在本論文中，我們利用混合單調函數概念證明在偏序完備度量空間中收縮型函數的偶合同值點定理和偶合固定點定理。這些定理推廣了[22]的結果。我們也證明在緊緻度量空間中收縮型函數的偶合同值點定理和偶合固定點定理。我們的定理推廣了一些學者的研究成果。

In this paper, we first prove a coupled coincidence point theorem and a coupled fixed point theorem for contractive type mappings in partially ordered complete metric space by using the conception of mixed function monotone. These theorems extend the result of [4]. Secondly, we prove a coupled coincidence point theorem and a coupled fixed point theorem for contractive type mappings in compact metric space. Our theorems extend early results of some authors, for example, see [3].

[1] T. G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal.TMA65 (2006) 1379-1393.
[2] T. Gnana Bhaskar, V. Lakshmikantham, J. Vasundhara Devi, Monotone iterative technique for functional differential equations with retardation and anticipation, Nonlinear Anal. TMA 66 (10) (2007) 2237-2242.
[3] M. Edelstein, On fixed and periodic points under contractive mappings, J.
London Math. Soc., 37(1962), 74-79.
[4] V. Lakshmikantham, Ljubomir . Ćirić, Coupled fixed point theorems for
nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. TMA 70 (2009) 4341-4349.
[5] A. C. M. Ran, M. C. B. Reurings, A fixed point theorem in partially ordered sets
and some applications to matrix equations, Proc. Amer. Math. Soc. 132(2004)
1435-1443.