Functions with positive real part in a half-plane

1962 ◽  
Vol 29 (2) ◽  
pp. 333-339 ◽  
Author(s):  
J. L. Goldberg
Keyword(s):  
Half Plane ◽  
Positive Real Part ◽  
Positive Real

scholarly journals The Fréchet Schwartz Algebra of Uniformly Convergent Dirichlet Series

2018 ◽  
Vol 61 (4) ◽  
pp. 933-942 ◽  
Author(s):  
José Bonet
Keyword(s):  
Dirichlet Series ◽  
Half Plane ◽  
Composition Operators ◽  
Positive Real Part ◽  
Complex Numbers ◽  
Positive Real ◽  
Uniformly Convergent ◽  
Schwartz Algebra ◽  
Locally Convex Topology ◽  
Locally Convex

AbstractThe algebra of all Dirichlet series that are uniformly convergent in the half-plane of complex numbers with positive real part is investigated. When it is endowed with its natural locally convex topology, it is a non-nuclear Fréchet Schwartz space with basis. Moreover, it is a locally multiplicative algebra but not aQ-algebra. Composition operators on this space are also studied.

scholarly journals On the Largest Disc Mapped by Sum of Convex and Starlike Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Rosihan M. Ali ◽  
Naveen Kumar Jain ◽  
V. Ravichandran
Keyword(s):  
Analytic Function ◽  
Half Plane ◽  
Unit Disc ◽  
Starlike Functions ◽  
Positive Real Part ◽  
Positive Real ◽  
Convex And Starlike Functions ◽  
The Right

For a normalized analytic functionfdefined on the unit disc𝔻, letϕ(f,f′,f′′;z)be a function of positive real part in𝔻,ψ(f,f′,f′′;z)need not have that property in𝔻, andχ=ϕ+ψ. For certain choices ofϕandψ, a sharp radius constantρis determined,0<ρ<1, so thatχ(ρz)/ρmaps𝔻onto a specified region in the right half-plane.

scholarly journals Initial logarithmic coefficients for functions starlike with respect to symmetric points

2021 ◽  
Vol 27 (3) ◽  
Author(s):  
Paweł Zaprawa
Keyword(s):  
Exact Result ◽  
Positive Real Part ◽  
Additional Benefit ◽  
Extremal Functions ◽  
Positive Real ◽  
Logarithmic Coefficients ◽  
Symmetric Points

AbstractIn this paper, we obtain the bounds of the initial logarithmic coefficients for functions in the classes $${\mathcal {S}}_S^*$$ S S ∗ and $${\mathcal {K}}_S$$ K S of functions which are starlike with respect to symmetric points and convex with respect to symmetric points, respectively. In our research, we use a different approach than the usual one in which the coeffcients of f are expressed by the corresponding coeffcients of functions with positive real part. In what follows, we express the coeffcients of f in $${\mathcal {S}}_S^*$$ S S ∗ and $${\mathcal {K}}_S$$ K S by the corresponding coeffcients of Schwarz functions. In the proofs, we apply some inequalities for these functions obtained by Prokhorov and Szynal, by Carlson and by Efraimidis. This approach offers a additional benefit. In many cases, it is easily possible to predict the exact result and to select extremal functions. It is the case for $${\mathcal {S}}_S^*$$ S S ∗ and $${\mathcal {K}}_S$$ K S .

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