半序空间中一类算子方程的可解性及应用

刘展, 朱传喜

数学学报 ›› 2009, Vol. 52 ›› Issue (6) : 1181-1188.

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数学学报 ›› 2009, Vol. 52 ›› Issue (6) : 1181-1188. DOI: 10.12386/A2009sxxb0147
论文

半序空间中一类算子方程的可解性及应用

    刘展1, 朱传喜2
作者信息 +

Solvability Theorems with Applications of an Operator Equation in Partial Order Space

    Zhan LIU1, Chuan Xi ZHU2
Author information +
文章历史 +

摘要

本文在算子LN都不必连续的情况下,利用锥理论和半序方法,在完备度量空间中 和Banach空间中分别讨论了混合单调算子方程Lx = N(x,y)耦合拟解与解的存在性问题,构造出了新的非对称迭代序列研究了其逼近情况,得到了一些新的定理. 最后,我们将所获得的结果应用于对Hammerstain非线性积分方程的解的存在性问题的研究.

 

Abstract

In this paper, the theorem of cone and the techniques of partial order theory are used to discuss the existence of coupled quasi-solutions and solutions for a mixed monotone operator equation Lx = N(x,y) in complete metric space and Banach space, where neither L nor N need to be continuous. We also construct some new non-symmetric iterative sequences and study their approximation, then we get some new theorems. Finally, we apply the new results presented in this paper to Hammerstain integral equations.

 

关键词

半序 / 完备度量空间 / Banach空间

Key words

partial order / complete metric space / Banach space

引用本文

导出引用
刘展, 朱传喜. 半序空间中一类算子方程的可解性及应用. 数学学报, 2009, 52(6): 1181-1188 https://doi.org/10.12386/A2009sxxb0147
Zhan LIU, Chuan Xi ZHU. Solvability Theorems with Applications of an Operator Equation in Partial Order Space. Acta Mathematica Sinica, Chinese Series, 2009, 52(6): 1181-1188 https://doi.org/10.12386/A2009sxxb0147

参考文献


[1] Caristi J., Fixed point theorems for mappings satisfying inwardness conditions, Trans. Amer. Math. Soc., 1976,  215: 241--251.

[2] Feng Y. Q., Liu S. Y., Solveability of an operator equation in partial order space, Acta Mathematica Sinica, Chinese Series, 2003, 46: 411--416.

[3] Feng Y. Q., Liu S. Y., Solveability of an operator equation in partial order compiete metric space and partial order Banach space, Acta Mathematica Sinica, Chinese Series, 2005, 48: 109--114.

[4] Duan H. G., Fixed Point Theorems with Applications of Several Classes of Nonlinear Operators, Nanchang: Jiangxi Normal University, 2004.

[5] Guo D. J., Partial Order Methods in Nonlinear Analysis, Jinan: Shandong Science and Technology Press, 2000 (in Chinese).

[6] Zhu C. X., Generalizations of Krasnoselskii's theorem and Petryshyn's theorem, Appl. Math. Letters, 2006,  19: 628--632.

[7] Guo D. J., Existence and uniqueness of positive fixed points for mixed monotone operators and applications, Appl. Anal., 1992, 46: 91--100.

[8] Liang Z. D., Wang W. X., Li S. J., On concave operators, Acta Mathematica Sinica, English Series, 2006, 22(2): 577--582.

[9] Zhao Z. Q., Existence of positive fixed points for a convex operators with applications, Acta Mathematica Sinica, Chinese Series, 2006, 49(1): 139--144. indent=6mm

[10] Zhai C. B., Wang W. X., Zhang L. L., Generalizations for a class of concave and convex operators, Acta Mathematica Sinica, Chinese Series, 2008, 51(3): 529--540.

基金

国家自然科学基金资助项目(10461007,10761007);江西省自然科学基金资助项目(0411043);江西省教育厅科研项目2006[8]

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