LetN be the class of functions that convex in one direction and M denote zf′(z), where f∈N. In paper, third-order Hankel determinants for these classes are estimated. The estimates H3,1(f) obtained paper improved.

In this manuscript, we introduce concepts of (m1,m2)-logarithmically convex (AG-convex) functions and establish some Hermite-Hadamard type inequalities of these classes of functions.

Abstract Sharp upper and lower bounds of the Hermitian Toeplitz determinants second third orders are found for various subclasses close-to-convex functions.

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 ...

the object of this paper to derive certain sucient condi-tions for close-to-convexity of certain analytic functions dened on theunit disk

Using the notion of eta-convex functions as generalization of convex functions, we estimate the difference between the middle and right terms in Hermite-Hadamard-Fejer inequality for differentiable mappings. Also as an application we give an error estimate for midpoint formula.