several applications in science and engineering problems. To provide our study with more versatility, we define our class by employing a certain pseudo-starlike type analytic characterization quasi-subordinate to a more general function. We provide the conditions to obtain sufficient conditions for meromorphic starlikeness involving quasi-subordination. Our other main results include the solution to the Fekete–Szegő problem and inclusion relationships for functions belonging to the defined function classes. Several consequences of our main results are pointed out

On the Univalence Criterion of a General Integral Operator

In this paper we considered an general integral operator and three classes of univalent functions for which the second order derivative is equal to zero. By imposing supplimentary conditions for these functions we proved some univalent conditions for the considered general operator. Also some interesting particullar results are presented

Some Properties of Bazilevič Functions Involving Srivastava–Tomovski Operator

We introduce a new class of Bazilevič functions involving the Srivastava–Tomovski 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 Fekete–Szegö functional for functions belonging to the class

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

Study of the fuzzy q−spiral-like functions associated with the generalized linear operator

Nowadays, the subclasses of analytic functions in terms of fuzzy subsets are studied by various scholars and some of these concepts are extended using the $q-$theory of functions. In this inspiration, we introduce certain subclasses of analytic function by using the notion of fuzzy subsets along with the idea of $q-$calculus. We present the $q-$extensions of the fuzzy spiral-like functions of a complex order. We generalize this class using the $q-$analogues of the Ruscheweyh derivative and Srivastava-Attiya operators. Various interesting properties are examined for the newly defined subclasses. Also, some previously investigated results are deduced as the corollaries of our major results

Sufficient Univalence Conditions for Analytic Functions

<p/> <p>We consider a general integral operator and the class of analytic functions. We extend some univalent conditions of Becker's type for analytic functions using a general integral transform.</p