New concepts of fλ,μ\documentclass[12pt]{minimal}
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\begin{document}$f_{\lambda,\mu }$\end{document}-statistical convergence for double sequences of order α̃ and strong fλ,μ\documentclass[12pt]{minimal}
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\begin{document}$f_{\lambda,\mu }$\end{document}-Cesàro summability for double sequences of order α̃ are introduced for sequences of (complex or real) numbers. Furthermore, we give the relationship between the spaces wα˜,02(f,λ,μ)\documentclass[12pt]{minimal}
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\begin{document}$w_{\tilde{\alpha },0}^{2} ( f,\lambda,\mu )$\end{document}, wα˜2(f,λ,μ)\documentclass[12pt]{minimal}
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\begin{document}$w_{\tilde{\alpha }}^{2} ( f,\lambda,\mu ) $\end{document} and wα˜,∞2(f,λ,μ)\documentclass[12pt]{minimal}
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\begin{document}$w_{\tilde{\alpha},\infty }^{2} ( f,\lambda,\mu )$\end{document}. Then we express the properties of strong fλ,μ\documentclass[12pt]{minimal}
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\begin{document}$f_{\lambda,\mu }$\end{document}-Cesàro summability of order β̃ which is related to strong fλ,μ\documentclass[12pt]{minimal}
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\begin{document}$f_{\lambda,\mu }$\end{document}-Cesàro summability of order α̃. Also, some relations between fλ,μ\documentclass[12pt]{minimal}
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\begin{document}$f_{\lambda,\mu }$\end{document}-statistical convergence of order α̃ and strong fλ,μ\documentclass[12pt]{minimal}
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\begin{document}$f_{\lambda,\mu }$\end{document}-Cesàro summability of order α̃ are given.
