Convolution Properties of Certain Classes of Analytic Functions Defined by Jackson q-Derivative

In this paper, the Jackson q-derivative is used to investigate two classes of analytic functions in the open unit disc. The coefficient conditions and inclusion properties of the functions in these classes are established by convolution methods.

Application of q-Mittag-Leffer Function on Certain Subclasses of Analytic Functions

The main objective of this paper is to introduce and study the generality differential operator involving the q-Mittag-Leffler function on certain subclasses of analytic functions. Also, we investigate the inclusion properties of these classes, by using the concept of subordination between analytic functions.

On inclusion properties of discrete Morrey spaces

We discuss a necessary condition for inclusion relations of weak type discrete Morrey spaces which can be seen as an extension of the results in [H. Gunawan, E. Kikianty and C. Schwanke, Discrete Morrey spaces and their inclusion properties, Math. Nachr. 291 2018, 8–9, 1283–1296] and [D. D. Haroske and L. Skrzypczak, Morrey sequence spaces: Pitt’s theorem and compact embeddings, Constr. Approx. 51 2020, 3, 505–535]. We also prove a proper inclusion from weak type discrete Morrey spaces into discrete Morrey spaces. In addition, we give a necessary condition for this inclusion. Some connections between the inclusion properties of discrete Morrey spaces and those of Morrey spaces are also discussed.

Inclusion Properties of The Homogeneous Herz-Morrey Spaces With Variable Exponent

In this paper, we have discussed about the inclusion properties of the homogeneous Herz-Morrey spaces with variable exponent and the weak homogeneous spaces with variable exponent. We also studied the inclusion relation between those spaces.

Some Inclusion Properties of Certain Subclasses of Analytic Functions Defined by Using the Tremblay Fractional Derivative Operator

In this paper, we introduce new subclasses of analytic and p-valent functions related to starlike, convex, close-to-convex, and quasi-convex functions by using a p-valent analog of the Tremblay fractional derivative operator. Inclusion relationships for these subclasses are established.

Study on new integral operators defined using confluent hypergeometric function

Two new integral operators are defined in this paper using the classical Bernardi and Libera integral operators and the confluent (or Kummer) hypergeometric function. It is proved that the new operators preserve certain classes of univalent functions, such as classes of starlike and convex functions, and that they extend starlikeness of order $\frac{1}{2}$ 1 2 and convexity of order $\frac{1}{2}$ 1 2 to starlikeness and convexity, respectively. For obtaining the original results, the method of admissible functions is used, and the results are also written as differential inequalities and interpreted using inclusion properties for certain subsets of the complex plane. The example provided shows an application of the original results.

Functionalizable Glyconanoparticles for a Versatile Redox Platform

A series of new glyconanoparticles (GNPs) was obtained by self-assembly by direct nanoprecipitation of a mixture of two carbohydrate amphiphilic copolymers consisting of polystyrene-block-β-cyclodextrin and polystyrene-block-maltoheptaose with different mass ratios, respectively 0–100, 10–90, 50–50 and 0–100%. Characterizations for all these GNPs were achieved using dynamic light scattering, scanning and transmission electron microscopy techniques, highlighting their spherical morphology and their nanometric size (diameter range 20–40 nm). In addition, by using the inclusion properties of cyclodextrin, these glyconanoparticles were successfully post-functionalized using a water-soluble redox compound, such as anthraquinone sulfonate (AQS) and characterized by cyclic voltammetry. The resulting glyconanoparticles exhibit the classical electroactivity of free AQS in solution. The amount of AQS immobilized by host–guest interactions is proportional to the percentage of polystyrene-block-β-cyclodextrin entering into the composition of GNPs. The modulation of the surface density of the β-cyclodextrin at the shell of the GNPs may constitute an attractive way for the elaboration of different electroactive GNPs and even GNPs modified by biotinylated proteins.

A Class of p-valent Functions Defined by Differential Operator

In the present paper, we introduce the class A of p-valent analytic functions in the open unit disk We investigate some inclusion properties, coefficient bounds, distortion theorem, -neighborhoods and partial sums. Also we obtain integral representation, weighted and arithmetic mean.

Faber Polynomial for Holomorphic Functions Involving Differential Operator

The purpose of this paper, is to present differential operator for the univalent functions employ a Faber Polynomial . In addition, we will introduce some inclusion properties of the operator that were obtained employ the principle of subordination between holomorphic functions.