Some new fixed point theorems for a mixed monotone maps in partially ordered metric spaces

被引：1

作者：

Zhang L. ^{[1
]}

Song G. ^{[2
]}

Wang G. ^{[1
]}

Wang H. ^{[2
]}

机构：

[1] School of Mathematics and Computer Science, Shanxi Normal University, Shanxi, Linfen

[2] College of Science, China University of Petroleum, Shandong, Qingdao

来源：

Mathematical Sciences | 2013年 / 7卷 / 1期

关键词：

Coupled fixed point; Partially ordered set; Nonlinear contraction mapping; Monotone iterative technique MSC 2010 47H10;

D O I：

10.1186/2251-7456-7-31

中图分类号：

学科分类号：

摘要：

In this paper, we prove some new fixed point theorems for a mixed monotone mapping under more generalized nonlinear contractive conditions in a metric space endowed with partial order. Our results generalize and improve several results due to the work of Gnana Bhaskar and Lakshmikantham. © 2013, Zhang et al.; licensee Springer.

引用

共 15 条

[1]

Guo D.J., Lakshmikantham V., Coupled fixed points of nonlinear operators with applications, Nonlinear Anal, 11, pp. 623-632, (1987)

[2]

Guo D.J., Lakshmikantham V., Nonlinear problems in abstract cones, (1988)

[3]

Zhang Z., New fixed point theorems of mixed monotone operators and applications, J. Math. Anal. Appl, 204, pp. 307-319, (1996)

[4]

Guo D.J., Existence and uniqueness of positive fixed point for mixed monotone operators with applications, Appl. Anal, 46, pp. 91-100, (1992)

[5]

Zhang S.S., Ma Y.H., Coupled fixed points for mixed monotone condensing operators and an existence theorem of the solution for a class of functional equations arising in dynamic programing, J. Math. Anal. Appl, 160, pp. 468-479, (1991)

[6]

Guo D.J., Partial order methods in nonlinear analysis, (2000)

[7]

Song G., Iterative solutions for systems of nonlinear operator equations in Banach space, Acta Mathematica Scientia, 23B, pp. 461-466, (2003)

[8]

Song G., Sun X., Zhao Y., Wang G., New common fixed point theorems for maps on cone metric spaces, Appl. Math. Lett, 23, pp. 1033-1037, (2010)

[9]

Samet B., Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces, Nonlinear Anal, 72, pp. 4508-4517, (2010)

[10]

Amini-Harandi A., Emami H., A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations, Nonlinear Anal, 72, pp. 2238-2242, (2010)

← 1 2 →