Strong lacunary harmonic summability of fractional differences in q-rung orthopair fuzzy normed spaces

Abstract

We study strong lacunary harmonic summability of fractional difference sequences in q-rung orthopair fuzzy normed spaces. The fractional difference is defined on its convergence domain, with an explicit sufficient condition and a truncation estimate for bounded Banach-space-valued sequences. In the canonical norm model, the summability condition is equivalent, on bounded transformed sequences, to strong summability of the norms. We prove linearity, uniqueness and subsequence results for proper admissible ideals, and establish a transfer theorem for distinct lacunary partitions whose harmonic symmetric difference is negligible. In complete spaces, a Cauchy criterion is obtained under bounded normalized row mass; this mass bound holds automatically when beta = 1. Counterexamples explain the failure of a fixed-centre zero-limit condition and the obstruction caused by unbounded row mass. The general summability results concern the transformed sequence, whereas the domain and truncation estimates use the fractional coefficients explicitly.