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\begin{document}
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\noindent\parbox{2.95cm}{\includegraphics*[keepaspectratio=true,scale=0.125]{AFA.jpg}}
\noindent\parbox{4.85in}{\hspace{0.1mm}\\[1.5cm]\noindent
\qquad Ann. Funct. Anal. 2 (2011), no. 2, 114--129\\
{\footnotesize
\qquad \textsc{\textbf{$\mathscr{A}$}nnals of \textbf{$\mathscr{F}$}unctional
\textbf{$\mathscr{A}$}nalysis}\\
\qquad ISSN: 2008-8752 (electronic)\\
\qquad URL: \textcolor[rgb]{0.00,0.00,0.99}{www.emis.de/journals/AFA/}
}\\[.5in]}


\title[On Some Difference Sequence spaces]{On Some Difference Sequence Spaces of Weighted Means and Compact Operators }

\author[M. Ba\c{s}ar\i r, E.E. Kara]{Metin Ba\c{s}ar\i r$^1$$^{*}$ and  Emrah Evren Kara$^2$}

\address{$^{1}$  Department of Mathematics, Sakarya University, 54187, Sakarya, Turkey.}

\email{\textcolor[rgb]{0.00,0.00,0.84}{basarir@sakarya.edu.tr}}

\address{$^{2}$ Department of Mathematics, Bilecik University, 11200, Bilecik, Turkey.}
\email{\textcolor[rgb]{0.00,0.00,0.84}{emrah.kara@bilecik.edu.tr}}

\dedicatory{{\rm Communicated by D. H. Leung}}

\subjclass[2010]{Primary 46A45; Secondary 46B15, 46B50.}

\keywords{$BK$ spaces, Weighted mean, matrix mappings, compact
operators, Hausdorff measure of noncompactness.}

\date{Received: 14 September 2011; Accepted: 6 October 2011.
\newline \indent $^{*}$ Corresponding author}

\begin{abstract}
In the peresent paper, by using generalized weighted mean and difference
matrix of order $m,$ we introduce the sequence spaces $X(u,v,\Delta^{(m)})$,
where $X$ is one of the spaces $\ell_{\infty}$, $c$ or $c_{0}$. Also, we
determine the $\alpha$-, $\beta$- and $\gamma$-duals of those spaces and
construct their Schauder bases for $X\in\{c,c_{0}\}$. Morever, we give the
characterization of the matrix mappings on the spaces $X(u,v,\Delta^{m})$
\ for $X\in\{\ell_{\infty},c,c_{0}\}.$ \ Finally, we \ characterize \ some
classes of compact operators on the spaces $\ell_{\infty}(u,v,\Delta^{m})$ and
$c_{0}(u,v,\Delta^{m})$ by using the Hausdorff measure of noncompactness.
\end{abstract} \maketitle
 \vspace{1.5in}
\end{document}

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