Coupled coincidence point and common coupled fixed point theorems lacking the mixed monotone property

被引：0
作者：
Ravi P Agarwal
Wutiphol Sintunavarat
Poom Kumam
机构：
[1] Texas A&M University Kingsville,Department of Mathematics
[2] King Abdulaziz University,Department of Mathematics, Faculty of Science
[3] King Mongkut’s University of Technology Thonburi (KMUTT),Department of Mathematics, Faculty of Science
[4] Bang Mod,undefined
[5] Thrung Kru,undefined
来源：
Fixed Point Theory and Applications | / 2013卷
关键词：
cone metric spaces; common coupled fixed point; coupled coincidence point; -compatible mappings; mixed ; -monotone property;
D O I：
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摘要：
In this paper, we prove the coupled coincidence point theorems for a w∗-compatible mapping in partially ordered cone metric spaces over a solid cone without the mixed g-monotone property. In the case of a totally ordered space, these results are automatically obvious under the assumption given. Therefore, these results can be applied in a much wider class of problems. We also prove the uniqueness of a common coupled fixed point in this setup and give some example which is not applied to the existence of a common coupled fixed point by using the mixed g-monotone property but can be applied to our results.
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[1]  
Turinici M(1986)Abstract comparison principles and multivariable Gronwall-Bellman inequalities J. Math. Anal. Appl 117 100-127
[2]  
Ran ACM(2004)A fixed point theorem in partially ordered sets and some applications to matrix equations Proc. Am. Math. Soc 132 1435-1443
[3]  
Reurings MCB(2009)Fixed point and common fixed point theorems on ordered cone metric spaces Appl. Math. Lett 23 310-316
[4]  
Altun I(2011)Coincidence and common fixed point results in partially ordered cone metric spaces and applications to integral equations Nonlinear Anal 74 6814-6825
[5]  
Damjanović B(2010)Common fixed point theorems for ordered contractions and quasicontractions in ordered cone metric spaces Comput. Math. Appl 59 3148-3159
[6]  
Djorić D(2005)Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations Order 22 223-239
[7]  
Aydi H(1987)Coupled fixed points of nonlinear operators with applications Nonlinear Anal., Theory Methods Appl 11 623-632
[8]  
Nashine HK(2006)Fixed point theorems in partially ordered metric spaces and applications Nonlinear Anal 65 1379-1393
[9]  
Samet B(2011)Fixed point theorems for mixed monotone operators and applications to integral equations Nonlinear Anal 74 1749-1760
[10]  
Yazidi H(2011)Coupled fixed points in partially ordered metric spaces and application Nonlinear Anal 74 983-992
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