Sentence examples for class of close from inspiring English sources

We note that UCC ( 0, η, β ) is the class of close to convex univalent functions of order η and type β and UQC ( 0, η, β ) is the class of quasi-convex univalent functions of order η and type β.

then integral operator defined by (1.3) belongs to the class of close-to-convex functions.

then I n (f i, h i )(z) defined by (1.4) belongs to the class of close-to-convex functions.

The class is the well-known class of close-to-star functionswith argument 0. Silverman [1] introduced the class of functions F given by the formula.

They proved also that the class of starlike functions and the class of close-to-convex functions are closed under convolution with the class.

For (A=1), (B=-1), (C=1), (D=-1) and (k=0), we have the radius of convexity problem for the well-known class of close-to-convex functions studied by Kaplan [21].  .

For λ ∈ [ 0, 1 ] Koepf in [5] extended the above result for the class of close-to-convex functions showing that max f ∈ C Φ λ ( f ) = max f ∈ C 0 Φ λ ( f ).

The class C : = W ( ( z ( 1 − z ) 2, z 1 − z ) ; 1 + z 1 − z ) is the well-known class of close-to convex functions with argument β = 0.

Later Pfluger [2] used Jenkin's method to show that this result holds for complex μ such that Re μ 1 − μ ≥ 0. Keogh and Merkes [3] obtained the solution of the Fekete-Szegö problem for the class of close-to-convex functions.

Let f i (z) ∈ K, h i (z) ∈ S* for 1 ≤ i ≤ n and ∑ i = 1 n k 2 α i + β i - β i ≤ 1, then I n (f i, h i )(z) defined by (1.4) belongs to the class of close-to-convex functions.

Here, we extend the work of Vrugt and Sadegh (2013) and introduce several commonly used models of the soil water characteristic as new class of closed-form parametric expressions for the flow duration curve.