Lacunary Statistical Convergence of Order \(\alpha\) for Generalized Difference Sequences in Linear Partial Metric Space

In the present study, with the use of generalized difference operator \(\Delta^p\), we have the notion of \(\Delta^p\)-lacunary statistical \(\varphi\)-convergence and \(\Delta^p\)-lacunary strongly \(\varphi\)-Cesàro summability of order \(\alpha\), in partial metric space \((X,\varphi)\), where \(\varphi\) is a partial metric on \(X\). We also analyse these notions with the fusion of modulus function. In addition we also establish some relationship between these concepts.