Kluv\'{a}nek-Lewis-Henstock integral in a Banach space

We investigate some properties and convergence theorem of Kluv'{a}nek-Lewis-Henstock $\text{m}-$integrability for $\text{m}-$measurable functions that we introduced in \cite{ABH}. We give a $\text{m}-$a.e. convergence version of Dominated (resp. Bounded) Convergence Theorem for $\text{m}\mathrm{.}$ We introduce Kluv'{a}nek-Lewis-Henstock integrable of scalar-valued functions with respect to a set valued measure in a Banach space. Finally we introduce $(KL)-$type Dominated Convergence Theorem for the set-valued Kluv'{a}nek-Lewis-Henstock integral.