Existence of a common solution for a system of nonlinear integral equations via fixed point methods inb-metric spaces

Oratai Yamaod, Wutiphol Sintunavarat, and Yeol Je Cho. "Existence of a common solution for a system of nonlinear integral equations via fixed point methods inb-metric spaces." Open Mathematics 14.1 (2016): 128-145. <http://eudml.org/doc/276924>.

@article{OrataiYamaod2016,
abstract = {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,       \[\{x (t) = \int \limits \_a^b \{\{K\_1\}\} (t, r, x(r))dr, & & x(t) = \int \limits \_a^b \{\{K\_2\}\}(t, r, x(r))dr,\} \] 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.},
author = {Oratai Yamaod, Wutiphol Sintunavarat, Yeol Je Cho},
journal = {Open Mathematics},
keywords = {b-metric spaces; Coincidence points; Common fixed points; Integral equations; -metric spaces; coincidence points; common fixed points; integral equations},
language = {eng},
number = {1},
pages = {128-145},
title = {Existence of a common solution for a system of nonlinear integral equations via fixed point methods inb-metric spaces},
url = {http://eudml.org/doc/276924},
volume = {14},
year = {2016},
}

TY - JOUR
AU - Oratai Yamaod
AU - Wutiphol Sintunavarat
AU - Yeol Je Cho
TI - Existence of a common solution for a system of nonlinear integral equations via fixed point methods inb-metric spaces
JO - Open Mathematics
PY - 2016
VL - 14
IS - 1
SP - 128
EP - 145
AB - 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,       \[{x (t) = \int \limits _a^b {{K_1}} (t, r, x(r))dr, & & x(t) = \int \limits _a^b {{K_2}}(t, r, x(r))dr,} \] 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.
LA - eng
KW - b-metric spaces; Coincidence points; Common fixed points; Integral equations; -metric spaces; coincidence points; common fixed points; integral equations
UR - http://eudml.org/doc/276924
ER -