scholarly journals Convolution properties of meromorphically harmonic functions defined by a generalized convolution $ q $-derivative operator

2021 ◽  
Vol 6 (6) ◽  
pp. 5869-5885
Author(s):  
Hari Mohan Srivastava ◽  
◽  
Muhammad Arif ◽  
Mohsan Raza ◽  
◽  
...  
Keyword(s):  
Harmonic Functions ◽  
Generalized Convolution ◽  
Derivative Operator ◽  
Convolution Properties

scholarly journals Remarks on the Generalized Fractional Laplacian Operator

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 320 ◽  
Author(s):  
Chenkuan Li ◽  
Changpin Li ◽  
Thomas Humphries ◽  
Hunter Plowman
Keyword(s):  
Differential Equations ◽  
Fractional Laplacian ◽  
Laplacian Operator ◽  
Generalized Convolution ◽  
Riesz Fractional Derivative ◽  
Derivative Operator ◽  
Delta Sequence ◽  
Remote Sites ◽  
Definition Of ◽  
Fractional Laplacian Operator

The fractional Laplacian, also known as the Riesz fractional derivative operator, describes an unusual diffusion process due to random displacements executed by jumpers that are able to walk to neighbouring or nearby sites, as well as perform excursions to remote sites by way of Lévy flights. The fractional Laplacian has many applications in the boundary behaviours of solutions to differential equations. The goal of this paper is to investigate the half-order Laplacian operator ( − Δ ) 1 2 in the distributional sense, based on the generalized convolution and Temple’s delta sequence. Several interesting examples related to the fractional Laplacian operator of order 1 / 2 are presented with applications to differential equations, some of which cannot be obtained in the classical sense by the standard definition of the fractional Laplacian via Fourier transform.

scholarly journals Pascu-Type Harmonic Functions with Positive Coefficients Involving Salagean Operator

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
K. Vijaya ◽  
G. Murugusundaramoorthy ◽  
M. Kasthuri
Keyword(s):  
Harmonic Functions ◽  
Extreme Points ◽  
Partial Sums ◽  
Open Unit ◽  
New Class ◽  
Sălăgean Operator ◽  
Salagean Operator ◽  
Convolution Properties ◽  
Positive Coefficients ◽  
Complex Valued

Making use of a Salagean operator, we introduce a new class of complex valued harmonic functions which are orientation preserving and univalent in the open unit disc. Among the results presented in this paper including the coeffcient bounds, distortion inequality, and covering property, extreme points, certain inclusion results, convolution properties, and partial sums for this generalized class of functions are discussed.

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 On Harmonic Functions Defined by Derivative Operator

2008 ◽  
Vol 2008 ◽  
pp. 1-10 ◽  
Author(s):  
K. Al-Shaqsi ◽  
M. Darus
Keyword(s):  
Harmonic Functions ◽  
Derivative Operator

scholarly journals A unified class of harmonic functions with varying argument of coefficients

Filomat ◽  
2018 ◽  
Vol 32 (4) ◽  
pp. 1349-1357
Author(s):  
Grigore Sǎlǎgean ◽  
Páll-Szabó Orsolya
Keyword(s):  
Harmonic Functions ◽  
Integral Operators ◽  
Coefficient Estimates ◽  
Closure Properties ◽  
Principle Of Subordination ◽  
Distortion Theorems ◽  
Convolution Properties

In this paper we investigate several classes of harmonic functions with varying argument of coefficients which are defined by means of the principle of subordination between harmonic functions. Properties such as the coefficient estimates, distortion theorems, convolution properties, radii of convexity, starlikeness and the closure properties of these classes under the generalized Bernardi-Libera-Livingston integral operators are investigated.

scholarly journals Some applications of q-difference operator involving a family of meromorphic harmonic functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Neelam Khan ◽  
H. M. Srivastava ◽  
Ayesha Rafiq ◽  
Muhammad Arif ◽  
Sama Arjika
Keyword(s):  
Harmonic Functions ◽  
Difference Operator ◽  
Partial Sums ◽  
Derivative Operator ◽  
Sharp Bounds ◽  
The Real ◽  
New Criteria

AbstractIn this paper, we establish certain new subclasses of meromorphic harmonic functions using the principles of q-derivative operator. We obtain new criteria of sense preserving and univalency. We also address other important aspects, such as distortion limits, preservation of convolution, and convexity limitations. Additionally, with the help of sufficiency criteria, we estimate sharp bounds of the real parts of the ratios of meromorphic harmonic functions to their sequences of partial sums.

scholarly journals On a Generalized Convolution Operator

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2141
Author(s):  
Poonam Sharma ◽  
Ravinder Krishna Raina ◽  
Janusz Sokół
Keyword(s):  
Fractional Derivative ◽  
Convolution Operator ◽  
Analytic Functions ◽  
Linear Operators ◽  
Generalized Convolution ◽  
Derivative Operator ◽  
Special Cases ◽  
Lerch Zeta Function ◽  
The One ◽  
Appell Function

Recently in the paper [Mediterr. J. Math. 2016, 13, 1535–1553], the authors introduced and studied a new operator which was defined as a convolution of the three popular linear operators, namely the Sǎlǎgean operator, the Ruscheweyh operator and a fractional derivative operator. In the present paper, we consider an operator which is a convolution operator of only two linear operators (with lesser restricted parameters) that yield various well-known operators, defined by a symmetric way, including the one studied in the above-mentioned paper. Several results on the subordination of analytic functions to this operator (defined below) are investigated. Some of the results presented are shown to involve the familiar Appell function and Hurwitz–Lerch Zeta function. Special cases and interesting consequences being in symmetry of our main results are also mentioned.

scholarly journals A Subclass of Harmonic Univalent Functions with Varying Arguments Defined by Generalized Derivative Operator

2012 ◽  
Vol 2012 ◽  
pp. 1-8
Author(s):  
E. A. Eljamal ◽  
M. Darus
Keyword(s):  
Harmonic Functions ◽  
Univalent Functions ◽  
Extreme Points ◽  
Open Unit ◽  
Derivative Operator ◽  
Generalized Derivative ◽  
New Class ◽  
Complex Valued ◽  
Class Of Functions ◽  
Varying Arguments

Making use of the generalized derivative operator, we introduce a new class of complex valued harmonic functions which are orientation preserving and univalent in the open unit disc and are related to uniformly convex functions. We investigate the coefficient bounds, neighborhood, and extreme points for this generalized class of functions.

scholarly journals A Class of k-Symmetric Harmonic Functions Involving a Certain q-Derivative Operator

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1812
Author(s):  
Hari M. Srivastava ◽  
Nazar Khan ◽  
Shahid Khan ◽  
Qazi Zahoor Ahmad ◽  
Bilal Khan
Keyword(s):  
Harmonic Functions ◽  
Univalent Functions ◽  
Function Class ◽  
Distortion Theorem ◽  
Additional Parameter ◽  
Sufficient Condition ◽  
Closure Properties ◽  
Derivative Operator ◽  
New Class ◽  
Symmetric Points

In this paper, we introduce a new class of harmonic univalent functions with respect to k-symmetric points by using a newly-defined q-analog of the derivative operator for complex harmonic functions. For this harmonic univalent function class, we derive a sufficient condition, a representation theorem, and a distortion theorem. We also apply a generalized q-Bernardi–Libera–Livingston integral operator to examine the closure properties and coefficient bounds. Furthermore, we highlight some known consequences of our main results. In the concluding part of the article, we have finally reiterated the well-demonstrated fact that the results presented in this article can easily be rewritten as the so-called (p,q)-variations by making some straightforward simplifications, and it will be an inconsequential exercise, simply because the additional parameter p is obviously unnecessary.

scholarly journals Generalized convolution properties based on the modified Mittag-Leffler function

2017 ◽  
Vol 10 (08) ◽  
pp. 4284-4294 ◽  
Author(s):  
H. M. Srivastava ◽  
Adem Kılıçman ◽  
Zainab E. Abdulnaby ◽  
Rabha W. Ibrahim
Keyword(s):  
Generalized Convolution ◽  
Convolution Properties
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