Infinite Geraghty type extensions and their applications on integral equations

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 als...

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Bibliographic Details
Published in:Advances in difference equations 2021-10, Vol.2021 (1), p.1-19, Article 456
Main Authors: Bardhan, R., Ozel, C., Guran, L., Aydi, H., Park, Choonkil
Format: Article
Language:English
Subjects:
Analysis
Complete metric space
Difference and Functional Equations
Fixed point
Fixed Point Theory and Applications to Fractional Ordinary and Partial Difference and Differential Equations
Fredholm equations
Functional Analysis
Geraghty theorem
H k $H_{k}$ contraction
Infinite dimension
Integral equations
M k $M_{k}$ function
Mathematical analysis
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
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Summary: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.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-021-03583-7