Operational Identities for Circular and Hyperbolic Functions and Their Generalizations

2003 ◽  
Vol 10 (1) ◽  
pp. 45-56 ◽  
Author(s):  
C. Cassisa ◽  
P. E. Ricci ◽  
I. Tavkhelidze
Keyword(s):  
Analytic Functions ◽  
Operational Calculus ◽  
Hyperbolic Functions ◽  
Derivative Operator ◽  
Circular Functions

Abstract Starting from the exponential, some classes of analytic functions of the derivative operator are studied, including pseudo-hyperbolic and pseudo-circular functions. Some formulas related to operational calculus are deduced, and the important role played in such a context by Hermite–Kampé de Fériet polynomials is underlined.

scholarly journals Application of the Efros Theorem to the Function Represented by the Inverse Laplace Transform of s−μ exp(−sν)

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 354
Author(s):  
Alexander Apelblat ◽  
Francesco Mainardi
Keyword(s):  
Laplace Transform ◽  
Operational Calculus ◽  
Inverse Laplace Transform ◽  
Elementary Functions ◽  
Hyperbolic Functions ◽  
Error Functions ◽  
Convolution Integrals ◽  
Special Case ◽  
Integral Identities ◽  
Finite Integrals

Using a special case of the Efros theorem which was derived by Wlodarski, and operational calculus, it was possible to derive many infinite integrals, finite integrals and integral identities for the function represented by the inverse Laplace transform. The integral identities are mainly in terms of convolution integrals with the Mittag–Leffler and Volterra functions. The integrands of determined integrals include elementary functions (power, exponential, logarithmic, trigonometric and hyperbolic functions) and the error functions, the Mittag–Leffler functions and the Volterra functions. Some properties of the inverse Laplace transform of s−μexp(−sν) with μ≥0 and 0<ν<1 are presented.

scholarly journals Second Hankel determinant for a class of analytic functions defined by q-derivative operator

2019 ◽  
Vol 27 (2) ◽  
pp. 167-177
Author(s):  
Dorina Răducanu
Keyword(s):  
Analytic Function ◽  
Analytic Functions ◽  
Hankel Determinant ◽  
Derivative Operator ◽  
Second Hankel Determinant

AbstractIn this paper, we obtain the estimates for the second Hankel determinant for a class of analytic functions defined by q-derivative operator and subordinate to an analytic function.

scholarly journals Differential Subordination with Generalized Derivative Operator of Analytic Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Entisar El-Yagubi ◽  
Maslina Darus
Keyword(s):  
Analytic Functions ◽  
Differential Subordination ◽  
Derivative Operator ◽  
Generalized Derivative

Motivated by generalized derivative operator defined by the authors (El-Yagubi and Darus, 2013) and the technique of differential subordination, several interesting properties of the operator Dλ1,λ2,δm,b are given.

Results of differential subordination for a unified subclass of analytic functions defined using generalized Ruscheweyh derivative operator

2019 ◽  
Vol 12 (03) ◽  
pp. 1950035
Author(s):  
Ritu Agarwal ◽  
G. S. Paliwal ◽  
Parany Goswami
Keyword(s):  
Analytic Functions ◽  
Differential Subordination ◽  
Derivative Operator ◽  
Sandwich Theorem ◽  
Ruscheweyh Derivative Operator ◽  
Ruscheweyh Derivative ◽  
Principle Of Subordination ◽  
Coefficient Inequalities ◽  
Distortion Theorems

In this paper, we introduce a unified subclass of analytic functions by making use of the principle of subordination, involving generalized Ruscheweyh Derivative operator [Formula: see text]. The properties such as inclusion relationships, distortion theorems, coefficient inequalities and differential sandwich theorem for the above class have been discussed.

scholarly journals Faber Polynomial Coefficient Estimates for Bi-Univalent Functions Defined by Using Differential Subordination and a Certain Fractional Derivative Operator

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 172 ◽  
Author(s):  
Hari M. Srivastava ◽  
Ahmad Motamednezhad ◽  
Ebrahim Analouei Adegani
Keyword(s):  
Fractional Derivative ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Derivative Operator ◽  
Faber Polynomial

In this article, we introduce a general family of analytic and bi-univalent functions in the open unit disk, which is defined by applying the principle of differential subordination between analytic functions and the Tremblay fractional derivative operator. The upper bounds for the general coefficients | a n | of functions in this subclass are found by using the Faber polynomial expansion. We have thereby generalized and improved some of the previously published results.

scholarly journals The Attractors of the Common Differential Operator Are Determined by Hyperbolic and Lacunary Functions

2008 ◽  
Vol 2008 ◽  
pp. 1-19
Author(s):  
Wolf Bayer
Keyword(s):  
Differential Operator ◽  
Taylor Series ◽  
Analytic Functions ◽  
Chaotic Behavior ◽  
Higher Order ◽  
Limit Behavior ◽  
Hyperbolic Functions ◽  
Limit Sets ◽  
The Common

For analytic functions, we investigate the limit behavior of the sequence of their derivatives by means of Taylor series, the attractors are characterized by -limit sets. We describe four different classes of functions, with empty, finite, countable, and uncountable attractors. The paper reveals that Erdelyiéshyperbolic functions of higher orderandlacunary functionsplay an important role for orderly or chaotic behavior. Examples are given for the sake of confirmation.

scholarly journals Convolution Properties for Certain Classes of Analytic Functions Defined byq-Derivative Operator

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
T. M. Seoudy ◽  
M. K. Aouf
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc ◽  
Derivative Operator ◽  
Convolution Properties

We investigate convolution properties and coefficients estimates for two classes of analytic functions involving theq-derivative operator defined in the open unit disc. Some of our results improve previously known results.

scholarly journals Study on Certain Subclass of Analytic Functions Involving Mittag-Leffler Function

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Nazek Alessa ◽  
B. Venkateswarlu ◽  
K. Loganathan ◽  
P. Thirupathi Reddy ◽  
A. Shashikala ◽  
...  
Keyword(s):  
Analytic Functions ◽  
Extreme Points ◽  
Partial Sums ◽  
Derivative Operator ◽  
Regular Functions

We propose and explore a new subclass of regular functions described by a new derivative operator in this paper. Some coefficient estimations, growth and distortion aspects, extreme points, star-like radii, convexity, Fekete-Szego inequality, and partial sums are derived.

scholarly journals Inclusion and neighborhood properties of a certain subclasses of p-valent functions with negative coefficients

Filomat ◽  
2009 ◽  
Vol 23 (3) ◽  
pp. 1-13 ◽  
Author(s):  
R.M. El-Ashwah
Keyword(s):  
Differential Equation ◽  
Analytic Functions ◽  
Function Class ◽  
Derivative Operator ◽  
Coefficient Bounds ◽  
Ruscheweyh Derivative Operator ◽  
Ruscheweyh Derivative ◽  
Inclusion Relations

By means of Ruscheweyh derivative operator, we introduced and investigated two new subclasses of p-valent analytic functions. The various results obtained here for each of these function class include coefficient bounds and distortion inequalities, associated inclusion relations for the (n, ?)-neighborhoods of subclasses of analytic and multivalent functions with negative coefficients, which are defined by means of non-homogenous differential equation.

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