Skip to main content
SpringerLink
Log in

Existence of solutions of a nonlinear integral equations in a WC-Banach algebra

  • Published:
Ricerche di Matematica Aims and scope Submit manuscript

Abstract

The paper is devoted to prove the existence of solutions of a nonlinear integral equation in a WC-Banach algebra. Making use of the measure of weak noncompactness and the weak topology, we prove some fixed point theorems for operators not necessarily weakly sequentially continuous acting in WC-Banach algebra involving weakly compact operators.

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. Agarwal, R. P., Hussain, N., Taoudi, M. A.: Fixed point theorems in ordered Banach spaces and applications to nonlinear integral equations. Abstr. Appl. Anal. 2012, Art. ID 245872

  2. Appell, J., Banaś, J., Merentes, N.: Bounded Variation and Around. Series in Nonlinear Analysis and Applications. De Gruyter, Berlin (2014)

    MATH  Google Scholar 

  3. Banas, J., Olszowy, L.: On the equivalence of some concepts in the theory of Banach algebras. Ann. Funct. Anal. 10, 277–283 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  4. Banas, J., Taoudi, M.A.: Fixed points and solutions of operator equations for the weak topology in Banach algebras. Taiwan. J. Math. 18, 871–893 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  5. Ben Amar, A., Chouayekh, S., Jeribi, A.: New fixed point theorems in Banach algebras under weak topology features and applications to nonlinear integral equations. J. Funct. Anal. 259, 2215–2237 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  6. Ben Amar, A., Mnif, M.: Leray–Schauder alternatives for weakly sequentially continuous mappings and application to transport equation. Math. Methods Appl. Sci. 33, 80–90 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  7. De Blasi, F.S.: On a property of the unit sphere in Banach spaces. Bull. Math. Soc. Sci. Math. Roum. 21, 259–262 (1977)

    MathSciNet  MATH  Google Scholar 

  8. Dobrakov, I.: On representation of linear operators on \(C_0(T, X)\). Czechoslov. Math. J. 21(96), 13–30 (1971)

    Article  MATH  Google Scholar 

  9. Dunford, N., Schwartz, J.T.: Linear Operators \(I\). International Publications, Leyden (1963)

    MATH  Google Scholar 

  10. Jeribi, A., Krichen, B.: Nonlinear Functional Analysis in Banach Spaces and Banach Algebras: Fixed Point Theory under Weak Topology for Nonlinear Operators and Block Operator Matrices with Applications, Monographs and Research Notes in Mathematics. CRC Press Taylor and Francis, Boca Raton (2015)

    MATH  Google Scholar 

  11. Jeribi, A., Krichen, B., Mefteh, B.: Fixed point theory in WC-Banach algebras. Turk. J. Math. 40, 283–291 (2016)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences of Sfax, University of Sfax, Soukra Road Km 3.5, B.P. 1171, 3000, Sfax, Tunisia

    Bilel Mefteh

Authors
  1. Bilel Mefteh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bilel Mefteh.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mefteh, B. Existence of solutions of a nonlinear integral equations in a WC-Banach algebra. Ricerche mat 72, 1007–1022 (2023). https://doi.org/10.1007/s11587-021-00618-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11587-021-00618-9

Keywords

Mathematics Subject Classification

Search

Navigation