Harmonic

Quantum mechanics

Alternating series

Pure mathematics

Biology

Bohr radius

Power series

Lacunary function

Computer security

RADIUS

Computer science

Harmonic function

Bounded function

Bohr model

Paleontology

Physics

Analytic function

Mathematics

Unit disk

Mathematical analysis

Series (stratigraphy)

Quantum dot

Journal of Mathematical Analysis and Applications

We determine the Bohr radius for the class of all functions f of the form f(z)=zm∑k=0∞akpzkp analytic in the unit disk |z|<1 and satisfy the condition |f(z)|≤1 for all |z|<1. In particular, our result also contains a solution to a recent conjecture of Ali et al. [9] for the Bohr radius for odd analytic functions, solved by the authors in [17]. We consider a more flexible approach by introducing the p-Bohr radius for harmonic functions which in turn contains the classical Bohr radius as special case. Also, we prove several other new results and discuss p-Bohr radius for the class of odd harmonic bounded functions.

Bohr's inequalities for the analytic functions with lacunary series and harmonic functions