TY - JOUR

T1 - Infinite Geraghty type extensions and their applications on integral equations

AU - Bardhan, R.

AU - Ozel, C.

AU - Guran, L.

AU - Aydi, H.

AU - Park, Choonkil

N1 - Funding Information:
The authors would like to thank Suprokash Hazra who helped with his valuable comments to develop the key ideas of this paper.
Publisher Copyright:
© 2021, The Author(s).

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.

AB - 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.

KW - Complete metric space

KW - Fixed point

KW - Geraghty theorem

KW - H contraction

KW - Infinite dimension

KW - M function

KW - k-dimensional extension

UR - http://www.scopus.com/inward/record.url?scp=85117420364&partnerID=8YFLogxK

U2 - 10.1186/s13662-021-03583-7

DO - 10.1186/s13662-021-03583-7

M3 - Article

AN - SCOPUS:85117420364

VL - 2021

JO - Advances in Difference Equations

JF - Advances in Difference Equations

SN - 1687-1839

IS - 1

M1 - 456

ER -