On a New Class of Analytic Functions Related to Fractional Calculus

2020 ◽  
Author(s):  
Şahsene Altınkaya ◽  
Shigeyoshi Owa ◽  
Sibel Yalçın
Keyword(s):  
Fractional Calculus ◽  
Analytic Functions ◽  
New Class

scholarly journals Difference formula defined by a new differential symmetric operator for a class of meromorphically multivalent functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Rabha W. Ibrahim ◽  
Ibtisam Aldawish
Keyword(s):  
Differential Operator ◽  
Boundary Value Problems ◽  
Unit Disk ◽  
Spectral Theory ◽  
Analytic Functions ◽  
Special Class ◽  
Symmetric Operator ◽  
New Class ◽  
Difference Formula ◽  
Symmetric Operators

AbstractSymmetric operators have benefited in different fields not only in mathematics but also in other sciences. They appeared in the studies of boundary value problems and spectral theory. In this note, we present a new symmetric differential operator associated with a special class of meromorphically multivalent functions in the punctured unit disk. This study explores some of its geometric properties. We consider a new class of analytic functions employing the suggested symmetric differential operator.

scholarly journals Some Trapezium-Like Inequalities Involving Functions Having Strongly n-Polynomial Preinvexity Property of Higher Order

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Muhammad Uzair Awan ◽  
Sadia Talib ◽  
Muhammad Aslam Noor ◽  
Yu-Ming Chu ◽  
Khalida Inayat Noor
Keyword(s):  
Fractional Calculus ◽  
Higher Order ◽  
New Class ◽  
Special Cases ◽  
Preinvex Functions ◽  
Class Of Functions

The main objective of this paper is to introduce a new class of preinvex functions which is called as n-polynomial preinvex functions of a higher order. As applications of this class of functions, we discuss several new variants of trapezium-like inequalities. In order to obtain the main results of the paper, we use the concepts and techniques of k-fractional calculus. We also discuss some special cases of the obtained results which show that the main results of the paper are quite unifying one.

scholarly journals EXTREME POINTS OF INTEGRAL FAMILIES OF ANALYTIC FUNCTIONS

2013 ◽  
Vol 94 (2) ◽  
pp. 202-221
Author(s):  
KEIKO DOW ◽  
D. R. WILKEN
Keyword(s):  
Analytic Functions ◽  
Compact Convex ◽  
Extreme Points ◽  
Starlike Functions ◽  
Extremal Problems ◽  
Kernel Functions ◽  
Closed Convex Hull ◽  
New Class ◽  
Geometric Function ◽  
Derivatives Of

AbstractExtreme points of compact, convex integral families of analytic functions are investigated. Knowledge about extreme points provides a valuable tool in the optimization of linear extremal problems. The functions studied are determined by a two-parameter collection of kernel functions integrated against measures on the torus. For specific choices of the parameters many families from classical geometric function theory are included. These families include the closed convex hull of the derivatives of normalized close-to-convex functions, the ratio of starlike functions of different orders, as well as many others. The main result introduces a surprising new class of extreme points.

scholarly journals Fekete-Szegö Problem for a New Class of Analytic Functions

2011 ◽  
Vol 2011 ◽  
pp. 1-5 ◽  
Author(s):  
Deepak Bansal
Keyword(s):  
Analytic Functions ◽  
Complex Parameter ◽  
New Class

We consider the Fekete-Szegö problem with complex parameter for the class () of analytic functions.

Integral means of certain analytic functions for fractional calculus

2007 ◽  
Vol 187 (1) ◽  
pp. 425-432 ◽  
Author(s):  
Tadayuki Sekine ◽  
Shigeyoshi Owa ◽  
Kazuyuki Tsurumi
Keyword(s):  
Fractional Calculus ◽  
Analytic Functions ◽  
Integral Means

scholarly journals New classification of analytic functions with negative coefficients

1988 ◽  
Vol 11 (1) ◽  
pp. 55-69
Author(s):  
Shigeyoshi Owa ◽  
Milutin Obradovic
Keyword(s):  
Fractional Calculus ◽  
Analytic Functions ◽  
Negative Coefficient ◽  
New Classification ◽  
Distortion Theorems

New classification of analytic functions with negative coefficients is given by using the coefficients inequality, that is, new subclassA(p,n,Bk)of analytic functions with negative coefficient is defined. The object of the present paper is to prove various distortion theorems for functions inA(p,n,Bk), and for fractional calculus of functions belonging toA(p,n,Bk). Further, some properties of the classA(p,n,Bk)are shown.

Sign in / Sign up

Export Citation Format

Share Document