In this paper we introduce a property and use this property to prove some common fixed point theorems in b-metric space. We also give some fixed point results on b-metric spaces endowed with an arbitrary binary relation which can be regarded as consequences of our main results. As applications, we applying our result to prove the existence of a common solution for the following system of integral equations: x (t) = ∫ a b K 1 (t,r,x(r)) dr, x (t) = ∫ a b K 2 (t,r,x(r)) dr, where a, b ∈ ℝ with a < b, x ∈ C[a, b] (the set of continuous real functions defined on [a, b] ⊆ ℝ) and K1, K2 : [a, b] × [a, b] × ℝ → ℝ are given mappings. Finally, an example is also given in order to illustrate the effectiveness of such result.
@article{bwmeta1.element.doi-10_1515_math-2016-0010,
author = {Oratai Yamaod and Wutiphol Sintunavarat and Yeol Je Cho},
title = {Existence of a common solution for a system of nonlinear integral equations via fixed point methods inb-metric spaces},
journal = {Open Mathematics},
volume = {14},
year = {2016},
pages = {128-145},
zbl = {06632344},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2016-0010}
}
Oratai Yamaod; Wutiphol Sintunavarat; Yeol Je Cho. Existence of a common solution for a system of nonlinear integral equations via fixed point methods inb-metric spaces. Open Mathematics, Tome 14 (2016) pp. 128-145. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2016-0010/