On Difference Double Sequences and Their Applications

L. Nayak () and P. Baliarsingh ()
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L. Nayak: KIIT University, Department of Mathematics, School of Applied Sciences
P. Baliarsingh: KIIT University, Department of Mathematics, School of Applied Sciences

Chapter Chapter 20 in Current Trends in Mathematical Analysis and Its Interdisciplinary Applications, 2019, pp 809-829 from Springer

Abstract: Abstract Due to its numerous applications in the diverse fields of pure and applied sciences, recently the theory of difference single sequences has been attracted by several researchers. The applications of difference sequences become more apparent in linear algebra, approximation theory, and calculus in both classical and fractional cases. The idea of difference single sequence spaces based on order one has been introduced by Kızmaz (Can Math Bull 24(2):169–176, 1981) in the year 1981. Further, Et and Çolak (Soochow J Math 21(4):377–386, 1995) extended this idea to the case of an integral order in 1995. In order to stimulate its utility and applications, several extensions of this idea have been provided by many prominent authors. Quite recently, the notion of difference sequence spaces based on fractional order was provided by Baliarsingh (Appl Math Comput 219(18):9737–9742, 2013) (see also Baliarsingh and Dutta, Bol Soc Paran Mat 33(1):49–57, 2015; Baliarsingh and Dutta, Appl Math Comput 250:665–674 2015; Baliarsingh and Nayak, Alex Eng J 2017; Baliarsingh, Alex Eng J 55(2):1811–1816, 2016) and the idea was directly being used to study the fractional derivatives of certain functions and their geometrical interpretations.

Date: 2019
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DOI: 10.1007/978-3-030-15242-0_20

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