Vol. 2 No. 4 (2009)

We introduce new area Nevanlinna type spaces in the unit disk and polydisk and study the action of classical operator of differentiation on them. We substantially complement the list of previously known assertions of this type.

In the present paper we prove some coincidence common fixed point theorems for a family of hybrid pairs of mappings in metrically convex spaces by using the notion of pointwise R-weakly commuting mappings.

$k$-deficit Banach frames have been defined and studied. It has been proved that if a Banach space has a Banach frame having \mbox{$k$-deficit} $(k\geq 0)$, then its second conjugate space has a retro Banach frame. Also, we prove results regarding existence of \mbox{$k$-deficit} Banach frames in subspaces and super spaces of a Banach space and deduce that $\ell^\infty$ does not have a \mbox{$k$-deficit} Banach frame for any $k$. Finally, we prove the equivalence of two statements regarding Banach frames.