Abstract
The goal of this paper is to define and study λ-double almost statistical convergence of order α. Further some inclusion relations are examined. We also introduce a new sequence space by combining the double almost statistical convergence and an Orlicz function.
Highlights
The notion of statistical convergence was introduced by Fast [ ] and Schoenberg [ ] independently
Over the years and under different names, statistical convergence was discussed in the theory of Fourier analysis, ergodic theory and number theory
Later on it was further investigated from the sequence space point of view and linked with summability theory by Fridy [ ], Connor [ ], Salát [ ], Cakalli [ ], Miller [ ], Maddox [ ] and many others
Summary
The notion of statistical convergence was introduced by Fast [ ] and Schoenberg [ ] independently. Móricz and Rhoades [ ] defined the almost convergence of the double sequence as follows: x = (xij) is said to be almost convergent to a number L if The double statistical convergence of order α is defined as follows.
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