In this paper, we present new concepts of f-statistical convergence for double sequences of order \( \widetilde{\alpha }\) and strong f-Cesàro summability for double sequences of order \( \widetilde{\alpha }\) for sequences of (complex or real) numbers. Besides, we give the relationship between the spaces \( w_{\tilde{\alpha },0} ^{2}\left( f\right) , w_{\tilde{\alpha }}^{2}\left( f\right) \) and \( w_{\tilde{\alpha },\infty }^{2}\left( f\right) \). Furthermore, we express the properties of the strong f-Cesàro summability of order \( \widetilde{\beta }\) which is related to strong f-Cesàro summability of order \( \tilde{\alpha }\). Also some relations between f-statistical convergence of order \( \widetilde{\alpha }\) and strong f-Cesàro summability of order \( \widetilde{\alpha }\) are given. The main purpose of this paper is to introduce and examine the concept of f-double statistical convergence of order \( \widetilde{\alpha },\) where f-is an unbounded function and give relations between f-double statistical convergence of order \( \widetilde{\alpha }\) and strong f-Cesàro summability for double sequence of order \( \widetilde{\alpha }\) so as to fill up the existing gaps in the literature.

在本文中，我们的本新概念˚F用于顺序双序列-统计收敛\（\ widetilde {\阿尔法} \）和强˚F用于顺序双序列-Cesàro求和\（\ widetilde {\阿尔法} \）为（复数或实数）数字序列。此外，我们给出了空格之间的关系\（w _ {\ tilde {\ alpha}，0} ^ {2} \ left（f \ right），w _ {\ tilde {\ alpha}} ^ {2} \ left（ f \ right）\）和\（w _ {\ tilde {\ alpha}，\ infty} ^ {2} \ left（f \ right）\）。此外，我们表示强的性质˚F的顺序-Cesàro求和\（\ widetilde {\测试} \）其与强˚F的顺序-Cesàro求和\（\代字号{\阿尔法} \） 。还之间的一些关系˚F的顺序-统计收敛\（\ widetilde {\阿尔法} \）和强˚F的顺序-Cesàro求和\（\ widetilde {\阿尔法} \）中给出。本文的主要目的是介绍和检验f-阶\（\ widetilde {\ alpha}，\）的双重统计收敛性的概念，其中f-是无界函数，并给出f-阶的双重统计收敛性之间的关系\（\ widetilde {\ alpha} \）和强f- Cesàro可积性\（\ widetilde {\ alpha} \），以填补文献中现有的空白。