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Register a new userTwo Dimensional Integral Inequalities on Time Scales
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In this paper, we formulate and prove Wendroffs inequalities on time scales. Next, we deduct some of Pachpattes inequalities.
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We introduce and investigate the concept of harmonical $h$-convexity for interval-valued functions. Under this new concept, we prove some new Hermite-Hadamard type inequalities for the interval Riemann integral.
The common in ring, module and algebra is that they are Abelian group with respect to addition. This property is enough to study integration. I treat integral of measurable map into normed Abelian $Omega$-group. Theory of integration of maps into $Omega$-group has a lot of common with theory of integration of functions of real variable. However I had to change some statements, since they implicitly assume either compactness of range or total order in $Omega$-group.
This paper is focused on $f$-divergences, consisting of three main contributions. The first one introduces integral representations of a general $f$-divergence by means of the relative information spectrum. The second part provides a new approach for the derivation of $f$-divergence inequalities, and it exemplifies their utility in the setup of Bayesian binary hypothesis testing. The last part of this paper further studies the local behavior of $f$-divergences.
We study exponential stability for a kind of neural networks having time-varying delay. By extending the auxiliary function-based integral inequality, a novel integral inequality is derived by using weighted orthogonal functions of which one is discontinuous. Then, the new inequality is applied to investigate the exponential stability of time-delay neural networks via Lyapunov-Krasovskii functional (LKF) method. Numerical examples are given to verify the advantages of the proposed criterion.
We prove Cauchys formula for repeated integration on time scales. The obtained relation gives rise to new notions of fractional integration and differentiation on arbitrary nonempty closed sets.
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