in this paper, we introduce the notion of an action $y_x$as a generalization of the notion of a module,and the notion of a norm $vt: y_xto f$, where $f$ is a field and $vartriangle(xy)vartriangle(y') =$ $ vartriangle(y)vartriangle(xy')$ as well as the notion of fuzzy norm, where $vt: y_xto [0, 1]subseteq {bf r}$, with $bf r$  the set of all real numbers. a great many standard mappings on algebr...

Norm and essential norm of differences of differentiation composition operators between Bloch spaces have been estimated in this paper. As a result, we find characterizations for boundedness and compactness of these operators.

We present a proof that in Orlicz spaces the Amemiya norm and the Orlicz norm coincide for any Orlicz function ‘p. This gives the answer for an open problem. We also give a description of the Amemiya type for the Mazur-Orlicz F-norm.

In this note, we provide detailed characterization of operators in terms norm-attainability and norm estimates Banach algebras. particular, establish the necessary sufficient conditions for derivations also give their bounds norm-attainable classes.

concern over the depletion of natural resources in general, and water scarcity in particular, has stimulated the development and implementation of some policies aimed at changing farmers' behavior in terms of conserving water. in this regard, government has recently begun to invest on researches supporting the technical solutions on conserving water in the agricultural sector as the bigges...