On a class of extremal problems associated with regular functions with positive real part in the circle |𝑧|<1

1969 ◽  
pp. 215-226
Author(s):  
V. A. Zmorovič
Keyword(s):  
Extremal Problems ◽  
Positive Real Part ◽  
Positive Real ◽  
Regular Functions

scholarly journals Extremal problems for a class of functions of positive real part and applications

1986 ◽  
Vol 41 (2) ◽  
pp. 152-164
Author(s):  
V. V. Anh ◽  
P. D. Tuan
Keyword(s):  
Lower Bound ◽  
Extremal Problems ◽  
Positive Real Part ◽  
Positive Real ◽  
Sharp Bounds ◽  
The Family ◽  
Radius Of Convexity ◽  
Class Of Functions

AbstractIn this paper we determine the lower bound on |z| = r < 1 for the functional Re{αp(z) + β zp′(z)/p(z)}, α ≧0, β ≧ 0, over the class Pk (A, B). By means of this result, sharp bounds for |F(z)|, |F',(z)| in the family and the radius of convexity for are obtained. Furthermore, we establish the radius of starlikness of order β, 0 ≦ β < 1, for the functions F(z) = λf(Z) + (1-λ) zf′ (Z), |z| < 1, where ∞ < λ <1, and .

scholarly journals On certain extremal problems for functions with positive real part

1976 ◽  
Vol 61 (2) ◽  
pp. 329-329 ◽  
Author(s):  
Stephan Ruscheweyh ◽  
Vikramaditya Singh
Keyword(s):  
Extremal Problems ◽  
Positive Real Part ◽  
Positive Real

scholarly journals Univalence Conditions Related to a General Integral Operator

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Nicoleta Breaz ◽  
Virgil Pescar
Keyword(s):  
Integral Operator ◽  
Analytic Functions ◽  
Positive Real Part ◽  
Positive Real ◽  
Regular Functions ◽  
General Integral ◽  
General Integral Operator

We consider a general integral operator based on two types of analytic functions, namely, regular functions and, respectively, functions having a positive real part. Some univalence conditions for this integral operator are obtained.

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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