In this paper, for every unital $*$-ring $mathcal{S}$, we investigate the Jensen's inequality preserving maps on $C^*$-convex subsets of $mathcal{S}$, which we call them $C^*$-convex maps on $mathcal{S}$. We consider an ...

We consider $C^{bvarphi}(K)$ to be the space $C^b(K)$ equipped with the product $fcdot g=fvarphi g$ for all $f, gin C^b(K)$ where, $K=overline{B_1^{(0)}}$ is the closed unit ball of a non-zero normed vector space $A$ and ...

A Banach algebra $mathfrak{A}$ has a generalized Matrix representation if there exist the algebras $A, B$, $(A,B)$-module $M$ and $(B,A)$-module $N$ such that $mathfrak{A}$ is isomorphic to the generalized matrix Banach ...

Shannon's entropy plays an important role in information theory, dynamical systems and thermodynamics. In this paper we applying Jensen's inequality in information theory and we obtain some results for the Shannon's entropy ...