Generalized Lacunary Statistical Difference Sequence Spaces of Fractional Order

Abstract

We generalize the lacunary statistical convergence by introducing the generalized difference operator Δ ] of fractional order, where is a proper fraction and ] = (] ) is any fixed sequence of nonzero real or complex numbers. We study some properties of this operator and investigate the topological structures of related sequence spaces. Furthermore, we introduce some properties of the strongly Cesaro difference sequence spaces of fractional order involving lacunary sequences and examine various inclusion relations of these spaces. We also determine the relationship between lacunary statistical and strong Cesaro difference sequence spaces of fractional order.

The method of almost convergence with operator of the form fractional order and applications

“…Firstly, Baliarsingh [10] is introduced to the difference sequence spaces for fractional order. Later, this operator used in the theory of sequence spaces, in several studies( [25], [11], [12], [22], [27], [28]).…”

Generalized Difference Sequence Spaces of Fractional Order Defined by Orlicz Functions

“…1 as r ! 1: The intervals determined by will be denoted by I r = (k r 1 ; k r ] and the ratio kr kr 1 will be abbreviated by q r , and q 1 = k 1 for convenience: In recent years, lacunary sequences have been studied in ( [7], [8], [9], [21], [23], [24], [40]).…”

On a Generalized Difference Sequence Spaces of Fractional Order associated with Multiplier Sequence Defined by A Modulus Function

“…The studies on generalized difference sequence spaces of fractional orders were extended by Baliarsingh and Dutta [10,11] [26], Kadak [21,22], Furkan [28], Özger [29,30] etc. They studied different sequence spaces of fractional orders.…”

“…They studied different sequence spaces of fractional orders. Kadak in [23] determined a new classes of fractional difference sequence spaces Δ ( ) as follows:…”