Research on Some Problems for Nonlinear Operators in the Z-Z-B Space

Yiping Liu and Chuanxi Zhu
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Yiping Liu: School of Mathematics and Computer Science, Nanchang University, Nanchang 330031, China
Chuanxi Zhu: School of Mathematics and Computer Science, Nanchang University, Nanchang 330031, China

Mathematics, 2022, vol. 10, issue 13, 1-10

Abstract: In this paper, we first propose a new concept of Z-Z-B spaces, which is a generalization of Z-C-X spaces. Meanwhile, the new concept of the superior cone is introduced. Secondly, we study some new problems for semi-closed 1-set-contractive operators in the Z-Z-B space and obtain some new results. These new theorems are proven by combining partial order theory with fixed point index theory. Regarding these theorems, in the latter part of the paper, the proofs are omitted since the methods of proving these theorems are similar. Moreover, two important inequality lemmas are proven.

Keywords: Z-Z-B space; semi-closed 1-set-contractive operator; operator equation; excellent cone; fixed point; homotopy invariance property (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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