Geodesic
The solutions of a class of operator equations based on different inequality
Yan, Xiaofang1 ; Zhu, Chuanxi1 ; Wu, Zhaoqi1
1 Department of Mathematics, Nanchang University, Nanchang, 330031, P. R. China
Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 2, p. 370-376.

Voir la notice de l'article provenant de la source International Scientific Research Publications

In this paper, by using random fixed point index theory, some new boundary conditions based on strictly convex or strictly concave functions are established and some new theorems for the solutions of a class of random semi-closed 1-set-contractive operator equations $A(\omega; x) = \mu x$ are obtained, which extend and generalize some corresponding results of Wang [S. Wang, Fixed Point Theory Appl., 2011 (2011), 7 pages]. Finally, an application to a class of random nonlinear integral equations is given to illustrate the usability of the obtained results.
DOI : 10.22436/jnsa.009.02.03
Classification : 47H10, 60H25
Keywords: Real Banach space, random semi-closed 1-set-contractive operator, random topological degree.

Yan, Xiaofang 1 ; Zhu, Chuanxi 1 ; Wu, Zhaoqi 1

1 Department of Mathematics, Nanchang University, Nanchang, 330031, P. R. China 
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Yan, Xiaofang; Zhu, Chuanxi; Wu, Zhaoqi. The solutions of a class of operator equations based on different inequality. Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 2, p. 370-376. doi : 10.22436/jnsa.009.02.03. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.02.03/

[1] Itoh, S. Random fixed point theorems with an application to random differential equations in Banach spaces, J. Math. Anal. Appl., Volume 67 (1979), pp. 261-273

[2] Li, G. On random fixed point index and some random fixed point theorems of random 1-set-contractive operator, Acta Math. Appl. Sin., Volume 19 (1996), pp. 203-212

[3] G. Li The existence theorems of the random solutions for random Hammerstein equation with random kernel, Appl. Math. Lett., Volume 15 (2002), pp. 121-125

[4] Li, G.; Debnath, L. The existence theorems of the random solutions for random Hammerstein type nonlinear equation, Appl. Math. Lett., Volume 13 (2000), pp. 111-115

[5] Sun, J. X. Nonlinear Functional Analysis and Applications , Science Press, Beijing, 2007

[6] Z. K. Wang An introduction to random functional analysis, Adv. Math.(in Chinese), Volume 5 (1962), pp. 45-71

[7] S. Wang The fixed point theorems of 1-set-contractive operators in Banach spaces, Fixed Point Theory Appl., Volume 2011 (2011), pp. 1-7

[8] C. Zhu Research on some problems for nonlinear operators , Nonlinear Anal., Volume 71 (2009), pp. 4568-4571

[9] Zhu, C.; C. F.Chen Calculations of random fixed point index, J. Math. Anal. Appl., Volume 339 (2008), pp. 839-844

[10] Zhu, C.; Xu, Z. Inequalities and solution of an operator equation , Appl. Math. Lett., Volume 21 (2008), pp. 607-611

[11] Zhu, C.; J. D. Yin Calculations of a random fixed point index of a random semi-closed 1-set-contractive operator , Math. Comput. Modelling, Volume 51 (2010), pp. 1135-1139

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