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

Oratai Yamaod; Wutiphol Sintunavarat; Yeol Je Cho

Open Mathematics (2016)

- Volume: 14, Issue: 1, page 128-145
- ISSN: 2391-5455

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topOratai 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 -

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