Related papers: A new treatment of convex functions
First we recall the notion of conxity and log-convexity for real-valued. Then we generalize the trick used by Artin in his famous paper on the Gamma function to find log-convex solutions to the functional equations f(x+1)=g(x)f(x). This…
In this paper, we establish new some Hermite-Hadamard's type inequalities of convex functions of 2-variables on the co-ordinates.
In this paper, we study convex analysis and its theoretical applications. We first apply important tools of convex analysis to Optimization and to Analysis. We then show various deep applications of convex analysis and especially infimal…
The aim of this paper is to present some new Fejer-type results for convex functions. Improvements of Young's inequality (the arithmetic-geometric mean inequality) and other applications to special means are pointed as well.
In this paper, we establish two new convex dominated function and then we obtain new Hadamard type inequalities related to this denitions.
In this paper, we give more general definitions of weighted means and MN-convex functions. Using these definitions, we also obtain some generalized results related to properties of MN-convex functions. The importance of this study is that…
In this paper, we establish new general inequality for convex functions. Then we apply this inequality to obtain the midpoint, trapezoid and averaged midpoint-trapezoid integral inequality. Also, some applications for special means of real…
This research aimed to introduce the concept of harmonically m-convex set-valued functions, which is obtained from the combination of two definitions: harmonically m-convex functions and set-valued functions. In this work some properties…
Sub-additive and super-additive inequalities for concave and convex functions have been generalized to the case of matrices by several authors over a period of time. These lead to some interesting inequalities for matrices, which in some…
This work extends the Mond-Pecaric method to functions with multiple operators as arguments by providing arbitrarily close approximations of the original functions. Instead of using linear functions to establish lower and upper bounds for…
In this paper, we establish some Hadamard-type inequalities based on coordinated quasi-convexity. Also we define a new mapping associated to coordinated convexity and we prove some properties of this mapping.
In this paper, we establish several new inequalities for twice differantiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality. Some applications for special means of real numbers are also provided.
In the paper, the authors find some new integral inequalities of Hermite-Hadamard type for functions whose derivatives of the $n$-th order are $(\alpha,m)$-convex and deduce some known results. As applications of the newly-established…
Geodesic convexity (g-convexity) is a natural generalization of convexity to Riemannian manifolds. However, g-convexity lacks many desirable properties satisfied by Euclidean convexity. For instance, the natural notions of half-spaces and…
Some refinements of the Hermite-Hadamard inequality are obtained in the case of continuous convex functions defined on simplices.
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…
In this paper, we not only give the extensions of the results given in [7] by Gill et al. for log-convex functions, but also obtain some new Hadamard type inequalities for log-convex, m-convex and (alpha,m)-convex functions.
In this paper, we establish some new Hadamard type inequalities for s-logarithmically convex functions in the second sense via fractional integrals by using Lemma 1 which has been proved by Sarikaya et al. in the paper [3].
A considerable amount of literature in the theory of inequality is devoted to the study of Jensen's and Young's inequality. This article presents a number of new inequalities involving the log-convex functions and the geometrically convex…
In this paper, we establish a new refinement of the right-hand side of Hermite-Hadamard inequality for convex functions of several variables defined on simplices.