We establish a generalized Hyers–Ulam–Rassias stability theorem in the fuzzy sense. In particular, we introduce the notion of fuzzy approximate Jensen mapping and prove that if a fuzzy approximate Jensen mapping is continuous at a point, then we can approximate it by an everywhere continuous Jensen mapping. As a fuzzy version of a theorem of Schwaiger, we also show that if every fuzzy approxima...

Some new inequalities related to Jensen and Ostrowski inequalities for general Lebesgue integral are obtained. Applications for $f$-divergence measure are provided as well.

Entropy-based divergence measures have shown promising results in many areas of engineering and image processing. In this paper, we define a new generalized divergence measure, namely, the Jensen–Rényi divergence. Some properties such as convexity and its upper bound are derived. Based on the Jensen–Rényi divergence, we propose a new approach to the problem of image registration. Some appealing...

Abstract We investigate the use of parameterized families information-theoretic measures to generalize loss functions generative adversarial networks (GANs) with objective improving performance. A new generator function, least kth-order GAN (LkGAN), is introduced, generalizing squares GANs (LSGANs) by using a absolute error distortion measure k≥1 (which recovers LSGAN function when k=2). It sho...

We study metric properties of symmetric divergences on Hermitian positive definite matrices. In particular, we prove that the square root these is a distance metric. As corollary obtain proof property for Quantum Jensen-Shannon-(Tsallis) (parameterized by α∈[0,2]). When specialized to α=1, as Jensen-Shannon divergence was conjectured Lamberti et al. (2008) [13], and recently also proved Viroszt...