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 ...

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.

In this paper, we define new subclasses ${S}^{*}_{q}(alpha,Phi),$ ${M}_{q}(alpha,Phi)$ and ${L}_{q}(alpha,Phi)$ of analytic functions in the space of logistic sigmoid functions based on quasi--subordination and determine the initial coefficient estimates $|a_2|$ and $|a_3|$ and also determine the relevant connection to the classical Fekete--Szeg"o inequalities. Further, we discuss the improved ...