Related papers: Logarithmic mean inequality for generalized trigon…
Results involving various mean value properties are reviewed for harmonic, biharmonic and metaharmonic functions. It is also considered how the standard mean value property can be weakened to imply harmonicity and belonging to other classes…
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 our aim is to prove some monotonicity and convexity results for the modified Struve function of the second kind by using its integral representation. Moreover, as consequences of these results, we present some functional…
This paper contains a new concept to measure the width and thickness of a convex body in the hyperbolic plane. We compare the known concepts with the new one and prove some results on bodies of constant width, constant diameter and given…
In this paper, the notation of strongly log-convex functions with respect to c>0 is introduced and versions of Hermite Hadamard-type inequalities for strongly logarithmic convex functions are established.
In this paper, an integral identity for twice differentiable functions is generalized. Then, by using convexity of |f''| or q-th power of |f''| and with the aid of power mean and Holder's inequalities we achieved some new results. We also…
We study convexity or concavity of certain trace functions for the deformed logarithmic and exponential functions, and obtain in this way new trace inequalities for deformed exponentials that may be considered as generalizations of…
The aim of this paper is to prove new trigonometric and hyperbolic inequalities, which constitute among others refinements or analogs of famous Cusa-Huygens, Wu-Srivastava, and related inequalities. In most cases, the obtained results are…
This article is the collection of the six research papers, recently written by the authors. In these papers authors refine the inequalities of trigonometric and hyperbolic functions such as Adamovic-Mitrinovic inequality, Cusa-Huygens…
In this paper we established new integral inequalities which are more general results for coordinated convex functions on the coordinates by using some classical inequalities.
The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.
Extending the work of Freese, we further develop the theory of generalized trigonometric functions. In particular, we study to what extent the notion of polar form for the complex numbers may be generalized to arbitrary associative…
In this paper some Tur\'an type inequalities for the general Bessel function, monotonicity and bounds for its logarithmic derivative are derived. Moreover we find the series representation and the relative extrema of the Tur\'anian of…
In this paper we extend some notions, previously defined for log-concave functions, to the larger domain of so-called {\alpha}-concave functions. We begin with a detailed discussion of support functions - first for log-concave functions,…
We establish the log-concavity of the volume of central sections of dilations of the cross-polytope (the strong B-inequality for the cross-polytope and Lebesgue measure restricted to an arbitrary subspace).
In the paper we prove criteria for convexity and concavity of $f$-potentials ($f$-means, Kolmogorov means, weighted quasi-arithmetic means), which particular cases are the arithmetic, geometric, harmonic means, the thermodynamic potential…
We prove that the static convexity is preserved along two kinds of locally constrained curvature flows in hyperbolic space. Using the static convexity of the flow hypersurfaces, we prove new family of geometric inequalities for such…
In this paper, some new inequalities of the Hermite-Hadamard type for functions whose modulus of the derivatives are convex and applications for special means are given. Finally, some error estimates for the trapezoidal formula are…
Asymptotic mean value properties, their converse and some other related results are considered for solutions to the $m$-dimensional Helmholtz equation (metaharmonic functions) and solutions to its modified counterpart (panharmonic…
In this paper we prove a series of Rogers-Shephard type inequalities for convex bodies when dealing with measures on the Euclidean space with either radially decreasing densities, or quasi-concave densities attaining their maximum at the…