Difference Cesáro Function Space on Rooted Tree Defined by Musielak-Orlicz Function
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Abstract
This paper aims to investigate the algebraic and topological properties of a newly constructed difference function space on a rooted tree defined by Musielak-Orlicz function.
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References
- F. Basar, B. Altay, On the Space of Sequences of p-Bounded Variation and Related Matrix Mappings, Ukr. Math. J. 55 (2003), 136–147. https://doi.org/10.1023/A:1025080820961.
- M. Ba¸sarir, M. Kayikçi, On the Generalized B m-Riesz Difference Sequence Space and β-Property, J. Inequal. Appl. 2009 (2009), 385029. https://doi.org/10.1155/2009/385029.
- H. Dutta, M. Phil, On Some Difference Sequence Spaces, Pac. J. Sci. Technol. 10 (2009), 243-247.
- H. Dutta, Some Statistically Convergent Difference Sequence Spaces Defined Over Real 2-Normed Linear Space, Appl. Sci. 12 (2010), 37-47. https://eudml.org/doc/225854.
- M. Et, R. Çolak, On Some Genelalized Difference Sequence Spaces, Soochow J. Math. 21 (1995), 377-356.
- M. Et, M. Ba¸sarir, On Some New Genelalized Difference Sequence Spaces, Period. Math. Hung. 35 (1997), 169–175. https://doi.org/10.1023/A:1004597132128.
- B.D. Hassard, D.H. Hussein, On Cesaro Function Spaces, Tamgang. J. Math. 4 (1973), 19–25.
- H. Kizmaz, On Certain Sequence Spaces, Canad. Math. Bull. 24 (1981), 169–176. https://doi.org/10.4153/CMB-1981-027-5.
- D. Kubiak, A Note on Cesàro–Orlicz Sequence Spaces, J. Math. Anal. Appl. 349 (2009), 291–296. https://doi.org/10.1016/j.jmaa.2008.08.022.
- P.Y. Lee, Cesàro Sequence Spaces, Math. Chron. 13 (1984), 29-45.
- J. Lindenstrauss, L. Tzafriri, On Orlicz Sequence Spaces, Israel J. Math. 10 (1971), 379–390. https://doi.org/10.1007/BF02771656.
- S.K. Lim, P.Y. Lee, An Orlicz Extension of Cesaro Sequence Spaces, Comment. Math. 28 (1928), 117-128. https://eudml.org/doc/291736.
- L. Maligranda, Orlicz Spaces and Interpolation, Seminars in Mathematics, Polish Academy of Science, 1989.
- L. Maligranda, N. Petrot, S. Suantai, On the James Constant and B-Convexity of Cesàro and Cesàro–Orlicz Sequence Spaces, J. Math. Anal. Appl. 326 (2007), 312–331. https://doi.org/10.1016/j.jmaa.2006.02.085.
- J. Musielak, Orlicz Spaces and Modular Spaces, Springer, Berlin, Heidelberg, 1983. https://doi.org/10.1007/BFb0072210.
- M. Mursaleen, S.K. Sharma, S.A. Mohiuddine, A. Kılıçman, New Difference Sequence Spaces Defined by MusielakOrlicz Function, Abstr. Appl. Anal. 2014 (2014), 691632. https://doi.org/10.1155/2014/691632.
- M. Mursaleen, A. Alotaibi, S.K. Sharma, Some New Lacunary Strong Convergent Vector-Valued Sequence Spaces, Abstr. Appl. Anal. 2014 (2014), 858504. https://doi.org/10.1155/2014/858504.
- M. Mursaleen, S.K. Sharma, Entire sequence spaces defined on locally convex Hausdorff topological space, Iran. J. Sci. Technol. 38 (2014), 105–109.
- P. Muthukumar, S. Ponnusamy, Discrete Analogue of Generalized Hardy Spaces and Multiplication Operators on Homogenous Trees, Anal. Math. Phys. 7 (2017), 267–283. https://doi.org/10.1007/s13324-016-0141-9.
- P. Muthukumar, S. Ponnusamy, Composition Operators on the Discrete Analogue of Generalized Hardy Space on Homogenous Trees, Bull. Malays. Math. Sci. Soc. 40 (2017), 1801–1815. https://doi.org/10.1007/s40840-016-0419-y.
- N. Petrot, S. Suantai, Some Geometric Properties in Cesáro-Orlicz Sequence Spaces, ScienceAsia 31 (2005), 173-177.
- K. Raj, C. Sharma, S. Pandoh, Multiplication Operators on Cesàro-Orlicz Sequence Spaces, Fasc. Math. 57 (2016), 137–145. https://doi.org/10.1515/fascmath-2016-0021.
- A.K. Sharma, V. Kumar, Discrete Cesaro Operator between Weighted Banach Spaces on Homogenous Trees, Adv. Oper. Theory 5 (2020), 1667–1683. https://doi.org/10.1007/s43036-020-00078-2.
- J.S. Shiue, On the Cesàro Sequence Spaces, Tamkang J. Math. 1 (1970), 19-25.
- J.S. Shiue, A Note on Cesaro Function Space, Tamkang J. Math. 1 (1970), 91-95.
- W. Sanhan, S. Suantai, On k-Nearly Uniform Convex Property in Generalized Cesàro Sequence Spaces, Int. J. Math. Math. Sci. 2003 (2003), 3599–3607. https://doi.org/10.1155/S0161171203301267.