scholarly journals On a new class of generalized difference sequence spaces of fractional order defined by modulus function

2019 ◽  
Vol 38 (3) ◽  
pp. 485-497
Author(s):  
Taja Yaying
Keyword(s):  
Fractional Order ◽  
Sequence Spaces ◽  
Modulus Function ◽  
Difference Sequence ◽  
New Class ◽  
Difference Sequence Spaces

scholarly journals On some generalized difference sequences with respect to a modulus function

Filomat ◽  
2003 ◽  
pp. 23-33 ◽  
Author(s):  
Mikail Et ◽  
Yavuz Altin ◽  
Hifsi Altinok
Keyword(s):  
Banach Space ◽  
Sequence Spaces ◽  
Modulus Function ◽  
Difference Sequence ◽  
Difference Sequences ◽  
Inclusion Relations ◽  
Difference Sequence Spaces

The idea of difference sequence spaces was intro- duced by Kizmaz [9] and generalized by Et and Colak [6]. In this paper we introduce the sequence spaces [V, ?, f, p]0 (?r, E), [V, ?, f, p]1 (?r, E), [V, ?, f, p]? (?r, E) S? (?r, E) and S?0 (?r, E) where E is any Banach space, examine them and give various properties and inclusion relations on these spaces. We also show that the space S? (?r, E) may be represented as a [V, ?, f, p]1 (?r, E)space.

scholarly journals Generalized rough lacunary statistical triple difference sequence spaces in probability of fractional order defined by Musielak-Orlicz functionGeneralized rough lacunary statistical triple difference sequence spaces in probability of fractional order defined by Musielak-Orlicz function

2017 ◽  
Vol 37 (1) ◽  
pp. 55-62
Author(s):  
Shyamal Debnath ◽  
N. Subramanian
Keyword(s):  
Fractional Order ◽  
Orlicz Function ◽  
Lacunary Sequence ◽  
Sequence Spaces ◽  
Arbitrary Sequence ◽  
Difference Sequence ◽  
Positive Real ◽  
Topological Structures ◽  
Triple Difference ◽  
Difference Sequence Spaces

We generalized the concepts in probability of rough lacunary statistical by introducing the diference operator of fractional order, where is a proper fraction and = (mnk ) is anyxed sequence of nonzero real or complex numbers. We study some properties of this operator involving lacunary sequence and arbitrary sequence p = (prst) of strictly positive real numbers and investigate the topological structures of related triple diference sequence spaces. The main focus of the present paper is to generalized rough lacunary statistical of triple diference sequence spaces and investigate their topological structures as well as some inclusion concerning the operator :

scholarly journals Some New Difference Sequence Spaces of Invariant Means Defined by Ideal and Modulus Function

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Sudhir Kumar ◽  
Vijay Kumar ◽  
S. S. Bhatia
Keyword(s):  
Sequence Spaces ◽  
Modulus Function ◽  
Difference Sequence ◽  
Topological Properties ◽  
Ideal Convergence ◽  
Difference Sequences ◽  
Invariant Means ◽  
Difference Sequence Spaces

The main objective of this paper is to introduce a new kind of sequence spaces by combining the concepts of modulus function, invariant means, difference sequences, and ideal convergence. We also examine some topological properties of the resulting sequence spaces. Further, we introduce a new concept of SθσΔm(I)-convergence and obtain a condition under which this convergence coincides with above-mentioned sequence spaces.

Sign in / Sign up

Export Citation Format

Share Document