Existence of a solution of integral equations via fixed point theorem

Authors :: Vladimir Rakočević
Selma Gülyaz
Peyman Salimi
Erdal Karapınar
[Gulyaz, Selma] Cumhuriyet Univ, Dept Math, Sivas, Turkey -- [Karapinar, Erdal] Atilim Univ, Dept Math, TR-06836 Ankara, Turkey -- [Rakocevic, Vladimir] Univ Nis, Fac Sci & Math, Nish 18000, Serbia -- [Salimi, Peyman] Islamic Azad Univ, Young Researchers & Elite Club, Rasht, Iran
KARAPINAR, ERDAL -- 0000-0002-6798-3254
GULYAZ, Selma -- 0000-0002-1876-6560
Publication Year :: 2013
Publisher :: SPRINGEROPEN, 2013.
Abstract: WOS: 000327463000006<br />In this paper, we establish a solution to the following integral equation: u(t) = integral(T)(0) G(t, s)f(s, u(s)) ds for all t is an element of [0,T], (1) where T > 0, f : [0, T] x R -> R and G : [0, T] x [0, T] -> [0, infinity) are continuous functions. For this purpose, we also obtain some auxiliary fixed point results which generalize, improve and unify some fixed point theorems in the literature.<br />Ministry of Science, Technology and Development, Republic of Serbia [174025]<br />The authors thank the anonymous referees for their remarkable comments, suggestions and ideas that helped to improve this paper. The third author (V Rakocevic) is supported by Grant No. 174025 of the Ministry of Science, Technology and Development, Republic of Serbia.