THE ESTIMATION OF THE GRAPH BOX DIMENSION OF A CLASS OF FRACTALS ALINA BˆRBULESCU Ovidius University, Constanta, Romania Abstract Fractal dimensions are the most important attributes of fractals and the Box counting dimension is widely used. Usually it is not so easy to determine dimensions. In some papers we have considered a class of functions and we have studied the finitude of the Hausdorff h-measures of the graph, ˆ, of an element of this class. In this paper we determine the Box dimension of ˆ. Keywords: Box dimension, Haudorff h-measure, Hadamard condition 1. INTRODUCTION The importance of the fractal sets in sciences increases in the last years. The most important attributes of fractals are the dimensions. For the Besicovitch functions, given by         1 2 cos k k s k t t B , (1) where , 2 1   s 0   and      k k lim , the fractal dimension have been estimated, in some cases ([5]), but their exact fractal dimension is unknown. Definition 1 Let R n be the Euclidean n - dimensional space. If 0 0  r is a given number, then, a continuous function h(r), defined on [0, 0 r ), nondecreasing and such that   0 lim 0   r h r is called a measure function. If , 0   E is a nonempty and bounded subset of R n and h is a measure function then, the Hausdorff h - measure of E is defined by:                    i i h h E H inf lim 0 , The 7 th Balkan Conference on Operational Research BACOR 05 Constanta, May 2005, Romania