Abstract
Some new coupled coincidence point and coupled fixed point theorems are established in partially ordered metric-like spaces, which generalize many results in corresponding literatures. An example is given to support our main results. As an application, we discuss the existence of the solutions for a class of nonlinear integral equations.
Highlights
Introduction and PreliminariesAs we all know, the fixed point theory is one of the most important tools in the field of nonlinear analysis
In this paper, inspired by the above literatures, we propose some new coupled coincidence point and coupled fixed point theorems in partially ordered metric-like spaces, which extend the theorems of B
Let T : X × X → X and g : X → X be two mappings such that the following conditions are satisfied: (i) T(X × X) ⊆ g(X). (ii) g(X) is closed. (iii) T has the mixed g-monotone property. (iv) There exist x0, y0 ∈ X such that gx0 ⪯ T(x0, y0) and T(y0, x0) ⪯ gy0. (v)
Summary
The fixed point theory is one of the most important tools in the field of nonlinear analysis. The coupled fixed point theorems in partially ordered metric-like spaces are very valuable for discussing the existence and uniqueness of solutions of any nonlinear problem in fields of mathematics and physics. Many authors proved various fixed point theorems in partial metric spaces (see [2,3,4,5,6,7,8,9]). Some authors discussed the fixed point and coincidence point results in generalized metric spaces. [20] generalized some previous results and gave some new common fixed point theorems in metric-like spaces. In this paper, inspired by the above literatures, we propose some new coupled coincidence point and coupled fixed point theorems in partially ordered metric-like spaces, which extend the theorems of B.
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