Several Fixed Point Theorems on Partially Ordered Banach Spaces and Applications

zbMATH Open1479.47049arXiv1706.06722MaRDI QIDQ5165101

Jinlu Li

Publication date: 15 November 2021

Abstract: In this paper, we prove several fixed point theorems on both of normal partially ordered Banach spaces and regular partially ordered Banach spaces by using the normality, regularity, full regularity, and chain -complete property. Then, by applying these theorems, we provide some existence and uniqueness of solutions to some integral equations. We also prove the solvability of some equilibrium problems in Banach spaces.

Full work available at URL: https://arxiv.org/abs/1706.06722

zbMATH Keywords

fixed pointpartially ordered Banach spaceuniversally inductive poset

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Applications of operator theory to differential and integral equations (47N20) Ordered topological linear spaces, vector lattices (46A40)

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