Refinement of Jensen’s Inequality with Applications to Cyclic Mixed Symmetric Means and Cauchy Means Ilko Brnetić, Khuram

Refinements of Results about Weighted Mixed Symmetric Means and Related Cauchy Means

A parameter-dependent refinement of the discrete Jensen's inequality for convex and mid-convex functions

Correspondence: lhorvath@almos. vein.hu Department of Mathematics, University of Pannonia, 8200 Veszprém, Egyetem u. 10., Hungary Abstract In this paper, a new parameter-dependent refinement of the discrete Jensen’s inequality is given for convex and mid-convex functions. The convergence of the introduced sequences is also studied. One of the proofs requires an interesting convergence theorem w...

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.

On generalization of refinement of Jensen’s inequality using Fink’s identity and Abel-Gontscharoff Green function

In this paper, we formulate new Abel-Gontscharoff type identities involving new Green functions for the 'two-point right focal' problem. We use Fink's identity and a new Abel-Gontscharoff-type Green's function for a 'two-point right focal' to generalize the refinement of Jensen's inequality given in (Horváth and Pečarić in Math. Inequal. Appl. 14: 777-791, 2011) from convex function to higher o...

One Refinement of Jensen’s Discrete Inequality and Applications

Jensen’s inequality induces different forms of functionals which enables refinements for many classic inequalities ([5]). Several refinements of Jensen’s inequalities were given in [4]. In this paper we refine Jensen’s inequality by separating a discrete domain of it. At the end, we give some applications. Mathematics subject classification (2000): 26D15.