Abstract
This paper is concerned with mixed g-monotone mappings in partially ordered metric spaces. We establish several coupled coincidence and coupled common fixed point theorems, which generalize and complement some known results. Especially, our main results complement some recent results due to Lakshmikantham and Ciric. Two examples are given to illustrate the usability of our results. Mathematics Subject Classification(2010): 47H10, 54H25.
Highlights
1 Introduction The existence of fixed points for monotone mappings in partially ordered metric spaces was initialed in [1], and such problems have been of great interest for many mathematicians
The existence of coupled fixed points for mixed monotone mappings in partially ordered metric spaces was firstly studied by Bhaskar and Lakshmikantham [7], where some applications to periodic boundary value problems are studied
Lakshmikantham and Ćirić [13] introduced a new concept of mixed g-monotone mapping: Definition 1.1
Summary
The existence of fixed points for monotone mappings in partially ordered metric spaces was initialed in [1], and such problems have been of great interest for many mathematicians (see, e.g, [2,3,4,5,6] and references therein).The existence of coupled fixed points for mixed monotone mappings in partially ordered metric spaces was firstly studied by Bhaskar and Lakshmikantham [7], where some applications to periodic boundary value problems are studied. Lakshmikantham and Ćirić [13] established several coupled coincidence and coupled fixed point theorems for mixed g-monotone mappings in a partially ordered metric space. We have d(gxn+1, gxn) ≤ φ[max{d(gxn, gxn−1), d(gyn, gyn−1)}], (2:1) 0. d (gxn, gxn+1) = d (gyn, gyn+1) = 0, which means that (2.1) and (2.2) hold.
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