The logarithmic coefficient inequality for close-to-convex functions of complex order

The Logarithmic Coefficient Inequality for Close–to–convex Functions of Complex Order

We prove that if n 2 for each close-to-convex functions of complex order b in S whose n− th logarithmic coefficients γn satisfies |γn| An−1 logn, where A is an absolute constant. Mathematics subject classification (2010): 30C45.

JENSEN’S INEQUALITY FOR GG-CONVEX FUNCTIONS

In this paper, we obtain Jensen’s inequality for GG-convex functions. Also, we get in- equalities alike to Hermite-Hadamard inequality for GG-convex functions. Some examples are given.

Higher order close-to-convex functions associated with Attiya-Srivastava operator

In this paper‎, ‎we introduce a new class$T_{k}^{s,a}[A,B,alpha‎ ,‎beta ]$ of analytic functions by using a‎ ‎newly defined convolution operator‎. ‎This class contains many known classes of‎ ‎analytic and univalent functions as special cases‎. ‎We derived some‎ ‎interesting results including inclusion relationships‎, ‎a radius problem and‎ ‎sharp coefficient bound for this class‎.

An inequality related to $eta$-convex functions (II)

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.

Some Properties of Certain Subclasses of Close-to-Convex and Quasi-convex Functions with Respect to 2k-Symmetric Conjugate Points