Acta Mathematica Scientia 2011,31B(3):953–959 http://actams.wipm.ac.cn λ-STATISTICAL CONVERGENCE OF ORDER α ∗ R. C ¸ olak C ¸. A. Bekta¸ s Department of Mathematics, Firat University, 23119, Elazı˘ g T¨ urkiye E-mail: rftcolak@hotmail.com; cigdemas@hotmail.com Abstract In this paper, we introduce the concept of λ-statistical convergence of order α. Also some relations between the λ-statistical convergence of order α and strong (V,λ)- summability of order α are given. Key words sequences; statistical convergence; Ces`aro summability 2000 MR Subject Classification 40A35; 40A05; 40C05; 46A45 1 Introduction The idea of statistical convergence was given by Zygmund [22] in the first edition of his monograph published in Warsaw in 1935. The concept of statistical convergence was introduced by Steinhaus [19] and Fast [5] and later reintroduced by Schoenberg [18] independently. Over the years and under different names statistical convergence was discussed in the theory of Fourier analysis, ergodic theory, number theory, measure theory, trigonometric series, turnpike theory and Banach spaces. Later on it was further investigated from the sequence space point of view and linked with summability theory by Fridy [6], Connor [3], Sava¸ s [17], Mursaleen [12], Fridy and Orhan [7], M´ oricz [11], Rath and Tripathy [14], Salat [16], Bhardwaj [1] and many others. In recent years, generalizations of statistical convergence appeared in the study of strong integral summability and the structure of ideals of bounded continuous functions on locally compact spaces. Statistical convergence and its generalizations were also connected with subsets of the Stone- ˇ Cech compactification of the natural numbers. Moreover, statistical convergence is closely related to the concept of convergence in probability. A sequence x =(x k ) is said to be statistical convergent to the number L if, for every ε> 0, lim n→∞ 1 n |{k ≤ n : |x k - L|≥ ε}| =0, where the vertical bars indicate the number of elements in the enclosed set. In this case, we write S - lim x = L or x k → L(S) and S denotes the set of all statistically convergent sequences. The statistical convergence with degree 0 <β< 1 was given by Gadjiev and Orhan [8] for a number sequence, and then it was generalized for the method of A-statistical convergence * Received June 15, 2009; revised November 4, 2009. This research was supported by FUBAP under the Project no. 1683.