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Generalization of Darbo-Type Fixed Point Theorem and Applications to Integral Equations

In: Advances in Metric Fixed Point Theory and Applications

Author

Listed:
  • Hemant Kumar Nashine

    (Vellore Institute of Technology, Department of Mathematics, School of Advanced Sciences
    University of Johannesburg, Department of Mathematics and Applied Mathematics)

  • Rabha W. Ibrahim

    (Ton Duc Thang University, Informetrics Research Group
    Ton Duc Thang University, Faculty of Mathematics and Statistics)

  • Reza Arab

    (Islamic Azad University, Department of Mathematics, Sari Branch)

  • M. Rabbani

    (Islamic Azad University, Department of Mathematics, Sari Branch)

Abstract

We propose a new notation of $$\mu $$ μ -set contractive mappings for two classes of functions involving a measure of noncompactness in Banach space and Darbo-type fixed point and n-tupled fixed point results. These results include and extend the results of Falset and Latrach [Falset, J. G., Latrach, K.: On Darbo–Sadovskii’s fixed point theorems type for abstract measures of (weak) noncompactness, Bull. Belg. Math. Soc. Simon Stevin 22 (2015), 797–812.] The results are also correlated with the classical generalized Banach fixed point theorems. Finally, we apply these results to two different Volterra integral equations in Banach algebras with an illustration.

Suggested Citation

  • Hemant Kumar Nashine & Rabha W. Ibrahim & Reza Arab & M. Rabbani, 2021. "Generalization of Darbo-Type Fixed Point Theorem and Applications to Integral Equations," Springer Books, in: Yeol Je Cho & Mohamed Jleli & Mohammad Mursaleen & Bessem Samet & Calogero Vetro (ed.), Advances in Metric Fixed Point Theory and Applications, chapter 0, pages 333-364, Springer.
    • Handle: RePEc:spr:sprchp:978-981-33-6647-3_14
    DOI: 10.1007/978-981-33-6647-3_14
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