Ehsan Lotfali Ghasab, Hamid Majani, Ghasem Soleimani Rad, “Fixed points of set-valued <nobr>$F$</nobr>-contraction operators in quasi-ordered metric spaces with an application to integral equations”, J. Sib. Fed. Univ. Math. Phys., 2021, Volume 14, Issue 2,Pages <nobr>150

Fixed points of set-valued $F$-contraction operators in quasi-ordered metric spaces with an application to integral equations

Ehsan Lotfali Ghasab^a, Hamid Majani^a, Ghasem Soleimani Rad^b

^a Department of Mathematics Shahid Chamran University of Ahvaz, Ahvaz, Iran
^b Young Researchers and Elite club, West Tehran Branch, Islamic Azad University, Tehran, Iran

Abstract: In this paper, we prove some new fixed point theorems involving set-valued $F$-contractions in the setting of quasi-ordered metric spaces. Our results are significant since we present Banach contraction principle in a different manner from that which is known in the present literature. Some examples and an application to existence of solution of Volterra-type integral equation are given to support the obtained results.

Keywords: fixed point, sequentially complete metric spaces, $F$-contraction, ordered-close operator.

UDC: 517.9

Received: 01.01.2020
Received in revised form: 22.09.2020
Accepted: 20.11.2020

Language: English

DOI: 10.17516/1997-1397-2021-14-2-150-158