Existence of unique common solution to the system of non-linear integral equations via fixed point results in incomplete metric spaces

Mian Bahadur Zada; Muhammad Sarwar; Stojan Radenović

doi:10.1186/s13660-016-1286-7

Existence of unique common solution to the system of non-linear integral equations via fixed point results in incomplete metric spaces

J Inequal Appl. 2017;2017(1):22. doi: 10.1186/s13660-016-1286-7. Epub 2017 Jan 18.

Authors

Mian Bahadur Zada¹, Muhammad Sarwar¹, Stojan Radenović²

Affiliations

¹ Department of Mathematics, University of Malakand, Chakdara, Dir(L) Pakistan.
² Faculty of Mechanical Engineering, Universitry of Belgrade, Kraljice Marije 16, Beograd, 11 120 Serbia.

Abstract

In this article, we apply common fixed point results in incomplete metric spaces to examine the existence of a unique common solution for the following systems of Urysohn integral equations and Volterra-Hammerstein integral equations, respectively: [Formula: see text] where [Formula: see text]; [Formula: see text] and [Formula: see text], [Formula: see text] and [Formula: see text] where [Formula: see text], [Formula: see text], u, [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text], are real-valued measurable functions both in s and r on [Formula: see text].

Keywords: Urysohn integral equations; Volterra-Hammerstein integral equations; common [Formula: see text]-property; common fixed point; weakly compatible maps.