Random fixed point theorems in Banach spaces applied to a random nonlinear integral equation of the Hammerstein type

被引：0
作者：
Okeke G.A. [1 ]
Bishop S.A. [2 ]
Akewe H. [3 ]
机构：
[1] Department of Mathematics, School of Physical Sciences, Federal University of Technology, Owerri
[2] Department of Mathematics, Covenant University, Ota
[3] Department of Mathematics, University of Lagos, Akoka
来源：
Fixed Point Theory and Applications | / 2019卷 / 1期
关键词：
Almost sure T-stability; Bochner integrable; Generalized ϕ-weakly contraction of the rational type; Nonlinear integral equation of the Hammerstein type; Random fixed point; Random iterative process;
D O I：
10.1186/s13663-019-0665-4
中图分类号：
学科分类号：
摘要：
The purpose of this paper is to define a new random operator called the generalized ϕ-weakly contraction of the rational type. This new random operator includes those studied by Khan et al. (Filomat 31(12):3611–3626, 2017) and Zhang et al. (Appl. Math. Mech. 32(6):805–810, 2011) as special cases. We prove some convergence, existence, and stability results in separable Banach spaces. Moreover, we produce some numerical examples to demonstrate the applicability of our analytical results. Furthermore, we apply our results in proving the existence of a solution of a nonlinear integral equation of the Hammerstein type. © 2019, The Author(s).
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