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 - 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
SN - 1687-1839
VL - 2021
JO - Advances in Difference Equations
JF - Advances in Difference Equations
IS - 1
M1 - 456
ER -