I-convergence and I-continuity

We introduce and study of I-convergence of sequences in metric spaces, where I is an ideal of subsets of the set N of positive integers. We extend this concept to I-convergence of sequence of real functions defined on a metric space and prove some theorems and basic properties of this concepts. This basic properties deal with extremal I-limit points. Further the concept of statistical convergence generalize to I-convergence and the conclusions of statistical convergence extend to I- convergence. Besides we introduce a new notion of continuity, which is the generalization of statistical continuity of functions. We generalize the notion of I-continuity, which was defined for real functions by transforming to functions on arbitrary topological spaces. Further we show the equvalence of I-continuity and continuity for metric spaces and sequential spaces as well.