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Research Article | Open Access

Fixed points of generalized φ-concave-convex operators with mixed monotonicity and applications

Shaoyuan Xu1, Li Fan2, Yan Han2( )
School of Mathematics and Statistics, Hanshan Normal University, Chaozhou, Guangdong, China
School of Mathematics and Statistics, Zhaotong University, Zhaotong, Yunnan, China
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Abstract

In this paper, we introduced a new concept of generalized φ-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.

Keywords

generalized φ-concave-convex operatormixed monotone operatorfixed point
CLC number: 47H10

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AIMS Mathematics
Volume 9 Issue 11,
November 2024
Pages 32442-32462
DOI: 10.3934/math.20241555

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Cite this article:
Xu S, Fan L, Han Y. Fixed points of generalized φ-concave-convex operators with mixed monotonicity and applications. AIMS Mathematics, 2024, 9(11): 32442-32462. https://doi.org/10.3934/math.20241555

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Received: 03 September 2024
Revised: 27 October 2024
Accepted: 07 November 2024
Published: 15 November 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)