Coefficient bounds for new subclasses of bi-univalent functions

By Murat cCauglar, Halit Orhan, Nihat Yaugmur. 2012

122 citations recorded by the source corpus.

In the present investigation, we consider two new subclasses N_{\Sigma}^{\mu}({\alpha},{\lambda}) and N_{\Sigma}^{\mu}({\beta},{\lambda}) of bi-univalent functions defined in the open unit disk U={z:|z|<1}. Besides, we find upper bounds for the second and third coefficients for functions in these new subclasses.

Subfields: Electronic, Optical and Magnetic Materials, Geometry and Topology, Polymers and Plastics

View Paper: https://www.semanticscholar.org/paper/0f62e1ba1ab6651f5e32d8b468c7e158cbb6fb7e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Electronic, Optical and Magnetic Materials

1. Hari M. Srivastava
2. Nanjundan Magesh
3. Serap Bulut
4. Rosihan M. Ali

In Geometry and Topology

1. Hari M. Srivastava
2. Nanjundan Magesh
3. Halit Orhan
4. Serap Bulut
5. Erhan Deniz
6. Deepak Bansal
7. Murat Çaglar
8. Rosihan M. Ali

In Polymers and Plastics

1. Hari M. Srivastava
2. Nanjundan Magesh
3. Deepak Bansal
4. Serap Bulut
5. Halit Orhan
6. V. K. Balaji
7. Erhan Deniz

Citations in the corpus

• Coefficient Bounds for a Certain Class of Analytic and Bi-Univalent Functions (2015, background): “In fact, judging by the remarkable flood of papers on the subject (see, for example, [5–7, 9–12, 15–17, 19–21, 23, 26, 27, 29, 30]), the recent pioneering work of Srivastava et al.”
• Second Hankel determinant for certain subclasses ofbi-univalent functions (2017, background): “In particular, several results on coefficient estimates for the initial coefficients |a2| , |a3| , and |a4| were proved for various subclasses of σ (see, for example, [1, 4, 5, 10, 12, 14, 16, 25, 28, 29, 32, 33]).”
• Initial coefficient bounds for a general class of bi-univalent functions (2013, background): “[22], there has been triggering interest to study the coefficient problems for the different subclasses of bi-univalent functions (see, for example, [1, 3, 6, 7, 27, 29],).”
• Coefficient estimates for a subclass of analytic and bi-univalent functions (2015, result): “In fact, judging by the remarkable flood of papers on non-sharp estimates on the first two coefficients ja2j and ja3j of various subclasses of the bi-univalent function class R (see, for example, [19–30,35,31–34,15,36–38]), the above-cited recent pioneering work of Srivastava et al.”
• Coefficient estimates for a general subclass of analytic and bi-univalent functions of the Ma–Minda type (2017, unknown): “(see [3]) Let the function f (z) given by the Taylor-Maclaurin series expansion (1) be in the class N Σ ( β, λ ) (0 5 β < 1; λ = 1; μ = 0).”
• Chebyshev polynomial coefficient estimates for a class of analytic bi-univalent functions related to pseudo-starlike functions (2017, background): “For a history and examples of functions which are (or which are not) in the class , together with various other properties of subclasses of bi-univalent functions one can refer [1,4,6,13,15,17,19,21].”
• Coefficient bounds for certain subclasses of bi-univalent functions (2016, background): “2.2 Certain Subclasses of Analytic and Bi-Univalent Functions Srivastava et aI., (2010) have introduced two subclasses of normalized analytic and univalent functions in the open unit disc E whose inverse has univalently analytic continuation to E which are defined by '}(ff and XE(P) and found the bo”
• Faber polynomial coefficient estimates for a comprehensive subclass of analytic bi-univalent functions (2014, unknown): “(See [10].”
• Estimates of Initial Coefficients for Bi-Univalent Functions (2014, background): “In the papers [1–15], the authors present some estimates for a 2 and a 3 , whilef is taken from various subclasses of Σ.”
• Bounds for the second Hankel determinant of certain bi-univalent functions (2015, unknown): “[5] Çağlar M, Orhan H and Yağmur N.”