LACUNARY STATISTICAL CONVERGENCE ON TIME SCALES Yavuz ALTIN, Emrah YILMAZ and Mahmut IŞIK Firat University, Department of Mathematics, 23119 Elazıg,Turkey Firat University, Department of Statistics, 23119 Elazıg, Turkey [email protected] [email protected] [email protected] Abstract: In this study, we introduce the concepts of lacunary density of a set and lacunary statistical convergence on an arbitrary time scale. Furthermore, some relations about these new notations are also obtained. We obtain various characterizations on lacunary statistical convergence which generalize the results in . Keywords : Lacunary Statistical Convergence, Sequence Spaces, Time Scales. AMS Subject Classification: 40A35; 46A45; 47B39; 34N05. References 1. C. Turan and O. Duman, Convergence methods on time scales, 11th international conference of numerical analysis and applied mathematics, AIP conference proceedings, 1558 (2013), 1120-1123. 2. S. Hilger, Analysis on measure chains-A unified approach to continuous and discrete calculus, Results in Mathematics, 18 (1990), 19-56. 3. J. S. Connor, The statistical and strong p-Cesàro convergence of sequences, Analysis, 8 (1988), 47-63. 4. J. A. Fridy and C. Orhan, Lacunary statistical convergence, Pacific Journal of Mathematics, 160 (1993), no. 1, 43--51.