In this paper several tensorial norm inequalities for continuous functions of selfadjoint operators in Hilbert space have been obtained. The
recent progression of the Hilbert space inequalities following the definition of the convex operator inequality has lead researchers to explore the
concept of Hilbert space inequalities even further. The motivation for
this paper stems from the recent development in the theory of tensorial
and Hilbert space inequalities. Multiple inequalities are obtained with
variations due to the convexity properties of the mapping $f$
$$\bigg|\bigg|\frac{1}{6}\left(\operatorname{exp}(A)\otimes 1+4\operatorname{exp}\left(\frac{A\otimes 1+1\otimes B}{2}\right)+1\otimes \operatorname{exp}(B)\right)$$
$$-\frac{1}{4}\bigg(\int_{0}^{1}\operatorname{exp}\left(\left(\frac{1-k}{2}\right)A\otimes 1+\left(\frac{1+k}{2}\right)1\otimes B\right)k^{-\frac{1}{2}}dk$$
$$+\int_{0}^{1}\operatorname{exp}\left(\left(1-\frac{k}{2}\right)A\otimes 1+\frac{k}{2}1\otimes B\right)(1-k)^{-\frac{1}{2}}dk\bigg)\bigg|\bigg|$$
$$\leq \frac{47}{360}\norm{1\otimes B-A\otimes 1}^{2}(\norm{\operatorname{exp}(A)}+\norm{\operatorname{exp}(B)}).$$
Tensorial version of a Lemma given by Hezenci is derived and utilized
to obtain the desired inequalities. In the introduction section is given a
brief history of the inequalities, while in the preliminary section we give
necessary Lemmas and results in order to understand the paper. Structure and novelty of the paper are discussed at the end of the introduction section.