By appealing to the familiar convolution structure of analytic functions, we investigate various useful properties and characteristics of a general class of multivalently analytic functions using the techniques of differential subordination. Several results are presented exhibiting relevant connections with some of the results presented here and those obtained in earlier works.

In this paper we introduce a new class of analytic functions of complex order involving a family of generalized differential operators and we discuss the sufficient conditions, estimation of coefficients and certain subordination results. Using this one can derive numerous known results as special cases. 2000 Mathematics Subject Classification: 30C45.

We introduce a subclass Mp(λ, μ,A,B) of p-valent analytic functions and derive certain properties of functions belonging to this class by using the techniques of Briot-Bouquet differential subordination. Further, the integral preserving properties of Bazilevic functions in a sector are also considered.

In this paper we establish several strong differential subordinations regarding an extended new operator obtained as a linear combination of an extended Ruscheweyh derivative and an extended new multiplier transformation. A number of interesting consequences of these strong subordination results are discussed.

Using the fractional integral operator D−λ z and generalized SrivastavaAttiya operator J s,b , we introduce and study some differential subordination and superordination results for p-valent analytic functions in the open unit disk. These results are obtained by investigating appropriate classes of admissible functions.

This paper studies additive subordination, which we show is a useful technique for constructing time-inhomogeneous Markov processes with analytical tractability. This technique is a natural generalization of Bochner’s subordination that has proven to be extremely useful in financial modelling. Probabilistically, Bochner’s subordination corresponds to a stochastic time change with respect to an ...

This paper is related to fuzzy differential subordinations for meromorphic functions. Fuzzy subordination results are obtained using a new operator which the combination Hadamard product and integral function.

In this paper, by applying a generalized extended fractional differintegral operator S ,μ,η 0,z (z ∈ △; p ∈ N; μ,η ∈ R; μ < p+ 1;−∞ < λ < η + p+ 1) we define a new class convex functions CV λ ,μ,η p (α;A,B) and several sharp inclusion relationships and other interesting properties were discussed by using the techniques of differential subordination.

By introducing a new subcalss of p-valent functions with respect to (j, k)-symmetric points, we have obtained the integral representations and conditions for starlikeness by using differential subordination. Some already known results have been, incidentally, shown to be particular cases of the main results of the paper.