Related papers: Some integral inequalities on time scales
This paper uses differential spaces to obtain some new results in integrable Hamiltonian systems
In this paper, we establish some new integral inequalities for for m- and (alpha,m)-logarithmically convex functions.
We define a more general type of integral on time scales. The new diamond integral is a refined version of the diamond-alpha integral introduced in 2006 by Sheng et al. A mean value theorem for the diamond integral is proved, as well as…
This paper provides new summation inequalities in both single and double forms to be used in stability analysis of discrete-time systems with time-varying delays. The potential capability of the newly derived inequalities is demonstrated by…
We introduce a discrete-time fractional calculus of variations on the time scales $\mathbb{Z}$ and $(h\mathbb{Z})_a$. First and second order necessary optimality conditions are established. Some numerical examples illustrating the use of…
In this paper, we establish some new integral inequalities for $(\alpha, m)-$convex functions and quasi-convex functions, respectively. Our results in special cases recapture known results.
In this paper, new inequalities connected with the celebrated Steffensen's integral inequality are proved.
This paper contains a review of available methods for establishing improved interpolation inequalities on the sphere for subcritical exponents. Pushing further these techniques we also establish some new results, clarify the range of…
This paper deals with generalized elliptic integrals and generalized modular functions. Several new inequalities are given for these and related functions.
We offer new proofs, refinements as well as new results related to classical means of two variables, including the identric and logarithmic means.
We introduce two new inconsistency measures for the incomplete pairwise comparisons matrices and show several examples of their calculation. We also carry out a comparative analysis of the new inconsistency indices with the existing ones…
In this paper, an extension of the generalized free matrix based inequality is introduced in a unified form suitable for the estimation of integrals and sums of quadratic functions. The equivalences of several known variants are shown,…
This is a short overview of some recent tendencies in the theory of linear inequalities that are evoked by Boolean valued analysis.
In this short note, we provide an elementary complex analytic method for converting known real integrals into numerous strange and interesting looking real integrals.
We introduce a fractional calculus on time scales using the theory of delta (or nabla) dynamic equations. The basic notions of fractional order integral and fractional order derivative on an arbitrary time scale are proposed, using the…
We consider some integral-geometric quantities that have recently arisen in harmonic analysis and elsewhere, derive some sharp geometric inequalities relating them, and place them in a wider context.
In this article, we show multiple inequalities for the singular values of the difference of matrix means. The obtained results refine and complement some well established results in the literature. Although we target singular values…
We discuss the inequalities for $q$-integrals because of the fact that the inequalities can be very useful in the future mathematical research. Since $q$-integral of a function over an interval $[a,b]$ is defined by the difference of two…
This paper re-examines the first normalized incomplete moment, a well-established measure of inequality with wide applications in economic and social sciences. Despite the popularity of the measure itself, existing statistical inference…
This paper presents a brief survey of the most important and the most remarkable inequalities involving the basic arithmetic functions.