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• # Artykuł - szczegóły

## Open Mathematics

2016 | 14 | 1 | 128-145

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

EN

### Abstrakty

EN
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,       $$\matrix {x (t) = \int \limits_a^b {{K_1}} (t, r, x(r))dr, & & x(t) = \int \limits_a^b {{K_2}}(t, r, x(r))dr,}$$ 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.

EN

128-145

wydano
2016-01-01
otrzymano
2015-07-07
zaakceptowano
2016-02-08
online
2016-04-04

### Twórcy

autor
• Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani 12121,
• Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani 12121, , E-mail:
autor
• Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, Korea, and Department of Mathematics, King Abdulaziz University, Jeddah 21589,