Infinite Geraghty type extensions and their applications on integral equations

R. Bardhan, C. Ozel, L. Guran, H. Aydi*, Choonkil Park

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this article, we discuss about a series of infinite dimensional extensions of some theorems given in (Shumrani et al. in SER Math. Inform. 33(2):197–202, 2018), (Fisher in Math. Mag. 48(4):223–225, 1975), and (Fogh, Behnamian and Pashaie in Int. J. Maps in Mathematics 2(41):1–13, 2019). We also prove a similar Geraghty type construction for Fisher (Math. Mag. 48(4):223–225, 1975) in an infinite dimension using similar techniques as in (Shumrani et al. in SER Math. Inform. 33(2):197–202, 2018) and (Fogh, Behnamian and Pashaie in Int. J. Maps in Mathematics 2(41):1–13, 2019). As an application, we ensure the existence of solutions for infinite dimensional Fredholm integral equation and Uryshon type integral equation.

Original languageEnglish
Article number456
JournalAdvances in Difference Equations
Volume2021
Issue number1
DOIs
Publication statusPublished - Dec 2021
Externally publishedYes

Keywords

  • Complete metric space
  • Fixed point
  • Geraghty theorem
  • H contraction
  • Infinite dimension
  • M function
  • k-dimensional extension

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