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Infinite Geraghty type extensions and their applications on integral equationsopen access
- Authors
- Bardhan, R; Ozel, C; Guran, L; Aydi, H; Park, Choonkil
- Issue Date
- Oct-2021
- Publisher
- SPRINGER
- Keywords
- Fixed point; Geraghty theorem; Complete metric space; Infinite dimension; H-k contraction; M-k function; k-dimensional extension
- Citation
- ADVANCES IN DIFFERENCE EQUATIONS, v.2021, no.1, pp.1 - 19
- Indexed
- SCIE
SCOPUS
- Journal Title
- ADVANCES IN DIFFERENCE EQUATIONS
- Volume
- 2021
- Number
- 1
- Start Page
- 1
- End Page
- 19
- ISSN
- 1687-1839
- 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.
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