scholarly journals Applications of Fractionalq-Calculus to Certain Subclass of Analyticp-Valent Functions with Negative Coefficients

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Ben Wongsaijai ◽  
Nattakorn Sukantamala
Keyword(s):  
Differential Operator ◽  
Convex Function ◽  
Extreme Points ◽  
Negative Coefficient ◽  
Geometric Properties ◽  
New Class ◽  
General Properties ◽  
Inclusion Relations ◽  
Invariant Properties

By making use of the concept of fractionalq-calculus, we firstly defineq-extension of the generalization of the generalized Al-Oboudi differential operator. Then, we introduce new class ofq-analogue ofp-valently closed-to-convex function, and, consequently, new class by means of this new general differential operator. Our main purpose is to determine the general properties on such class and geometric properties for functions belonging to this class with negative coefficient. Further, theq-extension of interesting properties, such as distortion inequalities, inclusion relations, extreme points, radii of generalized starlikeness, convexity and close-to-convexity, quasi-Hadamard properties, and invariant properties, is obtained. Finally, we briefly indicate the relevant connections of our presented results to the former results.

scholarly journals A class of harmonic functions associated with a generalized differential operator

2020 ◽  
Vol 108 (122) ◽  
pp. 145-154
Author(s):  
Sarika Verma ◽  
Deepali Khurana ◽  
Raj Kumar
Keyword(s):  
Differential Operator ◽  
Harmonic Functions ◽  
Univalent Functions ◽  
Extreme Points ◽  
Coefficient Estimates ◽  
Geometric Properties ◽  
New Class ◽  
Inclusion Relations ◽  
Generalized Differential

We introduce a new class of harmonic univalent functions by using a generalized differential operator and investigate some of its geometric properties, like, coefficient estimates, extreme points and inclusion relations. Finally, we show that this class is invariant under Bernandi-Libera-Livingston integral for harmonic functions.

scholarly journals On the Generalization of a Class of Harmonic Univalent Functions Defined by Differential Operator

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 312
Author(s):  
Aqeel Ketab AL-khafaji ◽  
Waggas Galib Atshan ◽  
Salwa Salman Abed
Keyword(s):  
Differential Operator ◽  
Hadamard Product ◽  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Coefficient Estimates ◽  
Geometric Properties ◽  
New Class

In this article, a new class of harmonic univalent functions, defined by the differential operator, is introduced. Some geometric properties, like, coefficient estimates, extreme points, convex combination and convolution (Hadamard product) are obtained.

scholarly journals A Class of Harmonic Univalent Functions Defined by Differential Operator and the Generalization

2020 ◽  
pp. 1440-1445
Author(s):  
Faten Fakher Aubdulnabi ◽  
Kassim A. Jassim
Keyword(s):  
Differential Operator ◽  
Hadamard Product ◽  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Coefficient Estimates ◽  
Geometric Properties ◽  
New Class

In this paper, a new class of harmonic univalent functions was defined by the differential operator. We obtained some geometric properties, such as the coefficient estimates, convex combination, extreme points, and convolution (Hadamard product), which are required

scholarly journals New Family of Multivalent Analytic Functions Defined on Complex Hilbert Space

2020 ◽  
pp. 155-165 ◽  
Author(s):  
Abbas Kareem Wanas ◽  
S. R. Swamy
Keyword(s):  
Hilbert Space ◽  
Analytic Functions ◽  
Convex Set ◽  
Extreme Points ◽  
Complex Hilbert Space ◽  
Coefficient Estimates ◽  
Geometric Properties ◽  
New Class ◽  
New Family

In this article, we define a certain new class of multivalent analytic functions with negative coefficients on complex Hilbert space. We derive a number of important geometric properties, such as, coefficient estimates, radii of starlikeness and convexity, extreme points and convex set.

scholarly journals Some Geometric Properties Of Multivalent Convex Function For Operator On Hilbert Space

2018 ◽  
Vol 26 (8) ◽  
pp. 60-67
Author(s):  
Mohammed Hadi Lafta ◽  
Mazin Hashim Suhhiem
Keyword(s):  
Hilbert Space ◽  
Convex Function ◽  
Convex Functions ◽  
Convex Set ◽  
Extreme Points ◽  
Distortion Theorem ◽  
Weighted Mean ◽  
Geometric Properties ◽  
Closure Theorem ◽  
Coefficient Inequality

              By making use of the operator on Hilbert space, we introduce and study some properties of geometric of a subclass of multivalent convex functions with negative coefficients. Also, we obtain some geometric properties, such as coefficient inequality, growth and distortion theorem, extreme points, convex set, closure theorem, radius of close-to-convexity, weighted mean and inclusive properties.

scholarly journals On univalent functions defined by a generalized Sălăgean operator

2004 ◽  
Vol 2004 (27) ◽  
pp. 1429-1436 ◽  
Author(s):  
F. M. Al-Oboudi
Keyword(s):  
Differential Operator ◽  
Univalent Functions ◽  
Extreme Points ◽  
Sălăgean Operator ◽  
Salagean Operator ◽  
Inclusion Relations ◽  
Convolution Properties

We introduce a class of univalent functionsRn(λ,α)defined by a new differential operatorDnf(z),n∈ℕ0={0,1,2,…}, whereD0f(z)=f(z),D1f(z)=(1−λ)f(z)+λzf′(z)=Dλf(z),λ≥0, andDnf(z)=Dλ(Dn−1f(z)). Inclusion relations, extreme points ofRn(λ,α), some convolution properties of functions belonging toRn(λ,α), and other results are given.

scholarly journals Certain classes of analytic functions defined by fractional q-calculus operator

2018 ◽  
Vol 10 (1) ◽  
pp. 178-188 ◽  
Author(s):  
N. Ravikumar
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Extreme Points ◽  
Coefficient Estimates ◽  
Open Disc ◽  
Inclusion Relations

Abstract In this paper, the concept of fractional q-calculus and generalized Al-Oboudi differential operator defining certain classes of analytic functions in the open disc are used. The results investigated for these classes of functions include the coefficient estimates, inclusion relations, extreme points and some more properties.

scholarly journals Remarkable Classes of Almost 3-Contact Metric Manifolds

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 8
Author(s):  
Giulia Dileo
Keyword(s):  
Geometric Properties ◽  
New Class ◽  
Contact Metric Manifolds ◽  
Cosymplectic Manifolds ◽  
Sasaki Manifolds

We introduce a new class of almost 3-contact metric manifolds, called 3-(0,δ)-Sasaki manifolds. We show fundamental geometric properties of these manifolds, analyzing analogies and differences with the known classes of 3-(α,δ)-Sasaki (α≠0) and 3-δ-cosymplectic manifolds.

scholarly journals Partial sums and inclusion relations for analytic functions involving (p, q)-differential operator

2021 ◽  
Vol 19 (1) ◽  
pp. 329-337
Author(s):  
Huo Tang ◽  
Kaliappan Vijaya ◽  
Gangadharan Murugusundaramoorthy ◽  
Srikandan Sivasubramanian
Keyword(s):  
Analytic Function ◽  
Differential Operator ◽  
Lower Bounds ◽  
Analytic Functions ◽  
Function Class ◽  
Partial Sums ◽  
Generalized Function ◽  
Inclusion Relations ◽  
Alpha Beta

Abstract Let f k ( z ) = z + ∑ n = 2 k a n z n {f}_{k}\left(z)=z+{\sum }_{n=2}^{k}{a}_{n}{z}^{n} be the sequence of partial sums of the analytic function f ( z ) = z + ∑ n = 2 ∞ a n z n f\left(z)=z+{\sum }_{n=2}^{\infty }{a}_{n}{z}^{n} . In this paper, we determine sharp lower bounds for Re { f ( z ) / f k ( z ) } {\rm{Re}}\{f\left(z)\hspace{-0.08em}\text{/}\hspace{-0.08em}{f}_{k}\left(z)\} , Re { f k ( z ) / f ( z ) } {\rm{Re}}\{{f}_{k}\left(z)\hspace{-0.08em}\text{/}\hspace{-0.08em}f\left(z)\} , Re { f ′ ( z ) / f k ′ ( z ) } {\rm{Re}}\{{f}^{^{\prime} }\left(z)\hspace{-0.08em}\text{/}\hspace{-0.08em}{f}_{k}^{^{\prime} }\left(z)\} and Re { f k ′ ( z ) / f ′ ( z ) } {\rm{Re}}\{{f}_{k}^{^{\prime} }\left(z)\hspace{-0.08em}\text{/}\hspace{-0.08em}{f}^{^{\prime} }\left(z)\} , where f ( z ) f\left(z) belongs to the subclass J p , q m ( μ , α , β ) {{\mathcal{J}}}_{p,q}^{m}\left(\mu ,\alpha ,\beta ) of analytic functions, defined by Sălăgean ( p , q ) \left(p,q) -differential operator. In addition, the inclusion relations involving N δ ( e ) {N}_{\delta }\left(e) of this generalized function class are considered.

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.

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