Fixed point theorems of nondecreasing order-Ćirić-Lipschitz mappings in normed vector spaces without normalities of cones


Authors

Zhilong Li - School of Statistics, Jiangxi University of Finance and Economics, Nanchang 330013, China. - Research Center of Applied Statistics, Jiangxi University of Finance and Economics, Nanchang 330013, China. Shujun Jiang - Department of Mathematics, Jiangxi University of Finance and Economics, Nanchang 330013, China.


Abstract

We introduce the concept of order-Ćirić-Lipschitz mappings, and prove some fixed point theorems for such kind of mappings in normed vector spaces without assuming the normalities of cones by using upper and lower solutions method, which improve many existing results of order-Lipschitz mappings in Banach spaces or Banach algebras. It is worth mentioning that even in the setting of normal cones, the main results in this paper are still new since the sum of spectral radius or the sum of restricted constants may be greater than or equal to 1.


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