scholarly journals On a Subclass of Multivalent Functions with Bounded Positive Real Part

2019 ◽  
Vol 7 (1) ◽  
pp. 1
Author(s):  
Thirupathi Ganapathi
Keyword(s):  
Differential Subordination ◽  
Positive Real Part ◽  
Integral Representations ◽  
Positive Real ◽  
Symmetric Points ◽  
Bounded Positive Real Part

In the present paper, by introducing a new subclass of multivalent functions with respect to - symmetric points, we have obtained the integral representations and conditions for starlikeness using differential subordination.

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 .

scholarly journals Some characteristic properties of analytic functions

2016 ◽  
Vol 24 (1) ◽  
pp. 353-369
Author(s):  
R. K. Raina ◽  
Poonam Sharma ◽  
G. S. Sălăgean
Keyword(s):  
Convex Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Positive Real Part ◽  
Integral Representations ◽  
Open Unit ◽  
Open Unit Disk ◽  
Positive Real ◽  
Bilinear Mapping ◽  
Initial Coefficient

AbstractIn this paper, we consider a class L(λ, μ; ϕ) of analytic functions f defined in the open unit disk U satisfying the subordination condition that,where is the Sălăgean operator and ϕ(z) is a convex function with positive real part in U. We obtain some characteristic properties giving the coefficient inequality, radius and subordination results, and an inclusion result for the above class when the function ϕ(z) is a bilinear mapping in the open unit disk. For these functions f (z) ; sharp bounds for the initial coefficient and for the Fekete-Szegö functional are determined, and also some integral representations are given.

scholarly journals Starlike Functions Related to the Bell Numbers

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 219 ◽  
Author(s):  
Nak Cho ◽  
Sushil Kumar ◽  
Virendra Kumar ◽  
V. Ravichandran ◽  
H. Srivastava
Keyword(s):  
Starlike Functions ◽  
Differential Subordination ◽  
Positive Real Part ◽  
Bell Numbers ◽  
Positive Real ◽  
First Order

The present paper aims to establish the first order differential subordination relations between functions with a positive real part and starlike functions related to the Bell numbers. In addition, several sharp radii estimates for functions in the class of starlike functions associated with the Bell numbers are determined.

scholarly journals Coefficient estimate of p-valent Bazilevic functions with a bounded positive real part

2015 ◽  
Vol 34 (2) ◽  
pp. 63-73
Author(s):  
O. S. Babu ◽  
C. Selvaraj ◽  
S. Logu ◽  
Gangadharan Murugusundaramoorthy
Keyword(s):  
Unit Disk ◽  
Positive Real Part ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimate ◽  
Positive Real ◽  
Strip Domain ◽  
Bazilevic Functions ◽  
Bounded Positive Real Part

By considering a $p-$valent Bazilevi\v{c} function in the open unit disk$\triangle$ which maps $\triangle$ onto the strip domain $w$ with$p\alpha < \Re\, w < p \beta,$ we estimate bounds of coefficients and solve Fekete-Szeg\"{o} problem forfunctions in this class.\\

scholarly journals Applications of first order differential subordination for functions with positive real part

2018 ◽  
Vol 63 (3) ◽  
pp. 303-311 ◽  
Author(s):  
Om P. Ahuja ◽  
◽  
Sushil Kumar ◽  
V. Ravichandran ◽  
◽  
...  
Keyword(s):  
Differential Subordination ◽  
Positive Real Part ◽  
Positive Real ◽  
First Order

scholarly journals Differential subordination for Janowski functions with positive real part

2021 ◽  
Vol 66 (3) ◽  
pp. 457-470
Author(s):  
Swati Anand ◽  
V. Ravichandran ◽  
Sushil Kumar
Keyword(s):  
Sufficient Conditions ◽  
Starlike Functions ◽  
Differential Subordination ◽  
Positive Real Part ◽  
Algebraic Condition ◽  
Positive Real ◽  
First Order ◽  
Janowski Functions ◽  
Subordination Theory ◽  
Differential Subordinations

"Theory of differential subordination provides techniques to reduce differential subordination problems into verifying some simple algebraic condition called admissibility condition.We exploit the first order differential subordination theory to get several sufficient conditions for function satisfying several differential subordinations to be a Janowski function with positive real part. As applications, we obtain suffcient conditions for normalized analytic functions to be Janowski starlike functions."

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