scholarly journals Hölder continuous retractions and amenable semigroups of uniformly Lipschitzian mappings in Hilbert spaces

2016 ◽  
Vol 43 (1) ◽  
pp. 89
Author(s):  
Andrzej Wiśnicki
Keyword(s):  
Hilbert Spaces ◽  
Hölder Continuous ◽  
Lipschitzian Mappings ◽  
Amenable Semigroups

scholarly journals The Split Common Fixed Point Problem for Quasi-Total Asymptotically Nonexpansive Uniformly Lipschitzian Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Jing Na ◽  
Lin Wang ◽  
Zhaoli Ma
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Hilbert Spaces ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Lipschitzian Mappings ◽  
Common Fixed Point Problem ◽  
Asymptotically Nonexpansive ◽  
Uniformly Lipschitzian Mapping ◽  
Split Common Fixed Point

We introduce an algorithm for solving the split common fixed point problem for quasi-total asymptotically nonexpansive uniformly Lipschitzian mapping in Hilbert spaces. The results presented in this paper improve and extend some recent corresponding results.

scholarly journals Multi-Step Inertial Regularized Methods for Hierarchical Variational Inequality Problems Involving Generalized Lipschitzian Mappings

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2103
Author(s):  
Bingnan Jiang ◽  
Yuanheng Wang ◽  
Jen-Chih Yao
Keyword(s):  
Variational Inequality ◽  
Strong Convergence ◽  
Iterative Methods ◽  
Hilbert Spaces ◽  
Numerical Experiments ◽  
Variational Inequality Problems ◽  
Convergence Theorems ◽  
Lipschitzian Mappings ◽  
Regularized Methods

In this paper, we construct two multi-step inertial regularized methods for hierarchical inequality problems involving generalized Lipschitzian and hemicontinuous mappings in Hilbert spaces. Then we present two strong convergence theorems and some numerical experiments to show the effectiveness and feasibility of our new iterative methods.

scholarly journals Hölder Continuous Regularity of Stochastic Convolutions with Distributed Delay

2021 ◽  
Author(s):  
Kai Liu
Keyword(s):  
Differential Equations ◽  
Hilbert Spaces ◽  
Functional Differential Equations ◽  
Distributed Delay ◽  
Fundamental Solutions ◽  
Regularity Property ◽  
Hölder Continuous ◽  
Stochastic Convolutions ◽  
Retarded Functional Differential Equations ◽  
Functional Differential

AbstractIn this work, we consider the Hölder continuous regularity of stochastic convolutions for a class of linear stochastic retarded functional differential equations with distributed delay in Hilbert spaces. By focusing on distributed delays, we first establish some more delicate estimates for fundamental solutions than those given in Liu (Discrete Contin. Dyn. Syst. Ser. B 25(4), 1279–1298, 2020). Then we apply these estimates to stochastic convolutions incurred by distributed delay to study their regularity property. Last, we present some easily-verified results by considering the regularity of a class of systems whose delay operators have the same order derivatives as those in instantaneous ones.

scholarly journals Degenerate SDEs in Hilbert spaces with rough drifts

2015 ◽  
Vol 18 (04) ◽  
pp. 1550026 ◽  
Author(s):  
Feng-Yu Wang ◽  
Xicheng Zhang
Keyword(s):  
Differential Equations ◽  
Hilbert Spaces ◽  
Existence And Uniqueness ◽  
Stochastic Systems ◽  
Mild Solutions ◽  
The Other ◽  
Hölder Continuous ◽  
Finite Dimensional ◽  
Finite Dimensional Case ◽  
White Noises

The existence and uniqueness of mild solutions are proved for a class of degenerate stochastic differential equations on Hilbert spaces where the drift is Dini continuous in the component with noise and Hölder continuous of order larger than [Formula: see text] in the other component. In the finite-dimensional case the Dini continuity is further weakened. The main results are applied to solve second order stochastic systems driven by spacetime white noises.

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