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 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.

Automated summary

This article discusses a series of infinite dimensional extensions of theorems from previous studies and proves similar constructions in an infinite dimension using similar techniques. As an application, the existence of solutions for infinite dimensional Fredholm integral equation and Uryshon type integral equation is ensured.