SpringerLink
Log in

Topology on Geometric Sequence Spaces

  • Chapter
  • First Online:
Approximation Theory, Sequence Spaces and Applications

Part of the book series: Industrial and Applied Mathematics ((INAMA))

Abstract

Central theme of this chapter is to endow the geometric sequence spaces with geometric topology which is a non-linear topology. We shall explore salient features of the geometric topological sequence spaces. In the later sections, we shall discuss about normal topology and its properties. Then, we shall introduce perfect, simple, symmetric geometric sequence spaces and duality between perfect geometric sequence spaces.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
EUR 29.95
Price includes VAT (Germany)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
EUR 106.99
Price includes VAT (Germany)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
EUR 139.09
Price includes VAT (Germany)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info
Hardcover Book
EUR 139.09
Price includes VAT (Germany)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Bashirov, A.E.: Relativistic velocity addition and calculi based on hyperbolic tangent. In: Focus on Calculus, pp. 111–123. Nova Science Publisher, New York (2020). ISBN: 978-1-53617-337-6

    Google Scholar 

  2. Bashirov, A.E., Rıza, M.: On Complex multiplicative differentiation. TWMS J. Appl. Eng. Math. 1(1), 75–85 (2011)

    MathSciNet  MATH  Google Scholar 

  3. Bashirov, A.E., Mısırlı, E., Tandoǧdu, Y., Özyapıcı, A.: On modeling with multiplicative differential equations. Appl. Math. J. Chin. Univ. Ser. A 26(4), 425–438 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bashirov, A.E., Kurpınar, E.M., Özyapıcı, A.: Multiplicative Calculus and its applications. J. Math. Anal. Appl. 337, 36–48 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bashirov, A.E., Norozpour, S.: On an alternative view to complex calculus. Math. Methods Appl. Sci. 41, 7313–7324 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  6. Boruah, K., Hazarika, B.: Application of geometric calculus in numerical analysis and difference sequence spaces. J. Math. Anal. Appl. 449(2), 1265–1285 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  7. Boruah, K., Hazarika, B.: \(G\)-Calculus. TWMS J. Appl. Eng. Math. 8(1), 94–105 (2018)

    MathSciNet  MATH  Google Scholar 

  8. Boruah, K., Hazarika, B.: Bigeometric integral calculus. TWMS J. Appl. Eng. Math. 8(2), 374–385 (2018)

    MATH  Google Scholar 

  9. Boruah, K., Hazarika, B.: Some basic properties of bigeometric calculus and its applications in numerical analysis. Afrika Matematika 32(1–2), 211–227 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  10. Boruah, K., Hazarika, B., Bashirov, A.E.: Solvability of bigeometric differential equations by numerical methods. Boletim da Sociedade Paranaense de Matematica 39(2), 203–222 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  11. Boruah, K., Hazarika, B.: On some generalized geometric difference sequence spaces. Proyecciones 36(3), 373–395 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  12. Çakır, Z.: Spaces of continuous and bounded functions over the field of geometric complex numbers. J. Inequal. Appl. 2013(363), 5 (2013)

    Google Scholar 

  13. Çakmak, A.F., Başar, F.: On the classical sequence spaces and non-Newtonian calculus. J. Inequal. Appl. 2012, Art. ID 932734, 12 (2012)

    Google Scholar 

  14. Çakmak, A.F., Başar, F.: Certain spaces of functions over the field of non-Newtonian complex numbers. Abstr. Appl. Anal. 2014, Article ID 236124, 12 (2014)

    Google Scholar 

  15. Çakmak, A.F., Başar, F.: On line and double integrals in the non-Newtonian sense. AIP Conf. Proc. 1611, 415–423 (2014)

    Google Scholar 

  16. Çakmak, A.F., Başar, F.: Some sequence spaces and matrix transformations in multiplicative sense. TWMS J. Pure Appl. Math. 6(1), 27–37 (2015)

    MathSciNet  MATH  Google Scholar 

  17. Grossman, M.: Bigeometric Calculus: A System with a scale-Free Derivative. Archimedes Foundation, Massachusetts (1983)

    Google Scholar 

  18. Grossman, M., Katz, R.: Non-Newtonian Calculus. Lee Press, Piegon Cove, Massachusetts (1972)

    MATH  Google Scholar 

  19. Kadak, U., Özlük, M.: Generalized Runge-Kutta method with respect to non-Newtonian calculus. Abstr. Appl. Anal. 2015, Article ID 594685, 10 (2015)

    Google Scholar 

  20. Kadak, U., Efe, H.: Matrix transformation between certain sequence spaces over the non-newtonian complex field. Sci. World J. 2014, Article ID 705818, 12 (2014)

    Google Scholar 

  21. Kadak, U., Kirişçi, M., Çakmak, A.F.: On the classical paranormed sequence spaces and related duals over the non-Newtonian complex field. J. Funct. Spaces Appl. 2015, Article ID 416906, 11 (2015)

    Google Scholar 

  22. Stanley, D.: A multiplicative calculus. Primus IX 4, 310–326 (1999)

    Article  Google Scholar 

  23. Tekin, S., Başar, F.: Certain sequence spaces over the non-Newtonian complex field. Abstr. Appl. Anal. 2013, Article ID 739319, 11 (2013)

    Google Scholar 

  24. Türkmen, C., Başar, F.: Some basic results on the geometric calculus. Commun. Fac. Sci. Univ. Ankara Ser. \(A_1\)61(2), 17–34 (2012)

    Google Scholar 

  25. Türkmen, C., Başar, F.: Some basic results on the sets of sequences with geometric calculus. AIP Conf. Proc. 1470, 95–98 (2012)

    Article  MATH  Google Scholar 

  26. Uzer, A.: Multiplicative type complex calculus as an alternative to the classical calculus. Comput. Math. Appl. 60, 2725–2737 (2010)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Jengraimukh College, Majuli, 785105, Assam, India

    Khirod Boruah

  2. Department of Mathematics, Gauhati University, Guwahati, 781014, Assam, India

    Bipan Hazarika

Authors
  1. Khirod Boruah
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bipan Hazarika
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Khirod Boruah .

Editor information

Editors and Affiliations

  1. Department of General Required Courses, Mathematics, The Applied College, King Abdulaziz University, Jeddah, Saudi Arabia

    S. A. Mohiuddine

  2. Department of Mathematics, Gauhati University, Guwahati, Assam, India

    Bipan Hazarika

  3. Mathematics Division, School of Advanced Sciences and Languages, VIT Bhopal University, Bhopal, Madhya Pradesh, India

    Hemant Kumar Nashine

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Boruah, K., Hazarika, B. (2022). Topology on Geometric Sequence Spaces. In: Mohiuddine, S.A., Hazarika, B., Nashine, H.K. (eds) Approximation Theory, Sequence Spaces and Applications. Industrial and Applied Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-19-6116-8_1

Download citation

Publish with us

Policies and ethics

Search

Navigation