| Summary: | Abstract New concepts of f λ , μ $f_{\lambda,\mu }$ -statistical convergence for double sequences of order α̃ and strong f λ , μ $f_{\lambda,\mu }$ -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 w α ˜ , 0 2 ( f , λ , μ ) $w_{\tilde{\alpha },0}^{2} ( f,\lambda,\mu )$ , w α ˜ 2 ( f , λ , μ ) $w_{\tilde{\alpha }}^{2} ( f,\lambda,\mu ) $ and w α ˜ , ∞ 2 ( f , λ , μ ) $w_{\tilde{\alpha},\infty }^{2} ( f,\lambda,\mu )$ . Then we express the properties of strong f λ , μ $f_{\lambda,\mu }$ -Cesàro summability of order β̃ which is related to strong f λ , μ $f_{\lambda,\mu }$ -Cesàro summability of order α̃. Also, some relations between f λ , μ $f_{\lambda,\mu }$ -statistical convergence of order α̃ and strong f λ , μ $f_{\lambda,\mu }$ -Cesàro summability of order α̃ are given.
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