A COEFFICIENT INEQUALITY OF m-TH ROOT TRANSFORMATION ASSOCIATED WITH BAZILEVIČ FUNCTIONS

2019 ◽  
Vol 112 (1) ◽  
pp. 97-107
Author(s):  
R. Vijaya ◽  
S. Sivasubramanian ◽  
T. V. Sudharsan
2020 ◽  
Vol 53 (1) ◽  
pp. 27-37
Author(s):  
Sa’adatul Fitri ◽  
Derek K. Thomas ◽  
Ratno Bagus Edy Wibowo ◽  

AbstractLet f be analytic in {\mathbb{D}}=\{z:|z\mathrm{|\hspace{0.17em}\lt \hspace{0.17em}1\}} with f(z)=z+{\sum }_{n\mathrm{=2}}^{\infty }{a}_{n}{z}^{n}, and for α ≥ 0 and 0 < λ ≤ 1, let { {\mathcal B} }_{1}(\alpha ,\lambda ) denote the subclass of Bazilevič functions satisfying \left|f^{\prime} (z){\left(\frac{z}{f(z)}\right)}^{1-\alpha }-1\right|\lt \lambda for 0 < λ ≤ 1. We give sharp bounds for various coefficient problems when f\in { {\mathcal B} }_{1}(\alpha ,\lambda ), thus extending recent work in the case λ = 1.


2003 ◽  
Vol 2003 (59) ◽  
pp. 3753-3759
Author(s):  
Yaşar Polatoğlu ◽  
Metın Bolcal

The aim of this paper is to give a coefficient inequality for the class of analytic functions in the unit discD={z||z| <1}.


2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Muhammet Kamali ◽  
Fatma Sağsöz

The authors introduce two new subclasses denoted by and of the class of -valent analytic functions. They obtain coefficient inequality for the class . They investigate various properties of classes and . Furthermore, they derive partial sums associated with the class .


1985 ◽  
Vol 8 (4) ◽  
pp. 785-793
Author(s):  
Rabha Md. El-Ashwah ◽  
D. K. Thomas

Forα>0, letB(α)be the class of regular normalized Bazilevič functions defined in the unit disc. Choosing the associated starlike functiong(z)≡zgives a proper subclassB1(α)ofB(α). ForB(α), correct growth estimates in terms of the area function are unknown. Several results in this direction are given forB1(12).


Author(s):  
Khalida I. Noor ◽  
Sumayya A. Al-Bany

LetB(β)be the class of Bazilevic functions of typeβ(β>0). A functionf ϵ B(β)if it is analytic in the unit discEandRezf′(z)f1−β(z)gβ(z)>0, wheregis a starlike function. We generalize the classB(β)by takinggto be a function of radius rotation at mostkπ(k≥2). Archlength, difference of coefficient, Hankel determinant and some other problems are solved for this generalized class. Fork=2, we obtain some of these results for the classB(β)of Bazilevic functions of typeβ.


1988 ◽  
Vol 104 (1) ◽  
pp. 235-235
Author(s):  
R. R. London ◽  
D. K. Thomas
Keyword(s):  

1964 ◽  
Vol 6 (2) ◽  
pp. 169-178 ◽  
Author(s):  
R. V. Large

1. Thirty Suffolk × Half bred lambs were slaughtered at the following ages: two twin lambs at birth and two singles and two twins at 1, 2, 3, 4, 6, 8 and 16 weeks of age.2. The following weights were recorded: live-weight immediately before slaughter; and carcass, head, skin, feet, alimentary tract, heart, liver, kidneys, lungs and trachea, and blood immediately afterwards.3. The alimentary tract was emptied and weighed in four separate parts; reticulo-rumen, omasum-abomasum, small intestine, large intestine.4. The volumes of the reticulo-rumen and the omasum-abomasum were measured by immersing in water and filling the organs with water to 2 cm. pressure.5. The in vitro digestive efficiency of rumen liquor from lambs of 1, 2, 3 and 4 weeks of age was assessed.6. Empty body weight was considered to be valuable in comparing animals of different ages or from different feeding regimes or at different times of the year because variations in gut ‘fill’ were eliminated.7. There were no differences between singles and twins in the relationship of the fresh weights of the parts of the body to empty body weight, except that development of the liver and the blood was rather slower for singles.8. Little evidence was found of a difference in rate of development of the alimentary tract between singles an d twins, although the log an d square root transformation suggested a possible difference in reticulo-rumen size in favour of twins, significant at the 5% level.


1995 ◽  
Vol 43 (1) ◽  
pp. 1-5 ◽  
Author(s):  
H.J. Siefkes-Boer ◽  
M.J. Noonan ◽  
D.W. Bullock ◽  
A.J. Conner

Hairy roots were produced on faba bean (Vicia faba L.) and chickpea (Cicer arietinum L.) plants by inoculation with Agrobacterium root-inducing strains. Examination of 14 plant genotypes and eight Agrobacterium strains in all possible combinations revealed specific strain/genotype interactions. Hairy root size and morphology differed substantially between faba bean and chickpea hairy roots. Sixty percent of chickpea hairy roots were 10–15 mm in length and forty percent, 15–25 mm. All were <1.0 mm in thickness. Sixty-three percent of faba bean hairy roots were 15–25 mm long and thirty-seven percent, 25–40 mm. All faba bean hairy roots were between 1.0 and 1.5 mm in thickness.


2012 ◽  
Vol 68 (3) ◽  
pp. 459-465 ◽  
Author(s):  
Qingqin Cao ◽  
Rik Op den Camp ◽  
Maryam Seifi Kalhor ◽  
Ton Bisseling ◽  
Rene Geurts

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