Lacunary sequences of complex uncertain variables defined by Orlicz functions

Using the concept of Orlicz function and uncertainty theory, some new class of lacunary convergent sequences defined by Orlicz functions have been introduced with the lacunary convergence concepts in this paper. Some topological properties of the defined sequence spaces along with the inclusion relations have been investigated.

Kadec–Klee properties of Orlicz–Lorentz sequence spaces equipped with the Orlicz norm

The necessary and sufficient conditions for both the Kadec–Klee property as well as the Kadec–Klee property with respect to the coordinatewise convergence in Orlicz–Lorentz sequence spaces equipped with the Orlicz norm and generated by arbitrary Orlicz functions as well as any non-increasing weight sequences are given. Moreover, for their subspaces of elements with an order continuous norm the full characterization of the Kadec–Klee property with respect to the coordinatewise convergence is presented. Some tools useful in the proofs of the main results are also provided.