Coupled Random Fixed Point Theorems for Nonlinear Contractions in Partially Ordered Metric Spaces

被引：50

作者：

Ciric, Ljubomir ^{[1
]}

Lakshmikantham, V. ^{[2
]}

机构：

[1] Fac Mech Engn, Belgrade 11070, Serbia

[2] Florida Inst Technol, Dept Math Sci, Melbourne, FL 32901 USA

来源：

STOCHASTIC ANALYSIS AND APPLICATIONS | 2009年 / 27卷 / 06期

关键词：

Coupled coincidence; Coupled fixed point; Measurable mapping; Mixed monotone mapping; Random operator; MONOTONE ITERATIVE TECHNIQUE; RANDOM APPROXIMATIONS; SETS;

D O I：

10.1080/07362990903259967

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let (X, ) be a partially ordered set and suppose there is a metric d on X such that (X, d) is a complete separable metric space and (, sigma) be a measurable space. In this article a pair of random mappings F: x(XxX)X and g: xXX, where F has a mixed g-monotone property on X, and F and g satisfy the non-linear contractive condition (5) below, are introduced and investigated. Two coupled random coincidence and coupled random fixed point theorems are proved. These results are random versions and extensions of recent results of Lakshmikantham and Ciric [V. Lakshmikantham and Lj. Ciric, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces. Nonlinear Anal.Theor. 70(12) (2009): 4341-4349] and include several recent developments.

引用

页码：1246 / 1259

页数：14

共 36 条

[1] Agarwal R.P., 2004, APPL ANAL, V83, P711
[2] Generalized contractions in partially ordered metric spaces
Agarwal, Ravi P.
El-Gebeily, M. A.
O'Regan, Donal
[J]. APPLICABLE ANALYSIS, 2008, 87 (01) : 109 - 116
[3] Beg I., 1994, J. Appl. Math. Stochastic Anal., V7, P569, DOI [10.1155/S1048953394000444, DOI 10.1155/S1048953394000444]
[4] Monotone iterative technique for functional differential equations with retardation and anticipation
Bhaskar, T. Gnana
Lakshmikantham, V.
Devi, J. Vasundhara
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2007, 66 (10) : 2237 - 2242
[5] Fixed point theorems in partially ordered metric spaces and applications
Bhaskar, T. Gnana
Lakshmikantham, V.
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2006, 65 (07) : 1379 - 1393
[6] Ciric L., 2008, ITAL J PURE APPL MAT, V23, P37
[7] Monotone Generalized Nonlinear Contractions in Partially Ordered Metric Spaces
Ciric, Ljubomir
Cakic, Nenad
Rajovic, Miloje
Ume, Jeong Sheok
[J]. FIXED POINT THEORY AND APPLICATIONS, 2008, 2008 (1)
[8] On random coincidence and fixed points for a pair of multivalued and single-valued mappings
Ciric, Ljubomir B.
Ume, Jeong S.
Jesic, Sinisa N.
[J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2006, 2006 (1)
[9] Guo D., 1988, Nonlinear Problems in Abstract Cones
[10] Hadzic O., 1979, MAT VESNIK, V3, P397

← 1 2 3 4 →