scholarly journals Some Subclasses of Uniformly Univalent Functions with Respect to Symmetric Points

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 287 ◽  
Author(s):  
Shahid Mahmood ◽  
Hari Srivastava ◽  
Sarfraz Malik
Keyword(s):  
Growth Rate ◽  
Univalent Functions ◽  
Series Representation ◽  
Coefficient Estimate ◽  
Arc Length ◽  
Conic Domain ◽  
Special Cases ◽  
Symmetric Points ◽  
Inclusion Results ◽  
Taylor’S Series

This article presents the study of certain analytic functions defined by bounded radius rotations associated with conic domain. Many geometric properties like coefficient estimate, radii problems, arc length, integral representation, inclusion results and growth rate of coefficients of Taylor’s series representation are investigated. By varying the parameters in results, several well-known results in literature are obtained as special cases.

scholarly journals On Uniformly Bazilevic and Related Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Khalida Inayat Noor
Keyword(s):  
Open Unit ◽  
Arc Length ◽  
Open Unit Disc ◽  
New Class ◽  
Univalence Criterion ◽  
Distortion Bounds ◽  
Special Cases ◽  
Bazilevic Functions ◽  
Class Of Functions ◽  
Inclusion Results

We introduce a new class of functions analytic in the open unit disc, which contains the class of Bazilevic functions and also generalizes the concept of uniform convexity. We establish univalence criterion for the functions in this class and investigate rate of growth of coefficients, arc length problem, inclusion results, and distortion bounds. Some interesting results are derived as special cases.

scholarly journals Harmonic univalent functions defined by post quantum calculus operators

2019 ◽  
Vol 11 (1) ◽  
pp. 5-17 ◽  
Author(s):  
Om P. Ahuja ◽  
Asena Çetinkaya ◽  
V. Ravichandran
Keyword(s):  
Unit Disc ◽  
Univalent Functions ◽  
Extreme Points ◽  
Open Unit ◽  
Open Unit Disc ◽  
Quantum Calculus ◽  
Special Cases ◽  
The Family ◽  
Covering Theorems

Abstract We study a family of harmonic univalent functions in the open unit disc defined by using post quantum calculus operators. We first obtained a coefficient characterization of these functions. Using this, coefficients estimates, distortion and covering theorems were also obtained. The extreme points of the family and a radius result were also obtained. The results obtained include several known results as special cases.

scholarly journals Coefficient estimates for families of bi-univalent functions defined by Ruscheweyh derivative operator

2021 ◽  
Vol 25 (1) ◽  
pp. 71-80
Author(s):  
Serap Bulut ◽  
Wanas Kareem
Keyword(s):  
Univalent Functions ◽  
Upper Bounds ◽  
Coefficient Estimates ◽  
Derivative Operator ◽  
Ruscheweyh Derivative Operator ◽  
Ruscheweyh Derivative ◽  
Special Cases

The main purpose of this manuscript is to find upper bounds for the second and third Taylor-Maclaurin coefficients for two families of holomorphic and bi-univalent functions associated with Ruscheweyh derivative operator. Further, we point out certain special cases for our results.

scholarly journals Efficient algorithms for the reverse shortest path problem on trees under the hamming distance

2017 ◽  
Vol 27 (1) ◽  
pp. 46-60 ◽  
Author(s):  
Javad Tayyebi ◽  
Massoud Aman
Keyword(s):  
Shortest Path ◽  
Hamming Distance ◽  
Minimum Cost ◽  
Shortest Path Problem ◽  
Arc Length ◽  
Bound Constraints ◽  
Shortest Distance ◽  
Special Cases ◽  
Minimum Cost Flow Problem ◽  
Minimum Cut Problem

Given a network G(V,A,c) and a collection of origin-destination pairs with prescribed values, the reverse shortest path problem is to modify the arc length vector c as little as possible under some bound constraints such that the shortest distance between each origin-destination pair is upper bounded by the corresponding prescribed value. It is known that the reverse shortest path problem is NP-hard even on trees when the arc length modifications are measured by the weighted sum-type Hamming distance. In this paper, we consider two special cases of this problem which are polynomially solvable. The first is the case with uniform lengths. It is shown that this case transforms to a minimum cost flow problem on an auxiliary network. An efficient algorithm is also proposed for solving this case under the unit sum-type Hamming distance. The second case considered is the problem without bound constraints. It is shown that this case is reduced to a minimum cut problem on a tree-like network. Therefore, both cases studied can be solved in strongly polynomial time.

scholarly journals On $lambda$-Pseudo Bi-Starlike Functions with Respect to Symmetric Points Associated to Shell-Like Curves

2021 ◽  
Vol 45 (01) ◽  
pp. 103-114
Author(s):  
G. MURUGUSUNDARAMOORTHY ◽  
K. VIJAYA ◽  
H. ÖZLEM GÜNEY
Keyword(s):  
Fibonacci Numbers ◽  
Starlike Functions ◽  
Function Class ◽  
Special Cases ◽  
Symmetric Points

In this paper we define a new subclass λ−pseudo bi-starlike functions with respect to symmetric points of Σ related to shell-like curves connected with Fibonacci numbers and determine the initial Taylor-Maclaurin coefficients |a2| and |a3| for f ∈????????ℒs,Σλ(α,˜p (z)). Further we determine the Fekete-Szegö result for the function class ????????ℒs,Σλ(α,˜p (z)) and for special cases, corollaries are stated which some of them are new and have not been studied so far.

scholarly journals Some New Results Involving the Generalized Bose–Einstein and Fermi–Dirac Functions

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 63 ◽  
Author(s):  
Rekha Srivastava ◽  
Humera Naaz ◽  
Sabeena Kazi ◽  
Asifa Tassaddiq
Keyword(s):  
Fractional Derivatives ◽  
Series Representation ◽  
Zeta Functions ◽  
Weyl Transform ◽  
Special Cases ◽  
The Riemann Zeta Function ◽  
Riemann Zeta ◽  
Bose Einstein ◽  
Relationship Of ◽  
The Relationship

In this paper, we obtain a new series representation for the generalized Bose–Einstein and Fermi–Dirac functions by using fractional Weyl transform. To achieve this purpose, we obtain an analytic continuation for these functions by generalizing the domain of Riemann zeta functions from ( 0 < ℜ ( s ) < 1 ) to ( 0 < ℜ ( s ) < μ ) . This leads to fresh insights for a new generalization of the Riemann zeta function. The results are validated by obtaining the classical series representation of the polylogarithm and Hurwitz–Lerch zeta functions as special cases. Fractional derivatives and the relationship of the generalized Bose–Einstein and Fermi–Dirac functions with Apostol–Euler–Nörlund polynomials are established to prove new identities.

scholarly journals Coefficient Inequalities of Functions Associated with Petal Type Domains

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 298 ◽  
Author(s):  
Sarfraz Malik ◽  
Shahid Mahmood ◽  
Mohsan Raza ◽  
Sumbal Farman ◽  
Saira Zainab
Keyword(s):  
Taylor Series ◽  
Upper Bound ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Series Representation ◽  
Functional Inequalities ◽  
Major Interest ◽  
Coefficient Inequalities ◽  
Inverse Functions ◽  
Analytic And Univalent Functions

In the theory of analytic and univalent functions, coefficients of functions’ Taylor series representation and their related functional inequalities are of major interest and how they estimate functions’ growth in their specified domains. One of the important and useful functional inequalities is the Fekete-Szegö inequality. In this work, we aim to analyze the Fekete-Szegö functional and to find its upper bound for certain analytic functions which give parabolic and petal type regions as image domains. Coefficient inequalities and the Fekete-Szegö inequality of inverse functions to these certain analytic functions are also established in this work.

Notes on the stability problem for inhomogeneous equilibria

1983 ◽  
Vol 29 (2) ◽  
pp. 275-286 ◽  
Author(s):  
K. R. Symon
Keyword(s):  
Growth Rate ◽  
Normal Mode ◽  
Stability Problem ◽  
Normal Modes ◽  
Electromagnetic Mode ◽  
Spectral Matrix ◽  
First Order ◽  
Real Frequency ◽  
Special Cases ◽  
The Stability

Several conclusions regarding the stability of inhomogeneous Vlasov equilibria are drawn from earlier work. A technique is presented for generating first-order formulae for the change δω in the frequency of any normal mode, when a parameter λ characterizing the equilibrium is changed slightly. Several applications are given, including a first-order calculation of the growth rate or damping of an electromagnetic mode due to the presence of plasma. A condition is derived for the existence of a normal mode with real frequency. When there are ignorable co-ordinates, the normal modes can be written in the form of waves propagating in the ignorable directions. The character of the modes depends on certain symmetries in the dynamic spectral matrix. Special cases arise when the orbits can be approximated in certain ways.

Planar and Spatial Rigid Motion as Special Cases of Spherical and 3-Spherical Motion

1983 ◽  
Vol 105 (3) ◽  
pp. 569-575 ◽  
Author(s):  
J. M. McCarthy
Keyword(s):  
Rigid Motion ◽  
Arc Length ◽  
Spatial Motion ◽  
Special Cases ◽  
Curvature Theory ◽  
Rigid Motions ◽  
Spherical Motion ◽  
Smooth Transformation

This paper examines spherical and 3-spherical rigid motions with instantaneous invariants approaching zero. It is shown that these motions may be identified with planar and spatial motion, respectively. The instantaneous invariants are ratios of arc-length along the surface of the sphere to its radius, thus the process of shrinking their value may be viewed as expanding the sphere while bounding the instantaneous displacements on the sphere. This allows a smooth transformation of the results of the curvature theory of spherical and 3-spherical motion into their planar and spatial counterparts.

scholarly journals Initial Coefficients of Biunivalent Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
See Keong Lee ◽  
V. Ravichandran ◽  
Shamani Supramaniam
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Special Cases

An analytic functionfdefined on the open unit disk is biunivalent if the functionfand its inversef-1are univalent in𝔻. Estimates for the initial coefficients of biunivalent functionsfare investigated whenfandf-1, respectively, belong to some subclasses of univalent functions. Some earlier results are shown to be special cases of our results.

Sign in / Sign up

Export Citation Format

Share Document