Schwarz Lemma, and Distortion for Harmonic Functions Via Length and Area

On certain quasiconformal and elliptic mappings

“…Concerning the generalized form of inequality (1.9), Mateljević [26] proved the following result: Let f (z) = ∞ n=0 a n z n + ∞ n=1 b n z n be a harmonic mapping with ℓ f (1) < ∞. Then, for n ≥ 1, the inequality (1.11) |a n | + |b n | ≤ ℓ f (1) nπ holds (see [26,Theorem 10]).…”

“…Concerning the generalized form of inequality (1.9), Mateljević [26] proved the following result: Let f (z) = ∞ n=0 a n z n + ∞ n=1 b n z n be a harmonic mapping with ℓ f (1) < ∞. Then, for n ≥ 1, the inequality (1.11) |a n | + |b n | ≤ ℓ f (1) nπ holds (see [26,Theorem 10]). Moreover, Kalaj [19] improved the inequality (1.10) and obtained a sharp inequality for harmonic diffeomorphisms of D. It reads as follows.…”

“…We thank anonymous referees for drawing our attention to references [19,26] and providing us with a lot of valuable comments. This re-…”

Schwarz lemma for driving point impedance functions and its circuit applications

“…3) and its generalizations have important applications in geometric theory of functions, and they are still hot topics in the mathematics literature. 24,[26][27][28][29][30][31][32]…”

“…Also, unless f ( z ) = z p e iθ , θ real. Inequality and its generalizations have important applications in geometric theory of functions, and they are still hot topics in the mathematics literature …”