Skip to main content
SpringerLink
Log in

Some Geometric Properties of Generalized Cesàro-Musielak-Orlicz Spaces Equipped with the Amemiya Norm

  • Published:
Acta Mathematica Vietnamica Aims and scope Submit manuscript

Abstract

A generalized Cesàro-Musielak-Orlicz sequence space C e s Φ (q) endowed with the Amemiya norm is introduced. Criteria for the coordinatewise uniformly Kadec-Klee property and the uniform Opial property of the space C e s Φ (q) with respect to the Amemiya norm are obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Chen, S.T.: Geometry of Orlicz spaces. Dissertationes Math. 356, 1–204 (1996)

    Google Scholar 

  2. Cui, Y., Hudzik, H., Petrot, N., Suantai, S., Szymaszkiewicz, A.: Basic topological and geometric properties of Cesàro-Orlicz spaces. Proc. Indian Acad. Sci. (Math. Sci.) 115(4), 461–476 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  3. Cui, Y., Hudzik, H.: Maluta’s coefficient and Opial’s properties in Musielak-Orlicz sequence spaces equipped with the Luxemberg norm. Nonlinear Anal. 35, 475–485 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  4. Cui, Y., Hudzik, H.: On the uniform Opial property in some modular sequence spaces. Func. Approx. Comment. 26, 93–102 (1998)

    MathSciNet  MATH  Google Scholar 

  5. Cui, Y., Hudzik, H., Zhu, H.: Maluta’s coefficient in Musielak-Orlicz sequence spaces equipped with the Orlicz norm. Proc. Am. Math. Soc. 126(1), 115–121 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  6. Foralewski, P., Hudzik, H., Szymaszkiewicz, A.: Some remarks on Cesàro-Orlicz spaces. Math. Inequal. Appl. 13(2), 363–386 (2010)

    MathSciNet  MATH  Google Scholar 

  7. Foralewski, P., Hudzik, H.: On some geometrical and topological properties of generalized Calderón-Lozanovskiǐ sequence spaces. Houston J. Math. 25(3), 523–542 (1999)

    MathSciNet  MATH  Google Scholar 

  8. Gossez, J.P., Lami Dozo, E.: Some geometric properties related to fixed point theory for nonexpansive mappings. Pacific J. Math. 40, 565–573 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  9. Huff, R.: Banach spaces which are nearly uniformly convex. Rocky Mountain J. Math. 10, 743–749 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  10. Kadets, M.I.: The relation between some properties of convexity of the unit ball of a Banach space. Funct. Anal. Appl. 16(3), 204–206 (1982)

    Article  MathSciNet  Google Scholar 

  11. Kaminska, A.: Uniform rotundity of Musielak-Orlicz sequence spaces. J. Approx. Theory 47(4), 302–322 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  12. Kantorovich, L.V., Akilov, G.P.: Functional analysis, 2nd edn. Pergamon and “Nauka” (1982)

  13. Khan, V.A.: Some geometric properties of generalized Cesaro sequence spaces. Acta Math. Univ. Comenianae 79(1), 1–8 (2010)

    MATH  Google Scholar 

  14. Khan, V.A.: On Riesz-Musielak-Orlicz sequence spaces. Numer. Funct. Anal. Optim. 28(7-8), 883–895 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  15. Manna, A., Srivastava, P.D.: Some geometric properties of generalized Cesàro-Musielak-Orlicz sequence spaces. Mathematics and Computing 2013: International Conference in Haldia, India, Chapter 19, pp 283–296 (2014)

  16. Mongkolkeha, C., Kumam, P.: On H-property and uniform Opial property of generalized Cesàro sequence spaces. J. Inequal. Appl. 2012, 76 (2012). 9 pp

  17. Musielak, J.: Orlicz spaces and modular spaces, p 1034. Springer (1983)

  18. Opial, Z.: Weak convergence of the sequence of successive approximations for non expansive mappings. Bull. Am. Math. Soc. 73, 591–597 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  19. Orlicz, W.: A note on modular spaces I. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 9, 157–162 (1961)

    MathSciNet  MATH  Google Scholar 

  20. Petrot, N., Suantai, S.: Some geometric properties in Cesàro-Orlicz spaces. Sci. Asia 31, 173–177 (2005)

    Article  Google Scholar 

  21. Petrot, N., Suantai, S.: Uniform Opial properties in generalized Cesàro sequence spaces. Nonlinear Anal. 63, 1116–1125 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  22. Petrot, N., Suantai, S.: On uniform Kadec-Klee properties and rotundity in generalized Cesàro sequence spaces. Internat. J. Math. Math. Sci. 2004(2), 91–97 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  23. Prus, S.: Geometrical background of metric fixed point theory. In: Kirk, W. A., Sims, B. (eds.) Handbook of metric fixed point theory, pp 93–132. Kluwer Academic, Dordrecht (2001)

    Chapter  Google Scholar 

  24. Prus, S.: Banach spaces with uniform Opial property. Nonlinear Anal. Theory Appl. 18(8), 697–704 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  25. Shiue, J.S.: Cesàro sequence spaces. Tamkang J. Math. 1, 19–25 (1970)

    MathSciNet  MATH  Google Scholar 

  26. Wangkeeree, R.: On property (k- N U C) in Cesàro-Musielak-Orlicz sequence spaces. Thai J. Math. 1, 119–130 (2003)

    MathSciNet  MATH  Google Scholar 

  27. Zhang, T.: The coordinatewise uniformly Kadec-Klee property in some Banach spaces. Siberian Math. J. 44(2), 363–365 (2003)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

The authors are very much grateful to the editor and the anonymous referee for their careful reading and positive comments which improved the presentation of our manuscript. The first author is thankful to CSIR, New Delhi, Govt. of India, for the financial assistance during this work.

Author information

Authors and Affiliations

  1. Department of Mathematics, IIT Kharagpur, West Bengal, 721302, India

    Atanu Manna & P. D. Srivastava

Authors
  1. Atanu Manna
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. D. Srivastava
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Atanu Manna.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Manna, A., Srivastava, P.D. Some Geometric Properties of Generalized Cesàro-Musielak-Orlicz Spaces Equipped with the Amemiya Norm. Acta Math Vietnam 41, 91–102 (2016). https://doi.org/10.1007/s40306-014-0099-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40306-014-0099-3

Keywords

Mathematics Subject Classification (2010)

Search

Navigation