On the geometric properities of new type modular space

  • Mehmet Sengonul Faculty of Arts and Sciences, Department ofMathematics, Nev¸sehir Üniversitesi, 2000 EvlerMah. Züeyde Hanım Cad. 50300 NEVSEHIR.
Keywords: Modular spaces, Kadec-Klee property, Banach space, rotund, Nakano space

Abstract

In this paper, using a modular, we have defined the modular space $M_{m^*}(p)$ and we have shown that the sequence space $M_{m^*}(p)$ equipped with the Luxemburg norm is rotund and possesses H-property (or Kadec-Klee property) when $p=(p_k)$ is bounded with $p_k>1$ for all $k\in\mathbb{N}$.

Author Biography

Mehmet Sengonul, Faculty of Arts and Sciences, Department ofMathematics, Nev¸sehir Üniversitesi, 2000 EvlerMah. Züeyde Hanım Cad. 50300 NEVSEHIR.
Nevşehir Universitesi, Matematik bölümü

References

Y. Altin, M. Et and B. C. Tripathy, The sequence space $| overline N p | (M, r,q, s) $ on seminormed spaces, Applied Mathematics and Computation 154(2004), 423--430.

S. T. Chen, Geometry of Orlicz spaces, Dissertationes Math.,1996, pp.~356.

B. Cohuldhary and S. Nanda, Functional Analysis with Applications, John Wiley & Sons Inc. New Delhi. 1989.

Y. A. Cui, H. Hudzik and R. Pluciennik, Banach Saks property in some Banach sequence spaces, Ann. Math. Polinici 65(1997), 193--202.

Y. A. Cui and C. Meng, Banach--Saks property ($beta$) in Cesaro sequence spaces, SEA. Bull. Math. Tamkang J. Math. 24(2000), 201--210.

M.Et, Y. Altin, B. Choudhary and B. C. Tripathy , On some classes of sequences defined by sequences of Orlicz functions, Mathematical Inequalities and Applications, 9(2)(2006), 335--342.

Lindenstrauss, J. and Tzafriri, L., On Orlicz sequence classes, Israel J. Math. 10(1971), 379--390.

Y. Q. Lui, B. E. Wu and Y. P. Lee, Method of sequence spaces, Guangdong of science and Technology Press, (in Chine) 1996.

N. Petrot and S. Suantai, Uniform opial properties in generalized Cesaro sequence spaces, Nonlinear Analysis: Theory, Methods and Applications 63(2005), 1116--1125.

W. Sanhan, On geometric properties some Banach sequence spaces, Thesis for the degree of Master of Science in Mathematics, Chiang Mai University, 2000.

W. Sanhan and S. Suantai, Some geometric properties of Cesaro sequence space, Kyungpook Mathematical Journal,43(2003), 191--197.

J. S. Shue, Cesaro sequence spaces, Tamkang J. Math. 1(1970), 143--150.

N. c{S}imc{s}ek and V. Karakaya On some geometrical properties of generalized modular spaces of Cesaro type defined by weighted means, Journal of Inequalities and Applications, (2009).

B. C. Tripathy and S. Mahanta, On a class of generalized lacunary difference sequence spaces defined by Orlicz function, Acta Mathematica Applicata Sinica, 20(2004), 231--238.

B. C. Tripathy, Y. Altin and M. Et, Generalized difference sequences spaces on seminormed spaces defined by Orlicz functions, Mathematica Slovaca, 58(2008), 315--324.

B. C. Tripathy and B. Sarma, Sequence spaces of fuzzy real numbers defined by Orlicz functions, Mathematica Slovaca, 58(2008), 621--628.

B. C. Tripathy and S. Borgogain, The sequence space $m (M,f, Delta ^n_ m, p)^F$, Mathematical Modelling and Analysis 13(2008), 577--586.

B. C. Tripathy and B. Sarma, Vector valued double sequence spaces defined by Orlicz function, Mathematica Slovaca 59(2009), 767--776.

B. C. Tripathy and H. Dutta, On some new paranormed difference sequence spaces defined by Orlicz functions, Kyungpook Mathematical Journal 50(2010), 59--69.

B. C. Tripathy and B. Hazarika, I--convergent sequences spaces defined by Orlicz function, Acta Mathematica Applicatae Sinica 27 (2011) 149--154.

B. C. Tripathy and B. Sarma, Double sequence spaces of fuzzy numbers defined by Orlicz function, Acta Mathematica Scientia 31(2011), 134--140.

B. C. Tripathy and P. Chandra, On some generalized difference paranormed sequence spaces associated with multiplier sequences defined by modulus function, Anal. Theory Appl. 27 (2011), 21--27.

C. S. Wang, On Norlund sequence spaces, Tamkang Journal of Mathematics, 9 (1978), 269--274.

Published
2012-06-28
How to Cite
Sengonul, M. (2012). On the geometric properities of new type modular space. Tamkang Journal of Mathematics, 43(2), 159-170. https://doi.org/10.5556/j.tkjm.43.2012.687
Section
Papers