Displaying similar documents to “Contraction mappings in b -metric spaces”

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 (2016)

Open Mathematics

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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 ) = ∫ a b K 1 ( t , r , x ( r ) ) d r , x ( t ) = ∫ a b K 2 ( t , r , x ( r ) ) d r , where...