In a recent publication, Baliarsingh [5] introduced a new concept of generalized fractional difference sequences using the difference operator \(\Delta ^{p, q, r}\) . This research article introduces the notions of deferred statistical \(\Delta ^{p, q, r}_{\tau }\) – convergence and the corresponding deferred statistically \(\Delta ^{p,q,r}_{\tau }\) – Cauchy sequences of order \((\alpha , \beta )\) in the framework of locally solid Riesz spaces endowed with a topology \(\tau\) . We also develop the concept of deferred statistical \(\Delta ^{p,q,r}_{\tau ^{*}}\) – convergence of order \((\alpha , \beta )\) in locally solid Riesz spaces and study its relationship with the deferred statistical \(\Delta ^{p, q, r}_{\tau }\) – convergence of order \((\alpha , \beta )\) . Moreover, we explore the deferred statistical \(\Delta ^{p,q,r}_{\tau }\) – continuity of order \((\alpha , \beta )\) of functions defined on a locally solid Riesz space and investigate its relationship with uniform continuity.
