In this paper, our interest is devoted to study the convex combinations of form (1 ? ?) f + ?1, where (0, 1), biholomorphic mappings on Euclidean unit ball Bn in case several complex variables. Starting from a result proved by S. Trimble [26] and then extended P.N. Chichra R. Singh [3, Theorem 2] which says that if starlike such Re[f ?(z)] > 0, (1??)z+?f (z) also starlike, we are interested ...

A set of vertices $S$ a graph $G$ is $monophonically \ convex$ if every induced path joining two contained in $S$. The $monophonic convex hull$ $S$, $\langle S \rangle$, the smallest monophonically containing convexly independent$ $v \not\in \langle - \{v\} \rangle$ for \in S$. rank$ size largest monophonic independent $G$. We present characterization sets. Using this result, we show how to det...

Abstract In the present investigation, we introduce and study interesting properties of a new unified class of pre-starlike functions with negative coefficients in the open unit disk ∆. These properties include growth and distortion, radii of convexity, radii of starlikeness and radii of close to convexity. 2000 Mathematics Subject Classification: 30C45.

Abstract. In this present investigation, authors introduce certain subclasses of starlike and convex functions of complex order b, using a linear multiplier differential operator D λ,μf(z). In this paper, for these classes the Fekete–Szegö problem is completely solved. Various new special cases of our results are also pointed out.

Abstract. We introduce a new subclass corresponding to the class of k−uniformly convex and starlike functions associated with HurwitzLerch zeta functions and determine many properties like the coefficient estimates, extreme points, closure theorem, distortion bounds, radii of starlikeness and convexity. Furthermore, we obtain an integral transform results, neighborhood results, integral means i...