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...

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...