There exists a calculus for general nondifferentiable functions that englobes a large part of the familiar subdifferential calculus for convex nondifferentiable functions [1]. This development started with F.H. Clarke, who introduced a generalized gradient for functions that are locally Lipschitz, but (possibly) nondifferentiable. Generalized gradients turn out to be the subdifferentials, in th...

We introduce a polynomial time algorithm for optimizing the class of star-convex functions, under no Lipschitz or other smoothness assumptions whatsoever, and no restrictions except exponential boundedness on a region about the origin, and Lebesgue measurability. The algorithm’s performance is polynomial in the requested number of digits of accuracy and the dimension of the search domain. This ...

In 1999, Kanas and Rønning introduced the classes of starlike and convex functions, which are normalized with f (w) = f ′(w)− 1 = 0 and w a fixed point in U . In 2005, the authors introduced the classes of functions close to convex and α-convex, which are normalized in the same way. All these definitions are somewhat similar to the ones for the uniform-type functions and it is easy to see that ...

In this paper, we introduced and investigated starlike and convex functions of order α with respect to 2(j,k)-symmetric conjugate points and coefficient inequality for function belonging to these classes are provided . Also we obtain some convolution condition for functions belonging to this class.

Recently, Hermite-Hadamard-type inequalities and their applications have attracted considerable interest, as shown in the book [1], for example. These inequalities have been studied for various classes of functions such as convex functions [1], quasiconvex functions [2–4], p-functions [3, 5], Godnova-Levin type functions [5], r-convex functions [6], increasing convex-along-rays functions [7], a...

In this paper we will prove certain Hadamard and Fejer-Hadamard inequalities for the functions whose nth derivatives are convex by using Caputo k-fractional derivatives. These results have some relationship with inequalities for Caputo fractional derivatives.