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

• Autorzy: Oratai Yamaod , Wutiphol Sintunavarat , Yeol Je Cho
• Języki publikacji: 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.

Słowa kluczowe

EN

b-metric spaces; Coincidence points; Common fixed points; Integral equations

Kategorie tematyczne

• 47H09: Contraction-type mappings, nonexpansive mappings, A -proper mappings, etc.
• 47H10: Fixed-point theorems

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2016
• Tom: 14
• Numer: 1
• Strony: 128-145

Daty

wydano

2016-01-01

otrzymano

2015-07-07

zaakceptowano

2016-02-08

online

2016-04-04

Twórcy

autor

Oratai Yamaod

• Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani 12121,

autor

Wutiphol Sintunavarat

• Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani 12121, , E-mail:

autor

Yeol Je Cho

• Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, Korea, and Department of Mathematics, King Abdulaziz University, Jeddah 21589,

Identyfikatory

DOI

10.1515/math-2016-0010