## Abstract and Applied Analysis

### Certain Sequence Spaces over the Non-Newtonian Complex Field

#### Abstract

It is known from functional analysis that in classical calculus, the sets $\omega$, ${\ell }_{\mathrm{\infty }}$, $c$, ${c}_{\mathrm{0}}$ and ${\ell }_{p}$ of all bounded, convergent, null and $p$-absolutely summable sequences are Banach spaces with their natural norms and they are complete according to the metric reduced from their norm, where $0. In this study, our main goal is to construct the spaces ${\omega }^{\mathrm{*}}$, ${\ell }_{\mathrm{\infty }}^{\mathrm{*}}$, ${c}^{\mathrm{*}}$, ${c}_{\mathrm{0}}^{\mathrm{*}}$ and ${\ell }_{p}^{\mathrm{*}}$ over the non-Newtonian complex field ${ℂ}^{\mathrm{*}}$ and to obtain the corresponding results for these spaces, where $\stackrel{¨}{0}\stackrel{¨}{<}p\stackrel{¨}{<}\infty$.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 739319, 11 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393511955

Digital Object Identifier
doi:10.1155/2013/739319

Mathematical Reviews number (MathSciNet)
MR3073475

Zentralblatt MATH identifier
07095309

#### Citation

Tekin, Sebiha; Başar, Feyzi. Certain Sequence Spaces over the Non-Newtonian Complex Field. Abstr. Appl. Anal. 2013 (2013), Article ID 739319, 11 pages. doi:10.1155/2013/739319. https://projecteuclid.org/euclid.aaa/1393511955

#### References

• M. Grossman and R. Katz, Non-Newtonian Calculus, Lowell Technological Institute, 1972.
• A. E. Bashirov, E. M. Kurp\inar, and A. Özyap\ic\i, “Multiplicative calculus and its applications,” Journal of Mathematical Analysis and Applications, vol. 337, no. 1, pp. 36–48, 2008.
• A. Uzer, “Multiplicative type complex calculus as an alternative to the classical calculus,” Computers & Mathematics with Applications, vol. 60, no. 10, pp. 2725–2737, 2010.
• A. Bashirov and M. R\iza, “On complex multiplicative differentiation,” TWMS Journal of Applied and Engineering Mathematics, vol. 1, no. 1, pp. 75–85, 2011.
• A. E. Bashirov, E. M\is\irl\i, Y. Tandoğdu, and A. Özyap\ic\i, “On modeling with multiplicative differential equations,” Applied Mathematics, vol. 26, no. 4, pp. 425–438, 2011.
• C. Türkmen and F. Başar, “Some basic results on the sets of sequences with geometric calculus,” AIP Conference Proceedings, vol. 1470, pp. 95–98, 2012.
• C. Türkmen and F. Başar, “Some basic results on the geometric calculus,” Communications de la Faculté des Sciences de l'Université d'Ankara A$_{1}$, vol. 61, no. 2, pp. 17–34, 2012.
• A. F. Çakmak and F. Başar, “On the classical sequence spaces and non-Newtonian calculus,” Journal of Inequalities and Applications, vol. 2012, Article ID 932734, 13 pages, 2012.
• Ö. Talo and F. Başar, “Determination of the duals of classical sets of sequences of fuzzy numbers and related matrix transformations,” Computers & Mathematics with Applications, vol. 58, no. 4, pp. 717–733, 2009.