
广义e-ω-凹算子的不动点及其应用
Fixed Points of Generalized e-ω-Concave Operator and Application
给出广义e-ω-凹算子的定义,在假设算子A不是锥映射的前提下,得到了广义e-ω-凹算子的不动点的存在唯一性以及单调迭代列.最后, 将主要结果应用到一类Hammerstein型积分方程中去.
We present the definition of generalized e-ω-concave operator, under the assumption that A is not a cone mapping, we obtain the existence and uniqueness of the fixed point, and the monotone iterative sequence of the fixed point for generalized e-ω-concave operator. Finally, we apply the main results to a class of Hammerstein integral equations.
广义e-&omega / -凹算子 / 锥 / 不动点 {{custom_keyword}} /
generalized e-ω-concave operator / cone / fixed point {{custom_keyword}} /
[1] Cui Y. J., Sun J. X., Fixed point theorems for a class of nonlinear operators in Hilbert spaces and applications, Positivity, 2011, 15: 455-464.
[2] Deimling K., Nonlinear Functional Analysis, Springer-Verlag, Berlin, 1985.
[3] Guo D. J., Nonlinear Functional Analysis, Shandong Sci. Tech., Ji'nan, 2001 (in Chinese).
[4] Guo D. J., Lakshmikantham V., Nonlinear Problems in Abstract Cones, Academic Press, Boston, 1988.
[5] Krasnoselskii M. A., Zabreiko P. P., Geometrical Methods of Nonlinear Analysis, Springer-Verlag, New York, 1984.
[6] Li X. C., Zhao Z. Q., On a fixed point theorem of mixed monotone operators and applications, Elec. J. of Qual. Theory of Diff. Equ., 2011, 94: 1-7.
[7] Liang Z. D., Lian X. G., Zhang M. Y., A class of concave operators with applications, Nonlinear Anal. TMA, 2008, 68: 2507-2515.
[8] Liu Y. S., Global structure of solutions for a class of two-point boundary value problems involving singular and convex or concave nonlinearities, J. Math. Anal. Appl., 2006, 322: 75-86.
[9] Sang Y. B., A class of φ-concave operators and applications, Fixed Point Theory and Appl., 2013, 2013: Article ID 274.
[10] Sun J. X., Nonlinear Functional Analysis and Applications, Science Press, Bejing, 2007 (in Chinese).
[11] Xu B., Zhang Q. Y., Existence of a positive almost periodic solution for a nonlinear delay integral equation, Nonlinear Anal. TMA, 2011, 74: 5600-5605.
[12] Zhai C. B., Cao X. M., Fixed point theorems for τ-φ-concave operators and applications, Comput. Math. Appl., 2010, 59: 532-538.
[13] Zhai C. B., Xu L., Properties of positive solutions to a class of four-point boundary value problem of Caputo fractional differential equations with a parameter, Comm. Non. Sci. Numer. Simulat., 2014, 19: 2820-2827.
[14] Zhang Z. T., Wang K. L., On fixed point theorems of mixed monotone operators and applications, Nonlinear Anal. TMA, 2009, 70: 3279-3284.
[15] Zhao Z. Q., Existence and uniqueness of fixed points for some mixed monotone operators, Nonlinear Anal. TMA, 2010, 73: 1481-1490.
[16] Zhao Z. Q., Fixed points of τ-φ-convex operators and applications. Appl. Math. Lett., 2010, 23: 561-566.
[17] Zhao Z. Q., Multiple fixed points of a sum operator and applications, J. Math. Anal. Appl., 2009, 360: 1-6.
[18] Zhao Z. Q., Du X. S., Fixed points of generalized e-concave (generalized e-convex) operators and their applications, J. Math. Anal. Appl., 2007, 334: 1426-1438.
国家自然科学基金资助项目(11571197)
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