# Bohr Phenomenon for $K$-Quasiconformal harmonic mappings and Logarithmic Power Series

@inproceedings{Gangania2021BohrPF, title={Bohr Phenomenon for \$K\$-Quasiconformal harmonic mappings and Logarithmic Power Series}, author={Kamaljeet Gangania}, year={2021} }

In this article, we establish the Bohr inequalities for the sense-preservingK-quasiconformal harmonic mappings defined in the unit disk D involving classes of Ma-Minda starlike and convex univalent functions, usually denoted by S∗(ψ) and C(ψ) respectively, and for log(f(z)/z) where f belongs to the Ma-Minda classes or satisfies certain differential subordination. We also estimate Logarithmic coefficient’s bounds for the functions in C(ψ) for the case ψ(D) be convex. 2010 AMS Subject…

## References

SHOWING 1-10 OF 33 REFERENCES

Bohr’s phenomenon for the classes of Quasi-subordination and K-quasiregular harmonic mappings

- Mathematics
- 2020

In this paper, we investigate the Bohr radius for $K$-quasiregular sense-preserving harmonic mappings $f=h+\overline{g}$ in the unit disk $\mathbb{D}$ such that the translated analytic part…

Bohr Phenomenon for Locally Univalent Functions and Logarithmic Power Series

- MathematicsComputational Methods and Function Theory
- 2019

In this article we prove Bohr inequalities for sense-preserving $K$-quasiconformal harmonic mappings defined in $\mathbb{D}$ and obtain the corresponding results for sense-preserving harmonic…

Bohr radius for subordinating families of analytic functions and bounded harmonic mappings

- Mathematics
- 2014

Abstract The class consisting of analytic functions f in the unit disk satisfying f + α z f ′ + γ z 2 f ″ subordinated to some function h is considered. The Bohr radius for this class is obtained…

Bohr phenomenon for analytic functions subordinate to starlike or convex functions

- MathematicsJournal of Mathematical Analysis and Applications
- 2021

Abstract In this paper, we will obtain a new result on the Bohr phenomenon for analytic functions f which are subordinate to starlike functions g ∈ S ⁎ ( ϕ ) , where ϕ satisfies Ma-Minda conditions…

On the Bohr inequality with a fixed zero coefficient

- MathematicsProceedings of the American Mathematical Society
- 2019

In this paper, we introduce the study of the Bohr phenomenon for a quasisubordination family of functions, and establish the classical Bohr’s inequality for the class of quasisubordinate functions.…

Bohr Inequality for Odd Analytic Functions

- Mathematics
- 2017

We determine the Bohr radius for the class of odd functions f satisfying $$|f(z)|\le 1$$|f(z)|≤1 for all $$|z|<1$$|z|<1, solving the recent problem of Ali et al. (J Math Anal Appl 449(1):154–167,…

ON CERTAIN GENERALIZATIONS OF S∗(ψ)

- 2020

We deal with different kinds of generalizations of S∗(ψ), the class of Ma-Minda starlike functions, in addition to a majorization result of C(ψ), the class of Ma-Minda convex functions, which are…

Bohr Radius for Subordination and K-quasiconformal Harmonic Mappings

- MathematicsBulletin of the Malaysian Mathematical Sciences Society
- 2019

The present article concerns the Bohr radius for $K$-quasiconformal sense-preserving harmonic mappings $f=h+\overline{g}$ in the unit disk $\mathbb{D}$ for which the analytic part $h$ is subordinated…

Refined Bohr-type inequalities with area measure for bounded analytic functions

- Mathematics
- 2020

In this paper, we establish five new sharp versions of Bohr-type inequalities for bounded analytic functions in the unit disk by allowing Schwarz function in place of the initial coefficients in the…

A note on Bohr's phenomenon for power series

- Mathematics
- 2017

Abstract Bohr's phenomenon, first introduced by Harald Bohr in 1914, deals with the largest radius r , 0 r 1 , such that the inequality ∑ k = 0 ∞ | a k | r k ≤ 1 holds whenever the inequality | ∑ k =…