In this paper, we present new concepts of f-statistical convergence for double sequences of order ea and strong f-Cesaro summability for double sequences of order ea for sequences of (complex or real) numbers. Besides, we give the relationship between the spaces w2/alpha similar to;0o f THORN; w2/alpha (f ) THORN and w2/alpha;1(f) THORN. Furthermore, we express the properties of the strong f-Cesa` ro summability of order eb which is related to strong f-Cesaro summability of order alpha similar to. Also some relations between f-statistical convergence of order ea and strong f-Cesaro summability of order ea are given. The main purpose of this paper is to introduce and examine the concept of f-double statistical convergence of order alpha similar to where f-is an unbounded function and give relations between f-double statistical convergence of order ea and strong f-Cesaro summability for double sequence of order ea so as to fill up the existing gaps in the literature.
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