Quadruple Coincidence Point Theorems for Mixed <em>g</em>-Monotone Mappings in Partially Ordered Metric Spaces and Their Applications

XU Wen-qing; ZHU Chuan-xi; WU Zhao-qi

doi:10.3879/j.issn.1000-0887.2015.03.011

Volume 36 Issue 3

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XU Wen-qing, ZHU Chuan-xi, WU Zhao-qi. Quadruple Coincidence Point Theorems for Mixed g-Monotone Mappings in Partially Ordered Metric Spaces and Their Applications[J]. Applied Mathematics and Mechanics, 2015, 36(3): 332-342. doi: 10.3879/j.issn.1000-0887.2015.03.011

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Quadruple Coincidence Point Theorems for Mixed g-Monotone Mappings in Partially Ordered Metric Spaces and Their Applications

doi: 10.3879/j.issn.1000-0887.2015.03.011

Department of Mathematics, Nanchang University, Nanchang 330031, P.R.China

Funds: The National Natural Science Foundation of China(11361042;11326099;11071108;11461045)

Received Date: 2014-09-22
Rev Recd Date: 2014-12-30
Publish Date: 2015-03-15

Abstract

Abstract

The concepts of α-admissible mappings and compatible mappings for a pair of mappings F:X⁴→X and g:X→X in partially ordered metric spaces were constructed. Based on this, with the iterative method, existence and uniqueness of the quadruple coincidence points for the α-admissible and compatible mappings satisfying the mixed g-monotone properties under the α-ψ-contractive conditions in the partially ordered complete metric spaces were studied, and some new theorems were established. Finally, 2 examples were presented as applications of the main theorems. The results show that the work generalizes and improves several fixed point theorems and coincidence point theorems in the recent corresponding literatures.
- partially ordered metric space,
- quadruple coincidence point,
- α-admissible mapping,
- compatible mapping,
- mixed g-monotone property

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References(18)

References

[1]	王亚琴, 曾六川. Banach空间中广义混合平衡问题, 变分不等式问题和不动点问题的混杂投影方法[J]. 应用数学和力学, 2011,32(2): 241-252.(WANG Ya-qin, ZENG Lu-chuan. Hybrid projection method for generalized mixed equilibrium problems, variational inequality problems and fixed point problems in Banach spaces[J]. Applied Mathematics and Mechanics,2011,32(2): 241-252.(in Chinese))
[2]	张石生, 王雄瑞, 李向荣, 陈志坚. 分层不动点及变分不等式的粘性方法及应用[J]. 应用数学和力学, 2011,32(2): 232-240.(ZHANG Shi-sheng, WANG Xiong-rui, Joseph Lee H W, Chi Kin Chan. Viscosity method for hierarchical fixed point and variational inequalities with applications[J].Applied Mathematics and Mechanics,2011,32(2): 232-240.(in Chinese))
[3]	Ran A C M, Reurings M C B. A fixed point theorem in partially ordered sets and some applications to matrix equations[J].Proceedings of the American Mathematical Society,2004,132(5): 1435-1443.
[4]	Agarwal R P, El-Gebeily M A, O’Regan D. Generalized contractions in partially ordered metric spaces[J].Applicable Analysis,2008,87(1): 1-8.
[5]	Bhaskar G T, Lakshmikantham V. Fixed point theorems in partially ordered metric spaces and applications[J].Nonlinear Analysis,2006,65(7): 1379-1393.
[6]	Lakshmikantham V, Ciric L. Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces[J].Nonlinear Analysis,2009,70(12): 4341-4349.
[7]	Borcut M, Berinde V. Tripled coincidence theorems for contractive type mappings in partially ordered metric spaces[J].Applied Mathematics and Computation,2012,218(10): 5929-5936.
[8]	LIU Xiao-lan. Quadruple fixed point theorems in partially ordered metric spaces with mixed g-monotone property[J].Fixed Point Theory and Applications,2013,2013. doi: 10.1186/1687-1812-2013-147.
[9]	Berinde V, Morcut M. Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces[J].Nonlinear Analysis,2011,74(15): 4889-4897.
[10]	Turkoglu D, Sangurlu M. Coupled fixed point theorems for mixed g-monotone mappings in partially ordered metric spaces[J].Fixed Point Theory Applications,2013,2013. doi: 10.1186/1687-1812-2013-348.
[11]	Nashine H K, Samet B, Vetro C. Monotone generalized nonlinear contractions and fixed point theorems in ordered metric spaces[J].Mathematical and Computer Modelling,2011,54(1/2): 712-720.
[12]	Karapinar E, Berinde V. Quadruple fixed point theorems for nonlinear contractions in partially ordered metric spaces[J].Banach Journal of Mathematical Analysis,2012,6(1): 74-89.
[13]	Karapinar E, Shatanawi W, Mustafa Z. Quadruple fixed point theorems under nonlinear contractive conditions in partially ordered metric spaces[J].Journal of Applied Mathematic,2012,2012. article ID 951912.
[14]	刘展, 朱传喜. 半序空间中一类算子方程的可解性及应用[J]. 数学学报, 2009,52(6): 1182-1188.(LIU Zhan, ZHU Chuan-xi. Solvability theorems with applications of an operator equation in partial order space[J].Acta Mathematica Sinica,2009,52(6): 1182-1188.(in Chinese))
[15]	尹建东. 半序空间中二元算子方程的可解性及应用[J]. 系统科学与数学, 2012,32(11): 1449-1458.(YIN Jian-dong. Solvablity of binary operator equations in partial ordered spaces and applications[J].Journal of System Science and Mathematical Science,2012,32(11): 1449-1458.(in Chinese))
[16]	卜香娟. Banach空间中一类序压缩映射的不动点定理[J]. 纯粹数学与应用数学, 2012,28(3): 334-341.(BU Xiang-juan. Fixed point theorems for a class of ordered contraction mapping in ordered Banach spaces[J].Pure and Applied Mathematics,2012,28(3): 334-341.(in Chinese))
[17]	Samet B, Vetro C, Vetro P. Fixed point theorems for α-ψ-contractive type mappings[J].Nonlinear Analysis,2012,75(4): 2154-2165.
[18]	Mursaleen M, Mohiuddine S A, Agarwal R P. Coupled fixed point theorems for α-ψ-contractive type mappings in partially ordered metric spaces[J].Fixed Point Theory and Applications,2012,2012. doi: 10.1186/1687-1812-2012-228.