Fixed point theorems for the sum of three classes of mixed monotone operators and applications
In this paper we develop various new fixed point theorems for a class of operator equations with three general mixed monotone operators, namely A(x,x)+B(x,x)+C(x,x)=x on ordered Banach spaces, where A, B, C are the mixed monotone operators. A is such that for any t∈(0,1), there exists φ(t)∈(t,1] suc...
| Main Authors: | , , |
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| Format: | Journal Article |
| Published: |
SpringerOpen
2016
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| Online Access: | http://hdl.handle.net/20.500.11937/51922 |
| _version_ | 1848758801212112896 |
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| author | Zhang, X. Liu, Lishan Wu, Yong Hong |
| author_facet | Zhang, X. Liu, Lishan Wu, Yong Hong |
| author_sort | Zhang, X. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper we develop various new fixed point theorems for a class of operator equations with three general mixed monotone operators, namely A(x,x)+B(x,x)+C(x,x)=x on ordered Banach spaces, where A, B, C are the mixed monotone operators. A is such that for any t∈(0,1), there exists φ(t)∈(t,1] such that for all x,y∈P, A(tx,t−1y)≥φ(t)A(x,y); B is hypo-homogeneous, i.e. B satisfies that for any t∈(0,1), x,y∈P, B(tx,t−1y)≥tB(x,y); C is concave-convex, i.e. C satisfies that for fixed y, C(⋅,y):P→P is concave; for fixed x, C(x,⋅): P→P is convex. Also we study the solution of the nonlinear eigenvalue equation A(x,x)+B(x,x)+C(x,x)=λx and discuss its dependency to the parameter. Our work extends many existing results in the field of study. As an application, we utilize the results obtained in this paper for the operator equation to study the existence and uniqueness of positive solutions for a class of nonlinear fractional differential equations with integral boundary conditions. |
| first_indexed | 2025-11-14T09:49:45Z |
| format | Journal Article |
| id | curtin-20.500.11937-51922 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:49:45Z |
| publishDate | 2016 |
| publisher | SpringerOpen |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-519222021-01-08T07:54:29Z Fixed point theorems for the sum of three classes of mixed monotone operators and applications Zhang, X. Liu, Lishan Wu, Yong Hong In this paper we develop various new fixed point theorems for a class of operator equations with three general mixed monotone operators, namely A(x,x)+B(x,x)+C(x,x)=x on ordered Banach spaces, where A, B, C are the mixed monotone operators. A is such that for any t∈(0,1), there exists φ(t)∈(t,1] such that for all x,y∈P, A(tx,t−1y)≥φ(t)A(x,y); B is hypo-homogeneous, i.e. B satisfies that for any t∈(0,1), x,y∈P, B(tx,t−1y)≥tB(x,y); C is concave-convex, i.e. C satisfies that for fixed y, C(⋅,y):P→P is concave; for fixed x, C(x,⋅): P→P is convex. Also we study the solution of the nonlinear eigenvalue equation A(x,x)+B(x,x)+C(x,x)=λx and discuss its dependency to the parameter. Our work extends many existing results in the field of study. As an application, we utilize the results obtained in this paper for the operator equation to study the existence and uniqueness of positive solutions for a class of nonlinear fractional differential equations with integral boundary conditions. 2016 Journal Article http://hdl.handle.net/20.500.11937/51922 10.1186/s13663-016-0533-4 http://creativecommons.org/licenses/by/4.0/ SpringerOpen fulltext |
| spellingShingle | Zhang, X. Liu, Lishan Wu, Yong Hong Fixed point theorems for the sum of three classes of mixed monotone operators and applications |
| title | Fixed point theorems for the sum of three classes of mixed monotone operators and applications |
| title_full | Fixed point theorems for the sum of three classes of mixed monotone operators and applications |
| title_fullStr | Fixed point theorems for the sum of three classes of mixed monotone operators and applications |
| title_full_unstemmed | Fixed point theorems for the sum of three classes of mixed monotone operators and applications |
| title_short | Fixed point theorems for the sum of three classes of mixed monotone operators and applications |
| title_sort | fixed point theorems for the sum of three classes of mixed monotone operators and applications |
| url | http://hdl.handle.net/20.500.11937/51922 |