Abstract
This article is concerned with coupled coincidence points and common fixed points for two mappings in metric spaces and cone metric spaces. We first establish a coupled coincidence point theorem for two mappings and a common fixed point theorem for two w-compatible mappings in metric spaces. Then, by using a scalarization method, we extend our main theorems to cone metric spaces. Our results generalize and complement several earlier results in the literature. Especially, our main results complement a very recent result due to Abbas et al.
Highlights
1 Introduction Throughout this article, unless otherwise specified, we always suppose that N is the set of positive integers and X is a nonempty set
For convenience, we denote gx = g(x) for each x Î X and each mapping g : X ® X
The mappings g : X ® X and F : X × X ® X are called w-compatible if g(F(x, y)) = F(gx, gy) whenever gx = F(x, y) and gy = F(y, x). They established several coupled coincidence point theorems and common fixed point theorems for such mappings
Summary
1 Introduction Throughout this article, unless otherwise specified, we always suppose that N is the set of positive integers and X is a nonempty set. Let (X, d) be a complete metric space. Mn = max{d(gxn, gxn−1), d(gyn, gyn−1), d(gxn, gxn+1), d(gyn, gyn+1)}. Let us prove that for each n Î N, Mn = max{d(gxn, gxn−1), d(gyn, gyn−1)}.
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