We consider Lorentz–Karamata spaces, small and grand the so-called L $\mathcal {L}$ , R {R}$ LL {LL}$ LR {LR}$ RL {RL}$ RR {RR}$ spaces. The quasi-norms for a function f in each of these spaces can be defined via nonincreasing rearrangement ∗ $f^*$ or maximal $f^{**}$ . investigate when are equivalent. Most proofs based on Hardy-type inequalities. As an application, we demonstrate how our gener...

Recently, the algebraic theory of MV -algebras is intensively studied. In this paper, we extend the concept of derivation of $MV$-algebras and we give someillustrative examples. Moreover, as a generalization of derivations of $MV$ -algebraswe introduce the notion of $f$-derivations and $(f; g)$-derivations of $MV$-algebras.Also, we investigate some properties of them.