Infinite Geraghty type extensions and their applications on integral equations

R. Bardhan; C. Ozel; L. Guran; H. Aydi; Choonkil Park

doi:10.1186/s13662-021-03583-7

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 journal › Article › peer-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 language	English
Article number	456
Journal	Advances in Difference Equations
Volume	2021
Issue number	1
DOIs	https://doi.org/10.1186/s13662-021-03583-7
Publication status	Published - Dec 2021
Externally published	Yes

Keywords

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

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10.1186/s13662-021-03583-7

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title = "Infinite Geraghty type extensions and their applications on integral equations",

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.",

keywords = "Complete metric space, Fixed point, Geraghty theorem, H contraction, Infinite dimension, M function, k-dimensional extension",

author = "R. Bardhan and C. Ozel and L. Guran and H. Aydi and Choonkil Park",

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doi = "10.1186/s13662-021-03583-7",

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AU - Bardhan, R.

AU - Ozel, C.

AU - Guran, L.

AU - Aydi, H.

AU - Park, Choonkil

PY - 2021/12

Y1 - 2021/12

N2 - 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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KW - Complete metric space

KW - Fixed point

KW - Geraghty theorem

KW - H contraction

KW - Infinite dimension

KW - M function

KW - k-dimensional extension

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ER -

Infinite Geraghty type extensions and their applications on integral equations

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Keywords

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