## Abstract and Applied Analysis

### New Classes of Generalized Seminormed Difference Sequence Spaces

#### Abstract

The purpose of this paper is to introduce new classes of generalized seminormed difference sequence spaces defined by a Musielak-Orlicz function. We also study some topological properties and prove some inclusion relations between resulting sequence spaces.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 461081, 7 pages.

Dates
First available in Project Euclid: 7 October 2014

https://projecteuclid.org/euclid.aaa/1412687043

Digital Object Identifier
doi:10.1155/2014/461081

Mathematical Reviews number (MathSciNet)
MR3219373

Zentralblatt MATH identifier
07022422

#### Citation

Mursaleen, M.; Alotaibi, A.; Sharma, Sunil K. New Classes of Generalized Seminormed Difference Sequence Spaces. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 461081, 7 pages. doi:10.1155/2014/461081. https://projecteuclid.org/euclid.aaa/1412687043

#### References

• W. L. C. Sargent, “Some sequence spaces related to the ${l}^{p}$ spaces,” Journal of the London Mathematical Society, vol. 35, pp. 161–171, 1960.
• E. Malkowsky and Mursaleen, “Matrix transformations between FK-spaces and the sequence spaces $m(\varphi )$ and $n(\varphi )$,” Journal of Mathematical Analysis and Applications, vol. 196, no. 2, pp. 659–665, 1995.
• Mursaleen, “Some geometric properties of a sequence space related to ${l}^{p}$,” Bulletin of the Australian Mathematical Society, vol. 67, no. 2, pp. 343–347, 2003.
• M. Mursaleen, R. Çolak, and M. Et, “Some geometric inequalities in a new Banach sequence space,” Journal of Inequalities and Applications, vol. 2007, Article ID 86757, 6 pages, 2007.
• B. C. Tripathy and M. Sen, “On a new class of sequences related to the space ${l}^{p}$,” Tamkang Journal of Mathematics, vol. 33, no. 2, pp. 167–171, 2002.
• H. K\izmaz, “On certain sequence spaces,” Canadian Mathematical Bulletin, vol. 24, no. 2, pp. 169–176, 1981.
• Mursaleen, “Generalized spaces of difference sequences,” Journal of Mathematical Analysis and Applications, vol. 203, no. 3, pp. 738–745, 1996.
• M. Et and R. Çolak, “On some generalized difference sequence spaces,” Soochow Journal of Mathematics, vol. 21, no. 4, pp. 377–386, 1995.
• M. Et and M. Basarir, “On some new generalized difference sequence spaces,” Periodica Mathematica Hungarica, vol. 35, no. 3, pp. 169–175, 1997.
• H. Dutta, “On some difference sequence spaces,” The Pacific Journal of Science and Technology., vol. 10, pp. 243–247, 2009.
• H. Dutta, “Some statistically convergent difference sequence spaces defined over real 2-normed linear spaces,” Applied Sciences, vol. 12, pp. 37–47, 2010.
• E. Malkowsky, M. Mursaleen, and S. Suantai, “The dual spaces of sets of difference sequences of order $m$ and matrix transformations,” Acta Mathematica Sinica, vol. 23, no. 3, pp. 521–532, 2007.
• M. Mursaleen, V. Karakaya, H. Polat, and N. Simşek, “Measure of noncompactness of matrix operators on some difference sequence spaces of weighted means,” Computers & Mathematics with Applications, vol. 62, no. 2, pp. 814–820, 2011.
• M. Mursaleen and A. K. Noman, “On some new difference sequence spaces of non-absolute type,” Mathematical and Computer Modelling, vol. 52, no. 3-4, pp. 603–617, 2010.
• M. Mursaleen and A. K. Noman, “Compactness of matrix operators on some new difference sequence spaces,” Linear Algebra and its Applications, vol. 436, no. 1, pp. 41–52, 2012.
• K. Raj, S. K. Sharma, and A. K. Sharma, “Difference sequence spaces in $n$-normed spaces defined by Musielak-Orlicz function,” Armenian Journal of Mathematics, vol. 3, no. 3, pp. 127–141, 2010.
• K. Raj and S. K. Sharma, “Some sequence spaces in 2-normed spaces defined by Musielak-Orlicz function,” Acta Universitatis Sapientiae. Mathematica, vol. 3, no. 1, pp. 97–109, 2011.
• M. Mursaleen, S. K. Sharma, and A. K\il\içman, “Sequence spaces defined by Musielak-Orlicz function over $n$-normed spaces,” Abstract and Applied Analysis, vol. 2013, Article ID 364743, 10 pages, 2013.
• K. Raj and S. K. Sharma, “Some multiplier sequence spaces defined by a Musielak-Orlicz function in $n$-normed spaces,” New Zealand Journal of Mathematics, vol. 42, pp. 45–56, 2012.
• F. Başar and B. Altay, “On the space of sequences of $p$-bounded variation and related matrix mappings,” Ukrainian Mathematical Journal, vol. 55, no. 1, pp. 108–118, 2003.
• M. Başarir and M. Kayikçi, “On the generalized ${B}^{m}$-Riesz difference sequence space and $\beta$-property,” Journal of Inequalities and Applications, vol. 2009, Article ID 385029, 18 pages, 2009.
• J. Lindenstrauss and L. Tzafriri, “On Orlicz sequence spaces,” Israel Journal of Mathematics, vol. 10, pp. 379–390, 1971.
• L. Maligranda, Orlicz Spaces and Interpolation, Seminars in Mathematics, Polish Academy of Science, 1989.
• J. Musielak, Orlicz Spaces and Modular Spaces, vol. 1034 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1983.
• P. K. Kamthan and M. Gupta, Sequence Spaces and Series, Marcel Dekker, New York, NY, USA, 1980.
• T. Bilgin, “The sequence space $l(p,f,q,s)$ on seminormed spaces,” Bulletin of the Calcutta Mathematical Society, vol. 86, no. 4, pp. 295–304, 1994.
• A. Esi, “On a class of new type difference sequence spaces related to the space ${l}^{p}$,” Far East Journal of Mathematical Sciences, vol. 13, no. 2, pp. 167–172, 2004.
• B. C. Tripathy and S. Mahanta, “On a class of sequences related to the ${l}^{p}$ space defined by Orlicz functions,” Soochow Journal of Mathematics, vol. 29, no. 4, pp. 379–391, 2003. \endinput