Some Classes of Co-Schwarzian Functions and Its Coefficient Inequality that Is Sharp

In our present work, we defined an inequality called Fekete – Szegö Inequality for functions f(z) in the classes of starlike functions and convex functions along with subclasses of these classes.

Certain Classes of Analytic Functions Bound with Kober Operators in q -Calculus

Through applying the Kober fractional q -calculus apprehension, we preliminary implant and introduce new types of univalent analytical functions with a q -differintegral operator in the open disk U = ξ ∈ ℂ : ∣ ξ | < 1 . The coefficient inequality and distortion theorems are among the results examined with these forms of functions. Specific cases are responded and addressed immediately. The findings include an expansion of the numerous established results in the q -theory of analytical functions.

Comparing Global Inequality of Income and Wealth

This chapter is the first to compare global trends in income and wealth inequality this century. It is based on large income and wealth synthetic microdata samples designed to be representative of all countries. Measured by the Gini coefficient, inequality between countries accounts for about two-thirds of global income inequality, but noticeably less—around one half—of wealth inequality. Broadly similar results are found for different years and different inequality indices, bar the share of the top 1 per cent. Over time, changes in countries’ mean income and wealth, and in population sizes, have reduced world inequality. Income inequality has changed little within countries, so the downward trend remains intact. However, within-country wealth inequality has risen, halting the downward shift in global wealth inequality and raising the share of the top 1 per cent since 2007.

A Note on Meromorphic Functions Associated With Beseel Function Defined by Hilbert Sapce Operator

In this paper,we introduce and study a new subclass of meromorphic functions associated with a certain differential operator on Hilbert space. For this class, we obtain several properties like the coefficient inequality, growth and distortion theorem, radius of close-to-convexity, starlikeness and meromorphically convexity and integral transforms. Further, it is shown that this class is closed under convex linear combinations.

Certain Subclasses of Meromorphic Univalent Function Involving Differential Operator

The main object of the present paper is to introduce the class of meromorphic univalent function K* (σ,τ,S) defined by differential operator with study some geometric properties like coefficient inequality , growth theorem and distortion theorem, radii of starlikeness and convexity of f(z) in the class K* (σ,τ,S) .Also the concept of convolution (Hadamard product) investigate and Neighborhoods of the elements of class K* (σ,τ,S) are obtained.

On Quantum Differential Subordination Related with Certain Family of Analytic Functions

Recently, there is a rapid increase of research in the area of Quantum calculus (known as q -calculus) due to its widespread applications in many areas of study, such as geometric functions theory. To this end, using the concept of q -conic domains of Janowski type as well as q - calculus, new subclasses of analytic functions are introduced. This family of functions extends the notion of α -convex and quasi-convex functions. Furthermore, a coefficient inequality, sufficiency criteria, and covering results for these novel classes are derived. Besides, some remarkable consequences of our investigation are highlighted.

AMS subject classification:30C45 Meromorphically p-valent functions defined by integral operator involving ȴ-Function in new subclasses

Some relations in this paper we using in new subclass of meromorphically p-valent functions TK( ) defined by integral operator involving -function We derived some properties, like, coefficient inequality , growth and distortion bounds by theorems (2) and (3), Partial sums, convex set, radii of starlikeness and radii convexity.