Statistical approximation with a sequence of 2-Banach spaces

Let X¯={X¯n:n∈N} be a sequence of 22-Banach spaces, where XX denotes an arbitrary 22-Banach space, and let {Tn}{Tn} be a sequence of linear operators Tn:X→X¯. First, a relationship is constructed between X¯n and XX by means of TnTn and next the notion of statistical TT-convergence is introduced. Hence, a statistical approximation theory is constructed between the elements of X¯n and XX. Then, the properties of this statistical approximation theory are examined. On the other hand, the necessary and sufficient conditions for statistical TT-convergence of the elements of X¯n to an element of XX are investigated, and the methods of the determination of the statistical convergence velocity are examined. Finally, we define the statistical approximation and statistical stability conditions of linear operators, and give an application of our results.