A Note on Probability Convergence Defined by Unbounded Modulus Function and $alphabeta$-Statistical Convergence

Some New Type of Difference Sequence Spaces Defined by Modulus Function and Statistical Convergence

In this article we introduce the difference sequence spacesW0[ f ,∆m],W1[ f ,∆m], W∞[ f ,∆m] and S[ f ,∆m], defined by a modulus function f . We obtain a relation between W1[ f ,∆m]∩ l∞[ f ,∆m] and S[ f ,∆m]∩ l∞[ f ,∆m] and prove some inclusion results.

On I-statistical Convergence

In the present paper, we investigate the notion of I -statistical convergence and introduce I -st limit points and I -st cluster points of real number sequence and also studied some of its basic properties.

On statistical type convergence in uniform spaces

The concept of ${mathscr{F}}_{st}$-fundamentality is introduced in uniform spaces, generated by some filter ${mathscr{F}}$. Its equivalence to the concept of ${mathscr{F}}$-convergence in uniform spaces is proved. This convergence generalizes many kinds of convergence, including the well-known statistical convergence.

A note on convergence in fuzzy metric spaces

The sequential $p$-convergence in a fuzzy metric space, in the sense of George and Veeramani, was introduced by D. Mihet as a weaker concept than convergence. Here we introduce a stronger concept called $s$-convergence, and we characterize those fuzzy metric spaces in which convergent sequences are $s$-convergent. In such a case $M$ is called an $s$-fuzzy metric. If $(N_M,ast)$ is a fuzzy metri...

A Note on Subseries Convergence