In this article we study metric spaces which admit polynomial diameter-volume inequalities for k-dimensional cycles. These generalize the notion of cone type inequalities introduced by M. Gromov in his seminal paper Filling Riemannian manifolds. In a first part we prove a polynomial isoperimetric inequality for k-cycles in such spaces, generalizing Gromov’s isoperimetric inequality of Euclidean...

Here we have studied the notion of rough I-convergence as an extension work idea convergence in a cone metric space using ideals. We further introduced I∗-convergence sequences to find relationship between I and sequences.