Texture analysis using Horadam polynomial coefficient estimate for the class of Sakaguchi kind function

Theorem 4  A function f (z) = z + ∞ n=2 anzn ∈ A be in the class C(, t, ν) , then where

Corollary 5  A function f ∈A and of the form (1) is in the class C(t, ν) , then

Theorem 7  For any complex number τ , Let f (z) = z + ∞ n=2 anzn ∈ A be in the class C(, t, ν) then where and

Corollary 8  A function f ∈A and of the form (1) is in the class C(ν) , then Application The Horadam polynomial is an illustration of a mathematical sequence used in texture analysis and image pro- cessing. The Horadam polynomial, a specific kind of polynomial sequence, can be used to perform procedures like filtering and resampling. In image processing and computer vision, scale-space representations of images can be created and modified using the Horadam polynomial. This polynomial can be use

Definition 1  Starlike ­functions1 A simple connected domain D ⊂C is supposed to be starlike with regard to w0 ∈D , if there exists a line segment which joins w0 to any other point of D and it completly lies in D. Suppose u ∈S is claimed to be star-like function relevant to the origin, if u maps the unit disk U onto a star- like domain in view of the origin. The family S∗ denotes the collection of all star-like functions in view of origin. Equivalently, Definition 2  Convex functions (Goodman 19

Definition 3  A function f (z) = z + ∞ n=2 anzn ∈  is said to be in the class C(, t, ν) if it satisfies the following subordination conditions which are follows, S∗=