Fixed points of generalized $ \varphi $-concave-convex operators with mixed monotonicity and applications

Shaoyuan Xu; Li Fan; Yan Han; Shaoyuan Xu; Li Fan; Yan Han

doi:10.3934/math.20241555

AIMS Mathematics

2024, Volume 9, Issue 11: 32442-32462. doi: 10.3934/math.20241555

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Research article

Fixed points of generalized $ \varphi $-concave-convex operators with mixed monotonicity and applications

Shaoyuan Xu ¹,
Li Fan ²,
Yan Han ^{2
,
,}

1.
School of Mathematics and Statistics, Hanshan Normal University, Chaozhou, Guangdong, China
2.
School of Mathematics and Statistics, Zhaotong University, Zhaotong, Yunnan, China

Received: 03 September 2024 Revised: 27 October 2024 Accepted: 07 November 2024 Published: 15 November 2024
MSC : 47H10

In this paper, we introduced a new concept of generalized $ \varphi $-concave-convex operator and proved the existence and uniqueness of fixed points of such operators with mixed monotonicity. As consequences, several new fixed point results about mixed monotone operators with some concavity and convexity were gained. In addition, the main results were applied to nonlinear integral equations on unbounded regions. The research findings generalized and developed recent relevant results in the literature.
- generalized $ \varphi $-concave-convex operator,
- mixed monotone operator,
- fixed point
Citation: Shaoyuan Xu, Li Fan, Yan Han. Fixed points of generalized $ \varphi $-concave-convex operators with mixed monotonicity and applications[J]. AIMS Mathematics, 2024, 9(11): 32442-32462. doi: 10.3934/math.20241555

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Abstract

In this paper, we introduced a new concept of generalized $ \varphi $-concave-convex operator and proved the existence and uniqueness of fixed points of such operators with mixed monotonicity. As consequences, several new fixed point results about mixed monotone operators with some concavity and convexity were gained. In addition, the main results were applied to nonlinear integral equations on unbounded regions. The research findings generalized and developed recent relevant results in the literature.

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