We give several inequalities on generalized entropies involving Tsallis entropies, using some inequalities obtained by improvements of Young’s inequality. We also give a generalized Han’s inequality.

In this paper, we investigate Jordan ∗-homomorphisms on C∗-algebras associated with the following functional inequality ‖f( b−a 3 ) + f( a−3c 3 ) + f( 3a+3c−b 3 )‖ ≤ ‖f(a)‖. We moreover prove the superstability and the generalized Hyers-Ulam stability of Jordan ∗homomorphisms on C∗-algebras associated with the following functional equation f( b− a 3 ) + f( a− 3c 3 ) + f( 3a+ 3c− b 3 ) = f(a).

The focus of this article is on entropy and Markov processes. We study the properties of functionals which are invariant with respect to monotonic transformations and analyze two invariant “additivity” properties: (i) existence of a monotonic transformation which makes the functional additive with respect to the joining of independent systems and (ii) existence of a monotonic transformation whi...

In the present paper, we would like to draw attention to a possible generalized Fisher information that ts well in the formalism of nonextensive thermostatistics. This generalized Fisher information is de ned for densities on R. Just as the maximum Rényi or Tsallis entropy subject to an elliptic moment constraint is a generalized qGaussian, we show that the minimization of the generalized Fishe...

In this note we prove a discrete analogue of the continuous Halanay inequality and apply it to derive sufficient conditions for the global asymptotic stability of the equilibrium of certain generalized difference equations. The relation with some numerical schemes for functional delay differential equations is discussed.

We prove two kinds of Lyapunov type inequalities for pseudo-integrals. One discusses pseudo-integrals where pseudo-operations are given by a monotone and continuous function g. The other one focuses on the pseudo-integrals based on a semiring 0; 1 ½ Š; sup; ð Þ , where the pseudo-multiplication is generated. Some examples are given to illustrate the validity of these inequalities. As a generali...

In this paper, we establish an existence result of the solution for an generalized strong vector variational inequality already considered in the literature and as applications we obtain a new coincidence point theorem in Hilbert spaces.    

A generalized definition of the monogamy relation for entanglement measures is provided. equality rather than usual inequality presented based on weight, from which relations are given satisfied by ?th ( ? > 0 ) $(\alpha >0)$ power measures. Taking concurrence as an example, significance and advantages these further demonstrated. In addition, it shown that can be recovered considering multiple ...

A new generalized nonlinear variational-like inequality is introduced and studied. By applying the auxiliary principle technique and KKM theory, we construct a new iterative algorithm for solving the generalized nonlinear variational-like inequality. By means of the Banach fixed-point theorem, we establish the existence and uniqueness of solution for the generalized nonlinear variational-like i...