Bounded linear transformations in G-fuzzy normed linear space

الملخص EN

In a host of mathematical applications, the bounded linear transformation arises.

The aim of the present work is to report the definition of continuous for linear transformation by using the idea of G-fuzzy normed linear space (GFNLS) with proving the main theorem regarding the continuity.

Besides, the notion of a bounded linear transformation depending on GFNLS is presented and some basic properties related to this notion are proved.

Furthermore, the extension of a bounded linear transformation is discussed and proved.

Finally, a characterization for the notion G-B(X,Y) which is consisting of all bounded linear transformations is presented and proved that this characterization is a complete GFNLS if the space Y is complete.