## Topological Methods in Nonlinear Analysis

### New results of mixed monotone operator equations

#### Abstract

In this article, we study the existence and uniqueness of fixed points for some mixed monotone operators and monotone operators with perturbation. These mixed monotone operators and monotone operators are $e$-concave-convex operators and $e$-concave operators respectively. Without using compactness or continuity, we obtain the existence and uniqueness of fixed points by monotone iterative techniques and properties of cones. Our main results extended and improved some existing results. Also, we applied the results to some differential equations.

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 53, Number 1 (2019), 271-289.

Dates
First available in Project Euclid: 12 March 2019

https://projecteuclid.org/euclid.tmna/1552356036

Digital Object Identifier
doi:10.12775/TMNA.2019.003

Mathematical Reviews number (MathSciNet)
MR3939156

Zentralblatt MATH identifier
07068337

#### Citation

Wang, Tian; Hao, Zhaocai. New results of mixed monotone operator equations. Topol. Methods Nonlinear Anal. 53 (2019), no. 1, 271--289. doi:10.12775/TMNA.2019.003. https://projecteuclid.org/euclid.tmna/1552356036

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