In the geometric function s theory there are many subclasses of multivalent functions like coefficient bounds, radii of star likeness, convexity, harmonic, memomorphic functions, etc. Now we introduce some properties of geometric functions theory with negative coefficient of multivalent function s ( ݖ ) = ݖ ௣ − ∑ ௞ ݖ ௞ ା ௣ ∞ ௭ ୀ ௡ Which is analytic in unit disc ∪ = { ݖ : | ݖ | < 1 }

Many structures in nature like clouds, mountains, rocks, coastlines, trees, leaves, etc. has shapes which cannot be entirely described with Euclidean geometry i.e. in terms of lines , circles, spheres, cones, triangles, etc. Benoit B. Mandelbrot (20 Nov.1924—14 Oct. 2010) a Polish born, French- American Mathematician developed a theory to measure roughness in nature, for which he gave a name as Fractals