Urysohn integral equations approach by common fixed points in complex-valued metric spaces
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Author list: Sintunavarat W., Cho Y.J., Kumam P.
Publisher: SpringerOpen
Publication year: 2013
Journal: Advances in Difference Equations (1687-1839)
Volume number: 2013
ISSN: 1687-1839
eISSN: 1687-1847
Languages: English-Great Britain (EN-GB)
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Abstract
Recently, the complex-valued metric spaces which are more general than the metric spaces were first introduced by Azam et al. (Numer. Funct. Anal. Optim. 32:243-253, 2011). They also established the existence of fixed point theorems under the contraction condition in these spaces. The aim of this paper is to introduce the concepts of a C-Cauchy sequence and C-complete in complex-valued metric spaces and establish the existence of common fixed point theorems in C-complete complex-valued metric spaces. Furthermore, we apply our result to obtain the existence theorem for a common solution of the Urysohn integral equations x(t) = ∫ b a K1(t, s, x(s)) ds + g(t), x(t) = ∫ b a K2(t, s, x(s)) ds + h(t), where t ε [a, b] ⊆ ℝ, x, g, h ε C([a, b],ℝn) and K1, K2 : [a, b]×[a, b]×ℝn→ℝn. © 2013 Sintunavarat et al.
Keywords
Complex-valued metric spaces, Urysohn integral equations, Weakly compatible
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