Construction of Lacunary Sequence Spaces via Modulus Function and Nörlund-Mean of Order α
Year: 2026
Type: article
Abstract: In this work, we introduce new classes of lacunary sequence spaces based on Nörlund-type means, a sequence of modulus functions and the order parameter 0<α≤1. The main novelty is the incorporation of these components into a weighted Nörlund-lacunary framework. We establish inclusion and equivalence relations with classical Nörlund-type and lacunary sequence spaces under explicit conditions on the weight and lacunary sequences. We further characterize weighted lacunary statistical convergence of order α and investigate its relationships with the corresponding convergence spaces. Finally, we prove the completeness and topological properties of the resulting paranormed sequence spaces. These results extend existing frameworks for lacunary and Nörlund-type sequence spaces.
Source: Axioms
Authors: Hong-Wei Wang, Priyanka Sharma, Kuldip Raj, Sunil K. Sharma, Qing-Bo Cai
Institutions: Quanzhou Normal University, Shri Mata Vaishno Devi University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
OpenAlex ID: W7208754967