Construction of Lacunary Sequence Spaces via Modulus Function and Nörlund-Mean of Order α

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.