scholarly journals Multivalent Prestarlike Functions with Respect to Symmetric Points

Symmetry ◽  
2021 ◽  
Vol 14 (1) ◽  
pp. 20
Author(s):  
Daniel Breaz ◽  
Kadhavoor R. Karthikeyan ◽  
Alagiriswamy Senguttuvan
Keyword(s):  
Integral Representation ◽  
Function Class ◽  
Coefficient Estimates ◽  
Quantum Calculus ◽  
Complex Order ◽  
Inclusion Relations ◽  
Symmetric Points

A class of p-valent functions of complex order is defined with the primary motive of unifying the concept of prestarlike functions with various other classes of multivalent functions. Interesting properties such as inclusion relations, integral representation, coefficient estimates and the solution to the Fekete–Szegő problem are obtained for the defined function class. Further, we extended the results using quantum calculus. Several consequences of our main results are pointed out.

scholarly journals Some properties for \(\alpha\)-starlike functions with respect to \(k\)-symmetric points of complex order

2017 ◽  
Vol 71 (1) ◽  
pp. 1 ◽  
Author(s):  
H. E. Darwish ◽  
A. Y. Lashin ◽  
S. M. Sowileh
Keyword(s):  
Integral Representation ◽  
Unit Disc ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disc ◽  
Complex Order ◽  
Inclusion Relations ◽  
Symmetric Points

In the present work, we introduce the subclass \(\mathcal{T}_{\gamma ,\alpha<br />}^{k}(\varphi )\), of starlike functions with respect to \(k\)-symmetric points of complex order \(\gamma\) (\(\gamma \neq 0\)) in the open unit disc \(\vartriangle\). Some interesting subordination criteria, inclusion relations and the integral representation for functions belonging to this class are provided. The results obtained generalize some known results, and some other new results are obtained.

scholarly journals Certain Class of Analytic Functions with respect to Symmetric Points Defined by Q-Calculus

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
K. R. Karthikeyan ◽  
G. Murugusundaramoorthy ◽  
S. D. Purohit ◽  
D. L. Suthar
Keyword(s):  
Integral Representation ◽  
Representation Theorem ◽  
Analytic Functions ◽  
Type Star ◽  
Coefficient Bounds ◽  
Quantum Calculus ◽  
Complex Order ◽  
Special Cases ◽  
Symmetric Points

In this study, we familiarise a novel class of Janowski-type star-like functions of complex order with regard to j , k -symmetric points based on quantum calculus by subordinating with pedal-shaped regions. We found integral representation theorem and conditions for starlikeness. Furthermore, with regard to j , k -symmetric points, we successfully obtained the coefficient bounds for functions in the newly specified class. We also quantified few applications as special cases which are new (or known).

scholarly journals Harmonic Starlike Functions with Respect to Symmetric Points

Axioms ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 3 ◽  
Author(s):  
Nak Eun Cho ◽  
Jacek Dziok
Keyword(s):  
Integral Representation ◽  
Starlike Functions ◽  
Coefficient Estimates ◽  
Distortion Theorems ◽  
Harmonic Starlike ◽  
Symmetric Points

In the paper we define classes of harmonic starlike functions with respect to symmetric points and obtain some analytic conditions for these classes of functions. Some results connected to subordination properties, coefficient estimates, integral representation, and distortion theorems are also obtained.

scholarly journals Certain subclass of analytic functions with respect to symmetric points associated with conic region

2021 ◽  
Vol 6 (11) ◽  
pp. 12863-12877
Author(s):  
Huo Tang ◽  
◽  
Kadhavoor Ragavan Karthikeyan ◽  
Gangadharan Murugusundaramoorthy ◽  
◽  
...  
Keyword(s):  
Analytic Functions ◽  
Function Class ◽  
Quantum Calculus ◽  
Function Classes ◽  
Janowski Functions ◽  
Symmetric Points ◽  
Inverse Functions ◽  
Ordinary Derivative

<abstract><p>The purpose of this paper is to introduce and study a new subclass of analytic functions with respect to symmetric points associated to a conic region impacted by Janowski functions. Also, the study has been extended to quantum calculus by replacing the ordinary derivative with a $ q $-derivative in the defined function class. Interesting results such as initial coefficients of inverse functions and Fekete-Szegö inequalities are obtained for the defined function classes. Several applications, known or new of the main results are also presented.</p></abstract>

scholarly journals Starlike functions of complex order involving q-hypergeometric functions with fixed point

2014 ◽  
Vol 13 (1) ◽  
pp. 51-63
Author(s):  
Kaliappan Vijaya ◽  
Gangadharan Murugusundaramoorthy ◽  
Murugesan Kasthuri
Keyword(s):  
Fixed Point ◽  
Hypergeometric Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Function Class ◽  
Coefficient Estimates ◽  
Integral Means ◽  
Open Disc ◽  
Starlike And Convex Functions ◽  
Complex Order

AbstractRecently Kanas and Ronning introduced the classes of starlike and convex functions, which are normalized with ƒ(ξ) = ƒ0(ξ) − 1 = 0, ξ (|ξ| = d) is a fixed point in the open disc U = {z ∈ ℂ: |z| < 1}. In this paper we define a new subclass of starlike functions of complex order based on q-hypergeometric functions and continue to obtain coefficient estimates, extreme points, inclusion properties and neighbourhood results for the function class T Sξ(α, β,γ). Further, we obtain integral means inequalities for the function ƒ ∈ T Sξ(α, β,γ).

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 Coefficient Estimates and the Fekete–Szegö Problem for New Classes of m-Fold Symmetric Bi-Univalent Functions

Mathematics ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 129
Author(s):  
Georgia Irina Oros ◽  
Luminiţa-Ioana Cotîrlă
Keyword(s):  
Univalent Functions ◽  
Coefficient Estimates ◽  
Quantum Calculus

The results presented in this paper deal with the classical but still prevalent problem of introducing new classes of m-fold symmetric bi-univalent functions and studying properties related to coefficient estimates. Quantum calculus aspects are also considered in this study in order to enhance its novelty and to obtain more interesting results. We present three new classes of bi-univalent functions, generalizing certain previously studied classes. The relation between the known results and the new ones presented here is highlighted. Estimates on the Taylor–Maclaurin coefficients |am+1| and |a2m+1| are obtained and, furthermore, the much investigated aspect of Fekete–Szegő functional is also considered for each of the new classes.

scholarly journals Coefficient estimates for certain subclasses of spiral-like functions of complex order

2010 ◽  
Vol 23 (7) ◽  
pp. 763-768 ◽  
Author(s):  
H.M. Srivastava ◽  
Qing-Hua Xu ◽  
Guang-Ping Wu
Keyword(s):  
Coefficient Estimates ◽  
Complex Order

Coefficient Estimates for Certain Subclasses of m-Fold Symmetric Bi-univalent Functions Associated with Pseudo-Starlike Functions

2021 ◽  
pp. 209-223
Author(s):  
Timilehin G. Shaba ◽  
Amol B. Patil
Keyword(s):  
Unit Disk ◽  
Univalent Function ◽  
Univalent Functions ◽  
Starlike Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates

In the present investigation, we introduce the subclasses $\varLambda_{\Sigma}^{m}(\eta,\leftthreetimes,\phi)$ and $\varLambda_{\Sigma}^{m}(\eta,\leftthreetimes,\delta)$ of \textit{m}-fold symmetric bi-univalent function class $\Sigma_m$, which are associated with the pseudo-starlike functions and defined in the open unit disk $\mathbb{U}$. Moreover, we obtain estimates on the initial coefficients $|b_{m+1}|$ and $|b_{2m+1}|$ for the functions belong to these subclasses and identified correlations with some of the earlier known classes.

scholarly journals Research on Geometric Mappings in Complex Systems Analysis

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Yanyan Cui ◽  
Chaojun Wang ◽  
Sifeng Zhu
Keyword(s):  
Banach Spaces ◽  
Systems Analysis ◽  
Starlike Functions ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Coefficient Estimates ◽  
Positive Real ◽  
Reinhardt Domains ◽  
Complex Order ◽  
Starlike Mappings

We mainly discuss the properties of a new subclass of starlike functions, namely, almost starlike functions of complex order λ, in one and several complex variables. We get the growth and distortion results for almost starlike functions of complex order λ. By the properties of functions with positive real parts and considering the zero of order k, we obtain the coefficient estimates for almost starlike functions of complex order λ on D. We also discuss the invariance of almost starlike mappings of complex order λ on Reinhardt domains and on the unit ball B in complex Banach spaces. The conclusions contain and generalize some known results.

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