We derive theq-analogue of the well-known Ruscheweyh differential operator using the concept ofq-derivative. Here, we investigate several interesting properties of thisq-operator by making use of the method of differential subordination.

We have investigated a two-dimensional radiative flow of a boundary layer nature. The fluid under consideration is carbon nanotube (CNT)-based nanofluid and it flows over a curved surface. The heat transfer through the flow is analyzed under the influence of internal heat generation. Water (base fluid) along with single or multi-walled carbon nanotubes is taken to compose the nanofluid. After introducing the suitable similarity variables, the consequent equations are reduced to a system of nonlinear ordinary differential equations. The solution to the system is computed by using the shooting method accompanied by Runge–Kutta–Fehlberg algorithm. Various parameters, emerging in the governing equations, influences the flow and heat transfer distribution. These changes are captured and portrayed in the form of graphs. The changes in local rate of heat transfer and skin friction coefficient are also enlisted. To ensure the correctness of applied numerical scheme, the results are compared with some already existing studies.

In this note we obtain some inequalities of Hermite-Hadamardtype for functions whose second derivatives absolute values are quasi-convex.Applications for special means are also provided.

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