We denote by A the subclass of H a, 1 with the usual normalization f 0 f ′ 0 − 1 0, and denote by A the subclass ofA satisfying the condition h z h′ z / 0 for z ∈ U \ {0}. Let f and F be members of H. The function f is said to be subordinate to F, or F is said to be superordinate to f, if there exists a functionw analytic in Uwithw 0 0 and |w z | < 1 for z ∈ U and such that f z g w z z ∈ U . In...

In this paper authors introduced two new subclasses ∑ρτςξ mp α, β, η and ∑ (α, β, η) + ρτςξ mp of meromorphically multivalent functions which aredefined by means of a new differential operator. By making use of the principle of differential subordination, authors investigate several inclusion relationships and properties of certain subclasses which are defined here by means of a differential op...

By using a method based upon the Briot-Bouquet differential subordination, we investigate some subordination properties of the generalized fractional integral operator , , 0,z       p    which was defined by Owa, Saigo and Srivastava [1]. Some interesting further consequences are also considered.

In this paper, a subclass N(λ, α, A, B) of analytic functions is introduced, which is a generalized class of non-Bazilevič functions. The subordination relations, inclusion relations, distortion theorems and inequality properties are discussed by applying differential subordination method.

For $0\leq\alpha\leq 1,$ let $H_{\alpha}(x,y)$ be the convex weighted harmonic mean of $x$ and $y.$ We establish differential subordination implications form $$H_{\alpha}(p(z),p(z)\Theta(z)+zp'(z)\Phi(z))\prec h(z)\Rightarrow p(z)\prec h(z),$$ where $\Phi$, $\Theta$ are analytic functions $h$ is a univalent function satisfying some special properties. Further, we prove involving combination thr...