Related papers: New inequalities for $\eta$-quasiconvex functions
This is a continuation of our previous work 0712.4092. It is well known that various isoperimetric inequalities imply their functional ``counterparts'', but in general this is not an equivalence. We show that under certain convexity…
In this paper, we give some definitions on quasi-convex functions and we prove inequalities contain J-quasi-convex and W-quasi-convex functions. We give also some inclusions.
We continue a series of papers studying the parity of families of eta-quotients, which provide implications for the parity of the partition function as well as an overarching conjecture on related $q$-series. The present article focuses on…
In this paper, we extend some estimates of the right hand side of a Hermite- Hadamard type inequality for nonconvex functions whose second derivatives absolute values are \phi-convex, log-\phi-convex, and quasi-\phi-convex.
In this paper, the authors establish a new type integral inequalities for differentiable s-convex functions in the second sense. By the well-known H\"older inequality and power mean inequality, they obtain some integral inequalities related…
By considering a fixed point in unit disk $\Delta$, a new class of univalent convex functions is defined. Coefficient inequalities, integral operator and extreme points of this class are obtained.
This study focuses on convex functions and their generalized. Thus, we start this study by giving the definition of convex functions and some of their properties and discussing a simple geometric property. Then we generalize E-convex…
In this paper, we establish some new inequalities for class of SX(h,I) convex functions which are supermultiplicative or superadditive and nonnegative. And we also give some applications for special means.
Companions of Ostrowski's integral ineqaulity for absolutely continuous functions and applications for composite quadrature rules and for p.d.f.'s are provided.
The classes of n-Wright-convex functions and n-Jensen-convex functions are compared with each other. It is shown that for any odd natural number $n$ the first one is the proper subclass of the second one. To reach this aim new tools…
Two kinds of novel generalizations of Nesbitt's inequality are explored in various cases regarding dimensions and parameters in this article. Some other cases are also discussed elaborately by using the semiconcave-semiconvex theorem. The…
Recently Nikodem, Rajba and W\k{a}sowicz compared the classes of n-Wright-convex functions and n-Jensen-convex functions by showing that the first one is a proper subclass of the latter one, whenever n is an odd natural number. Till now the…
In this paper, we will improve and generalize inequality of Ostrowski type for mappings whose second derivatives belong to L$_{1}\left(a,b\right) $ . Some well known inequalities can be derived as special cases. In addition, perturbed…
In this paper some new inequalities are proved related to left hand side of Hermite-Hadamard inequality for the classes of functions whose derivatives of absolute values are m-convex. New bounds and estimations are obtained. Applications…
In this paper, two new subclasses of bi-univalent functions related to conic domains are defined by making use of symmetric $q$-differential operator. The initial bounds for Fekete-Szeg\"o inequality for the functions $f$ in these classes…
Let $\Omega$ denote the class of functions $f$ analytic in the open unit disc $\Delta$, normalized by the condition $f(0)=f'(0)-1=0$ and satisfying the inequality \begin{equation*} \left|zf'(z)-f(z)\right|<\frac{1}{2}\quad(z\in\Delta).…
Introduced by Polyak in 1966, the class of strongly quasiconvex functions includes some interesting nonconvex members, like the square root of the Euclidean norm or ratios with a nonnegative strongly convex numerator and a concave and…
Our objective in this paper is to introduce and investigate a newly-constructed subclass of normalized analytic and bi-univalent functions by means of the Chebyshev polynomials of the second kind. Upper bounds for the second and third…
In this paper, two new classes of convex functions as a generalization of convexity which is called (h-s)_{1,2}-convex functions are given. We also prove some Hadamard-type inequalities and applications to the special means are given.
In this paper, we establish (presumably new type) integral inequalities for convex functions via the Hermite--Hadamard's inequalities. As applications, we apply these new inequalities to construct inequalities involving special means of…