A STUDY ON LACUNARY STRONG CONVERGENCE ACCORDING TO MODULUS FUNCTIONS - Hatim, Mustafa I.; Bekta, Cigdem A. (Publ House Bulgarian Acad Sci, 2023)
In this article, we study a new generalization of the lacunary strongly convergent sequences and introduce the concept of lacunary strong convergence according to gk for sequences of complex (or real) numbers, where gk = g degrees g degrees center dot center dot center dot degrees g (k times) represents a composite modulus function. After that, we determine the connections of lacunary strong convergence and lacunary statistical convergence to lacunary strong convergence according to gk. Furthermore, we investigate several properties of this generalization.
Keywords: sequence space; modulus function; lacunary sequence; strong convergence; statistical convergence