Related papers: Gruss Type Discrete Inequalities in Inner Product …

In this paper, it is a fuction that is a GA-convex differentiable for a new identity. As a result of this identity, some new and general integral inequalities for differentiable GA-convex functions are obtained.

In this paper, we establish a broad class of new sharp Alexandrov-Fenchel inequalities involving general convex weight functions for static convex hypersurfaces in hyperbolic space. Additionally, we derive new weighted Minkowski-type…

In this paper, we establish two families of sharp geometric inequalities for closed hypersurfaces in space forms or other warped product manifolds. Both families of inequalities compare three distinct geometric quantities. The first family…

Well-known operations defined on a non-degenerate inner product vector space are extended to the case of a degenerate inner product. The main obstructions to the extension of these operations to the degenerate case are (1) the index…

In this paper, some new Gronwall type inequalities involving iterated integrals are given.

Some reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in Hilbert spaces are given. Applications for complex-valued functions are provided as well.

Let $V$ be a symmetric convex body in $\R^m$. We prove sharp Bernstein-type inequalities for entire functions of exponential type with the spectrum in $V$ and discuss certain properties of the extremal functions. Markov-type inequalities…

Simple inequalities for some integrals involving the modified Struve function of the first kind $\mathbf{L}_{\nu}(x)$ are established. In most cases, these inequalities have best possible constant. We also deduce a tight double inequality,…

A sharp Poincar\'e-type inequality is derived for the restriction of the Gaussian measure on the boundary of a convex set. In particular, it implies a Gaussian mean-curvature inequality and a Gaussian iso second-variation inequality. The…

In this paper, we first prove two new identities for multiplicative differentiable functions. Based on this identity, we establish a midpoint and trapezoid type inequalities for multiplicatively convex functions. Applications to special…

For submanifolds tangent to the structure vector field in cosymplectic space forms, we establish a basic inequality between the main intrinsic invariants of the submanifold, namely its sectional curvature and scalar curvature on one side;…

In this work, a generalization of Chebyshev functional is presented. New inequalities of Gruss type via Pompeiu's mean value theorem are established. Improvements of some old inequalities are proved. A generalization of pre-Gruss inequality…

In this paper, a general integral identity for convex functions is derived. Then, we establish new some inequalities of the Simpson and the Hermite-Hadamard's type for functions whose absolute values of derivatives are convex. Some…

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…

In this paper, we present a generalization of the Huygens types inequalities involving Bessel and modified Bessel functions of the first kind.

In this paper, we establish some weighted fractional inequalities for differentiable mappings whose derivatives in absolute value are convex. These results are connected with the celebrated Hermite-Hadamard-Fejer type integral inequality.…

We initiate a systematic study of intrinsic dimensional versions of classical functional inequalities which capture refined properties of the underlying objects. We focus on model spaces: Euclidean space, Hamming cube, and manifolds of…

The Jensen inequality has been recognized as a powerful tool to deal with the stability of time-delay systems. Recently, a new inequality that encompasses the Jensen inequality was proposed for the stability analysis of systems with finite…

In this work, we investigate the question of how knowledge about expectations $\mathbb{E}(f_i(X))$ of a random vector $X$ translate into inequalities for $\mathbb{E}(g(X))$ for given functions $f_i$, $g$ and a random vector $X$ whose…

Jensen's operator inequality for convexifiable functions is obtained. This result contains classical Jensen's operator inequality as a particular case. As a consequence, a new refinement and a reverse of Young's inequality is given.