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52. Analytic capacity

Author

Tolsa, Xavier, Bass, Hyman, Series editor, Lu, Jiang-Hua, Series editor, Oesterlé, Joseph, Series editor, Tschinkel, Yuri, Series editor, and Tolsa, Xavier

Published
2014
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53. Shape Evolution and Integrability

Author

Gustafsson, Björn, Teodorescu, Razvan, Vasil’ev, Alexander, Galdi, Giovanni P., Series editor, Heywood, John G., Series editor, Rannacher, Rolf, Series editor, Gustafsson, Björn, Teodorescu, Razvan, and Vasil’ev, Alexander

Published
2014
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54. Stochastic Löwner and Löwner–Kufarev Evolution

Author

Gustafsson, Björn, Teodorescu, Razvan, Vasil’ev, Alexander, Galdi, Giovanni P., Series editor, Heywood, John G., Series editor, Rannacher, Rolf, Series editor, Gustafsson, Björn, Teodorescu, Razvan, and Vasil’ev, Alexander

Published
2014
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55. Final Comments

Author

Hencl, Stanislav, Koskela, Pekka, Morel, Jean-Michel, Editor-in-chief, Teissier, Bernard, Editor-in-chief, De Lellis, Camillo, Series editor, di Bernardo, Mario, Series editor, Figalli, Alessio, Series editor, Khoshnevisan, Davar, Series editor, Kontoyiannis, Ioannis, Series editor, Lugosi, Gabor, Series editor, Podolskij, Mark, Series editor, Stroppel, Catharina, Series editor, Wienhard, Anna, Series editor, Hencl, Stanislav, and Koskela, Pekka

Published
2014
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56. A Class of Quantum Briot–Bouquet Differential Equations with Complex Coefficients

Author

Rabha W. Ibrahim, Rafida M. Elobaid, and Suzan J. Obaiys

Subjects
differential operator, unit disk, univalent function, analytic function, subordination, q-calculus, Mathematics, QA1-939
Abstract

Quantum inequalities (QI) are local restraints on the magnitude and range of formulas. Quantum inequalities have been established to have a different range of applications. In this paper, we aim to introduce a study of QI in a complex domain. The idea basically, comes from employing the notion of subordination. We shall formulate a new q-differential operator (generalized of Dunkl operator of the first type) and employ it to define the classes of QI. Moreover, we employ the q-Dunkl operator to extend the class of Briot–Bouquet differential equations. We investigate the upper solution and exam the oscillation solution under some analytic functions.

Published
2020
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57. Generalized Briot-Bouquet Differential Equation Based on New Differential Operator with Complex Connections

Author

Rabha W. Ibrahim, Rafida M. Elobaid, and Suzan J. Obaiys

Subjects
differential operator, univalent function, analytic function, subordination, unit disk, Mathematics, QA1-939
Abstract

A class of Briot–Bouquet differential equations is a magnificent part of investigating the geometric behaviors of analytic functions, using the subordination and superordination concepts. In this work, we aim to formulate a new differential operator with complex connections (coefficients) in the open unit disk and generalize a class of Briot–Bouquet differential equations (BBDEs). We study and generalize new classes of analytic functions based on the new differential operator. Consequently, we define a linear operator with applications.

Published
2020
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60. On the Computational Complexity of Erdős-Szekeres and Related Problems in ℝ3

Author

Giannopoulos, Panos, Knauer, Christian, Werner, Daniel, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Bodlaender, Hans L., editor, and Italiano, Giuseppe F., editor

Published
2013
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61. The Visible Perimeter of an Arrangement of Disks

Author

Nivasch, Gabriel, Pach, János, Tardos, Gábor, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Didimo, Walter, editor, and Patrignani, Maurizio, editor

Published
2013
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62. Partition

Author

Du, Ding-Zhu, Ko, Ker-I, Hu, Xiaodong, Du, Ding-Zhu, Ko, Ker-I, and Hu, Xiaodong

Published
2012
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63. String-Wrapped Rotating Disks

Author

O’Rourke, Joseph, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Márquez, Alberto, editor, Ramos, Pedro, editor, and Urrutia, Jorge, editor

Published
2012
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64. A Polynomial-Time Approximation Scheme for the Geometric Unique Coverage Problem on Unit Squares

Author

Ito, Takehiro, Nakano, Shin-Ichi, Okamoto, Yoshio, Otachi, Yota, Uehara, Ryuhei, Uno, Takeaki, Uno, Yushi, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Fomin, Fedor V., editor, and Kaski, Petteri, editor

Published
2012
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65. In-Place Algorithms for Computing a Largest Clique in Geometric Intersection Graphs

Author

De, Minati, Nandy, Subhas C., Roy, Sasanka, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Snoeyink, Jack, editor, Lu, Pinyan, editor, Su, Kaile, editor, and Wang, Lusheng, editor

Published
2012
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73. On Isolating Points Using Disks

Author

Gibson, Matt, Kanade, Gaurav, Varadarajan, Kasturi, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Demetrescu, Camil, editor, and Halldórsson, Magnús M., editor

Published
2011
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78. Geometric properties of the complex Baskakov-Stancu operators in the unit disk

Author

Rabha Ibrahim

Subjects
analytic function, bounded turning, univalent, partial sums, unit disk, Mathematics, QA1-939
Abstract

In this article, we determine certain conditions under which the partial sums involving thecomplex Baskakov-Stancu operators of analytic univalent functions of bounded turning are also of boundedturning. Moreover, we consider some geometric properties such as starlikeness and convexity for these partialsums. The lower bound of the partial sums of univalent functions is computed using the lower bound of thecomplex Baskakov-Stancu operators of analytic functions

Published
2015
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80. On Interpolation in the Unit Disk Based on Both Radon Projections and Function Values

Author

Georgieva, Irina, Uluchev, Rumen, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Lirkov, Ivan, editor, Margenov, Svetozar, editor, and Waśniewski, Jerzy, editor

Published
2010
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82. Near-minimal cubature formulae on the disk.

Author

Benouahmane, Brahim, Annie, Cuyt, and Yaman, Irem

Subjects
*CUBATURE formulas, *ORTHOGONAL polynomials, *ORTHOGONAL functions, *NUMERICAL integration, *NUMERICAL analysis
Abstract

The construction of (near-)minimal cubature formulae on the disk is still a complicated subject on which many results have been published. We restrict ourselves to the case of radial weight functions and make use of a recent connection between cubature and the concept of multivariate spherical orthogonal polynomials to derive a new system of equations defining the nodes and weights of (near-)minimal rules for general degree |$m=2n-1, n \ge 2$|⁠. The approach encompasses all previous derivations. The new system is small and may consist of only |$(n+1)^2/4$| equations when |$n$| is odd and |$n(n+2)/4$| equations when |$n$| is even. It is valid for general |$n$| and has a Prony-like structure. It may admit a unique solution (such as for |$n=3$|⁠) or an infinity of solutions (such as for |$n=7$|⁠). In Section 2, the new approach is described, whereas the new system is derived in Sections 3 and 4. All well-known (near-)minimal cubature rules can be reobtained. Some typical illustrations of how this works are given in Section 5. We expect that this unifying theory will shed new light on the topic of cubature, in particular with respect to the discovery of new bounds on the number of nodes and their connection with the zeros of multivariate orthogonal polynomials. [ABSTRACT FROM AUTHOR]

Published
2019
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83. On the computation of sets of points with low Lebesgue constant on the unit disk.

Author

Meurant, Gérard and Sommariva, Alvise

Subjects
*INTERPOLATION, *LEBESGUE integral, *LEBESGUE measure, *GEGENBAUER polynomials, *MATHEMATICAL analysis
Abstract

Abstract In this paper of numerical nature, we test the Lebesgue constant of several available point sets on the disk Ω and propose new ones that enjoy low Lebesgue constant. Furthermore we extend some results in Cuyt (2012), analyzing the case of Bos arrays whose radii are nonnegative Gauss–Gegenbauer–Lobatto nodes with exponent α , noticing that the optimal α still allows to achieve point sets on Ω with low Lebesgue constant Λ n for degrees n ≤ 30. Next we introduce an algorithm that through optimization determines point sets with the best known Lebesgue constants for n ≤ 25. Finally, we determine theoretically a point set with the best Lebesgue constant for the case n = 1. [ABSTRACT FROM AUTHOR]

Published
2019
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84. THE UNIVALENCE CONDITIONS FOR A GENERAL INTEGRAL OPERATOR.

Author

BĂRBATU, C. and BREAZ, D.

Subjects
INTEGRAL operators, MATHEMATICS, MATHEMATICAL functions, INTEGRALS, ANALYTIC functions
Abstract

In this paper, we obtain univalence conditions for a new general integral operator defined on the space of normalized analytic function in the open unit disk U. Some corollaries follow as special cases. [ABSTRACT FROM AUTHOR]

Published
2019
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85. GEOMETRIC VIRTUES OF THIRD-ORDER DIFFERENTIAL EQUATION USING ADMISSIBLE FUNCTIONS IN A COMPLEX DOMAIN.

Author

IBRAHIM, RABHA W.

Subjects
GEOMETRIC analysis, DIFFERENTIAL equations, MATHEMATICAL complexes, INTEGRAL domains, BANACH spaces
Abstract

We investigate geometric properties of solutions of the following third-order differential equation: w'''(z) + a(z)w''(z) + b(z)w'(z) + c(z)w(z) = 0, subject to the initial conditions w(0) = 0, w'(0) = 1 and w''(0) = 0, where a(z), b(z) and c(z) are analytic in the open unit disk (OUD). We indicate that the above differential equation has a univalent and starlike solution in the open unit disk. We employ the concept of admissible functions and we extend the study into some complex Banach spaces. [ABSTRACT FROM AUTHOR]

Published
2018

86. Practical Discrete Unit Disk Cover Using an Exact Line-Separable Algorithm

Author

Claude, Francisco, Dorrigiv, Reza, Durocher, Stephane, Fraser, Robert, López-Ortiz, Alejandro, Salinger, Alejandro, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Dong, Yingfei, editor, Du, Ding-Zhu, editor, and Ibarra, Oscar, editor

Published
2009
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87. Applications of Borel Distribution for a New Family of Bi-Univalent Functions Defined by Horadam Polynomials

Author

J. Nirmala, S. R. Swamy, Alina Alb Lupaş, and Abbas Kareem Wanas

Subjects
Pure mathematics, General Mathematics, Family functioning, Borel distribution, Unit disk, Mathematics
Abstract

In this paper, by making use of Borel distribution we introduce a new family GΣ(δ, γ, λ, τ, r) of normalized analytic and bi-univalent functions in the open unit disk U, which are associated with Horadam polynomials. We establish upper bounds for the initial Taylor-Maclaurin coefficients |a2| and |a3| of functions belonging to the analytic and bi-univalent function family which we have introduced here. Furthermore, we establish the Fekete-Szego problem of functions in this new family.

Published
2021
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88. On Sendov’s Conjecture

Author

W. M. Shah and G. M. Sofi

Subjects
Combinatorics, Polynomial, Conjecture, Mathematics::Complex Variables, General Mathematics, Sendov's conjecture, Line (geometry), Astrophysics::Earth and Planetary Astrophysics, Algebra over a field, Unit disk, Astrophysics::Galaxy Astrophysics, Critical point (mathematics), Mathematics
Abstract

Sendov’s Conjecture asserts that if all the zeros of a polynomial p lie inside the closed unit disk then a closed unit disk centered at each of its zeros contains a critical point of p . In this paper, we show that the Sendov’s Conjecture holds for a polynomial if all its zeros lie on a line or a circle inside the unit disk.

Published
2021
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89. A new analytic solution of complex Langevin differential equations

Author

Rabha W. Ibrahim

Subjects
Geometric function theory, Complex differential equation, Differential equation, Special functions, General Mathematics, Applied mathematics, Unit disk, Upper and lower bounds, Mathematics, Analytic function, Univalent function
Abstract

PurposeIn this study, the authors introduce a solvability of special type of Langevin differential equations (LDEs) in virtue of geometric function theory. The analytic solutions of the LDEs are considered by utilizing the Caratheodory functions joining the subordination concept. A class of Caratheodory functions involving special functions gives the upper bound solution.Design/methodology/approachThe methodology is based on the geometric function theory.FindingsThe authors present a new analytic function for a class of complex LDEs.Originality/valueThe authors introduced a new class of complex differential equation, presented a new technique to indicate the analytic solution and used some special functions.

Published
2021
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90. Concentration solutions to the singularly prescribed Gaussian and geodesic curvatures problem

Author

Chunyi Zhao and Liping Wang

Subjects
Geodesic, Applied Mathematics, Gaussian, Mathematical analysis, Boundary (topology), Unit disk, Exponential function, symbols.namesake, Neumann boundary condition, symbols, Gaussian curvature, Analysis, Geodesic curvature, Mathematics
Abstract

We consider the following Liouville-type equation with exponential Neumann boundary condition: { − Δ u ˜ = e 2 K ( x ) e 2 u ˜ , x ∈ D , ∂ u ˜ ∂ n + 1 = e κ ( x ) e u ˜ , x ∈ ∂ D , where D ⊂ R 2 is the unit disk, e 2 K ( x ) > 0 and e κ ( x ) > 0 stand for the prescribed Gaussian curvature and geodesic curvature of the boundary, respectively. We prove the existence of concentration solutions if κ ( x ) + K ( x ) + κ ( x ) 2 ( x ∈ ∂ D ) has a local extremum point, which is a new result for exponential Neumann boundary problems.

Published
2021
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91. Applications of a certain q-integral operator to the subclasses of analytic and bi-univalent functions

Author

Qazi Zahoor Ahmad, Bilal Khan, Nazar Khan, Hari M. Srivastava, Maslina Darus, and Muhammad Tahir

Subjects
q-derivative (or q-difference) operator, Pure mathematics, General Mathematics, Operator (physics), lcsh:Mathematics, Inverse, Function (mathematics), lcsh:QA1-939, Unit disk, taylor-maclaurin initial coefficients, bi-univalent functions, analytic functions, univalent functions, q-integral operator, Analytic function, Mathematics, taylor-maclaurin series expansions
Abstract

In the present investigation, our aim is to define a generalized subclass of analytic and bi-univalent functions associated with a certain $q$-integral operator in the open unit disk $\mathbb{U}$. We estimate bounds on the initial Taylor-Maclaurin coefficients $\left \vert a_{2}\right \vert$ and $\left \vert a_{3}\right \vert $ for normalized analytic functions $f$ in the open unit disk by considering the function $f$ and its inverse $g = f^{{-}{1}}$. Furthermore, we derive special consequences of the results presented here, which would apply to several (known or new) subclasses of analytic and bi-univalent functions.

Published
2021
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92. Geometric behavior of a class of algebraic differential equations in a complex domain using a majorization concept

Author

Dumitru Baleanu and Rabha W. Ibrahim

Subjects
Physics, Pure mathematics, Mathematics::Functional Analysis, General Mathematics, lcsh:Mathematics, Physics::Medical Physics, univalent function, lcsh:QA1-939, Unit disk, analytic function, subordination and superordination, Connection (algebraic framework), Algebraic number, Convex function, Majorization, Bernoulli number, majorization method, open unit disk, algebraic differential equations, Univalent function, Analytic function
Abstract

In this paper, a type of complex algebraic differential equations (CADEs) is considered formulating by $ \alpha [\varphi(z) \varphi" (z) +(\varphi' (z))^2]+ a_m \varphi^m(z)+a_{m-1} \varphi^{m-1}(z)+...+ a_1 \varphi(z)+ a_0 = 0. $ The conformal analysis (angle-preserving) of the CADEs is investigated. We present sufficient conditions to obtain analytic solutions of the CADEs. We show that these solutions are subordinated to analytic convex functions in terms of $e^z.$ Moreover, we investigate the connection estimates (coefficient bounds) of CADEs by employing the majorization method. We achieve that the coefficients bound are optimized by Bernoulli numbers.

Published
2021
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93. Coefficient Estimate of Toeplitz Determinant for a Certain Class of Close to Convex Functions

Author

Shaharuddin Cik Soh, Daud Mohamad, and Huzaifah Dzubaidi

Subjects
Class (set theory), Pure mathematics, Geometric function theory, Differential equation, General Mathematics, General Physics and Astronomy, General Chemistry, Taylor coefficients, Unit disk, General Biochemistry, Genetics and Molecular Biology, Toeplitz matrix, General Agricultural and Biological Sciences, Representation (mathematics), Convex function, Mathematics
Abstract

Let S denote the class of analytic and univalent functions in D, where D is defined as unit disk and having the Taylor representation form of S. We will determine the estimation for the Toeplitz determinants where the elements are the Taylor coefficients of the class close-to-convex functions in S.

Published
2021
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94. A Study of New Class of Star-Like Functions Associated by Symmetric <math xmlns='http://www.w3.org/1998/Math/MathML' id='M1'> <mfenced open='(' close=')' separators='|'> <mrow> <mi>p</mi> <mo>,</mo> <mi>q</mi> </mrow> </mfenced> </math>-Calculus

Author

Adnan, Khalid Akbar, Rashid Murtaza, Ilyas Khan, Md. Fayz-Al-Asad, and Umar Khan

Subjects
New class, General Mathematics, medicine, Calculus, Derivative, Star (graph theory), Quantum calculus, medicine.disease, Unit disk, Calculus (medicine), Analytic function, Mathematics
Abstract

As of late quantum calculus is broadly utilized in different parts of mathematics. Uniquely, the hypothesis of univalent functions can be newly portrayed by utilizing q -calculus. In this paper, we utilize our recently presented symmetric p , q -number m ˜ p , q to characterize new symmetric p , q -derivative D p , q of analytic function f in the open unit disk U . Utilizing D p , q , we introduce new class of analytic star-like functions and examine some fascinating results.

Published
2021
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95. The Bohr-type operator on analytic functions and sections

Author

Ming-Sheng Liu, Saminathan Ponnusamy, and Yong Huang

Subjects
Numerical Analysis, Pure mathematics, Mathematics - Complex Variables, Applied Mathematics, Operator (physics), Type (model theory), Unit disk, Bohr model, Computational Mathematics, symbols.namesake, Bounded function, FOS: Mathematics, symbols, Primary: 30A10, Complex Variables (math.CV), Analysis, Mathematics, Analytic function
Abstract

In this paper, firstly we prove two refined Bohr-type inequalities associated with area for bounded analytic functions $f(z)=\sum_{n=0}^{\infty}a_{n}z^{n}$ in the unit disk. Later, we establish the Bohr-type operator on analytic functions and sections., Comment: 14 pages

Published
2021
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96. Escobar constants of planar domains

Author

Asma Hassannezhad and Anna Siffert

Subjects
Mathematics - Differential Geometry, Discrete mathematics, math.OC, Computer Science::Computational Geometry, Unit disk, math.DG, Mathematics - Analysis of PDEs, Planar, Differential Geometry (math.DG), Differential geometry, Optimization and Control (math.OC), Bounded function, FOS: Mathematics, Geometry and Topology, Mathematics - Optimization and Control, math.AP, Computer Science::Formal Languages and Automata Theory, Analysis, Analysis of PDEs (math.AP), Mathematics
Abstract

We initiate the study of the higher-order Escobar constants $I_k(M)$, $k\geq 3$, on bounded planar domains $M$. The Escobar constants $I_k$ of the unit disk and a family of polygons are provided., Comment: 18 pages

Published
2021
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97. Area Estimates of Images of Disks under Analytic Functions

Author

Swadesh Kumar Sahoo and Vibhuti Arora

Subjects
Combinatorics, Dirichlet integral, symbols.namesake, Applied Mathematics, General Mathematics, Image (category theory), symbols, Unit disk, Mathematics, Analytic function
Abstract

Let $${\mathbb{D}_r}: = \{ z = x + {\rm{i}}y \in \mathbb{C}:\left| z \right| < r\} ,\,r \le 1$$ . For a normalized analytic function f in the unit disk $$\mathbb{D}: = {\mathbb{D}_1}$$ , estimating the Dirichlet integral $$\Delta (r,f) = \int {\,\int_{{\mathbb{D}_r}} {{{\left| {f\prime (z)} \right|}^2}dxdy} } $$ , z = x +iy, is an important classical problem in complex analysis. Geometrically, Δ(r, f) represents the area of the image of $${\mathbb{D}_r}$$ under f counting multiplicities. In this paper, our main objective is to estimate areas of images of $${\mathbb{D}_r}$$ under non-vanishing analytic functions of the form (z/f)μ, μ > 0, in principal powers, when f ranges over certain classes of analytic and univalent functions in $$\mathbb{D}$$ .

Published
2021
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98. On a geometric study of a class of normalized functions defined by Bernoulli’s formula

Author

Ibtisam Aldawish, Dumitru Baleanu, and Rabha W. Ibrahim

Subjects
Subordination and superordination, Class (set theory), Pure mathematics, Special function, Algebra and Number Theory, Partial differential equation, Functional analysis, Applied Mathematics, Univalent function, Unit disk, Bernoulli's principle, Analytic function, Ordinary differential equation, Open unit disk, Difference-differential operator, QA1-939, Hypergeometric function, Analysis, Mathematics
Abstract

The central purpose of this effort is to investigate analytic and geometric properties of a class of normalized analytic functions in the open unit disk involving Bernoulli’s formula. As a consequence, some solutions are indicated by the well-known hypergeometric function. The class of starlike functions is investigated containing the suggested class.

Published
2021

99. Commuting Toeplitz Operators and Hyperbolic Geometry

Author

Gohberg, I., editor, Alpay, D., editor, Arazy, J., editor, Atzmon, A., editor, Ball, J. A., editor, Bart, H., editor, Ben-Artzi, A., editor, Bercovici, H., editor, Böttcher, A., editor, Clancey, K., editor, Curto, R., editor, Davidson, K. R., editor, Demuth, M., editor, Dijksma, A., editor, Douglas, R. G., editor, Duduchava, R., editor, Ferreira dos Santos, A., editor, Frazho, A. E., editor, Fuhrmann, P. A., editor, Gramsch, B., editor, Kaper, H. G., editor, Kuroda, S. T., editor, Lerer, L. E., editor, Mityagin, B., editor, Olshevski, V., editor, Putinar, M., editor, Ran, A. C. M., editor, Rodman, L., editor, Rovnyak, J., editor, Schulze, B. -W., editor, Speck, F., editor, Spitkovsky, I. M., editor, Treil, S., editor, Tretter, C., editor, Upmeier, H., editor, Vasilevski, N., editor, Verduyn Lunel, S., editor, Voiculescu, D., editor, Xia, D., editor, Yafaev, D., editor, and Vasilevski, Nikolai L.

Published
2008
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100. Toeplitz Operators on the Unit Disk with Radial Symbols

Author

Gohberg, I., editor, Alpay, D., editor, Arazy, J., editor, Atzmon, A., editor, Ball, J. A., editor, Bart, H., editor, Ben-Artzi, A., editor, Bercovici, H., editor, Böttcher, A., editor, Clancey, K., editor, Curto, R., editor, Davidson, K. R., editor, Demuth, M., editor, Dijksma, A., editor, Douglas, R. G., editor, Duduchava, R., editor, Ferreira dos Santos, A., editor, Frazho, A. E., editor, Fuhrmann, P. A., editor, Gramsch, B., editor, Kaper, H. G., editor, Kuroda, S. T., editor, Lerer, L. E., editor, Mityagin, B., editor, Olshevski, V., editor, Putinar, M., editor, Ran, A. C. M., editor, Rodman, L., editor, Rovnyak, J., editor, Schulze, B. -W., editor, Speck, F., editor, Spitkovsky, I. M., editor, Treil, S., editor, Tretter, C., editor, Upmeier, H., editor, Vasilevski, N., editor, Verduyn Lunel, S., editor, Voiculescu, D., editor, Xia, D., editor, Yafaev, D., editor, and Vasilevski, Nikolai L.

Published
2008
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