Some Families of Analytic Functions in the Upper HalfPlane and Their Associated Differential Subordination and Differential Superordination Properties and Problems

The Principle of Differential Subordination and Its Application to Analytic and p-Valent Functions Defined by a Generalized Fractional Differintegral Operator

“…Hence, by applying Equations (25), (26) and (27) to Equation (24), we can find easily an upper bound for the right-hand side of Equation (24). Thus, the function I(z, t) satisfies the second condition of Lemma 5, which proves that I(z, t) is a subordination chain.…”

“…Our results give interesting new properties, and together with other papers that appeared in the last years could emphasize the perspective of the importance of differential subordinations and generalized fractional differintegral operators. We also note that, in recent years, several authors obtained many interesting results involving various linear and nonlinear operators associated with differential subordinations and their dual problrms (for details, see [21][22][23][24][25][26][27][28]).…”

Second-order differential superordination for analytic functions in the upper half-plane

“…Following the theory of second-order differential superordinations in the unit disk, which was introduced by Miller and Mocanu [12], Tang et al [22] considered the dual problem of determining properties of functions p(z) that satisfy the following second-order differential superordination:…”

“…Recently, Tang et al [20] (see also [22]) have considered the applications of these results to secondorder differential subordination for analytic functions in ∆.…”

Majorization problems for certain classes of multivalent analytic functions related with the Srivastava-Khairnar-More operator and exponential function

“…Later, Roberston [17] (see also [19]) gave the concept of quasi-subordination as below. and say f is subordinate to in U, denoted by (see [21]; also see [18,22,23,29])…”