scholarly journals A fixed point method to solve the nonlinear complementarity problem for a class of monotone operators

Filomat ◽  
2018 ◽  
Vol 32 (13) ◽  
pp. 4587-4590
Author(s):  
Dinu Teodorescu ◽  
Mohammad Khan
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Complementarity Problem ◽  
Real Hilbert Space ◽  
Nonlinear Complementarity Problem ◽  
Monotone Operators ◽  
Fixed Point Method ◽  
Banach Fixed Point Theorem ◽  
Nonlinear Complementarity

In this paper, using the classic Banach fixed point theorem, we study the nonlinear complementarity problem for a class of monotone operators in real Hilbert space.

scholarly journals Complete Controllability of Impulsive Stochastic Integrodifferential Systems in Hilbert Space

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Xisheng Dai ◽  
Feng Yang
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Wave Equation ◽  
Fixed Point Theorem ◽  
Semigroup Theory ◽  
Sufficient Conditions ◽  
Banach Fixed Point Theorem ◽  
Complete Controllability ◽  
Differential Systems ◽  
Stochastic Wave Equation

This paper concerns the complete controllability of the impulsive stochastic integrodifferential systems in Hilbert space. Based on the semigroup theory and Burkholder-Davis-Gundy's inequality, sufficient conditions of the complete controllability for impulsive stochastic integro-differential systems are established by using the Banach fixed point theorem. An example for the stochastic wave equation with impulsive effects is presented to illustrate the utility of the proposed result.

scholarly journals A nonlinear complementarity problem in mathematical programming in Hilbert space

1979 ◽  
Vol 20 (2) ◽  
pp. 233-236 ◽  
Author(s):  
Sribatsa Nanda ◽  
Sudarsan Nanda
Keyword(s):  
Hilbert Space ◽  
Complementarity Problem ◽  
Existence And Uniqueness ◽  
Nonlinear Complementarity Problem ◽  
Closed Convex Cone ◽  
Existence And Uniqueness Theorem ◽  
Polar Cone ◽  
Nonlinear Complementarity ◽  
Banach Contraction ◽  
The Banach Contraction Principle

In this paper we prove the following existence and uniqueness theorem for the nonlinear complementarity problem by using the Banach contraction principle. If T: K → H is strongly monotone and lipschitzian with k2 < 2c < k2+1, then there is a unique y ∈ K, such that Ty ∈ K* and (Ty, y) = 0 where H is a Hilbert space, K is a closed convex cone in H, and K* the polar cone.

scholarly journals On Almost Automorphic Mild Solutions for Nonautonomous Stochastic Evolution Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Jing Cui ◽  
Litan Yan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Banach Fixed Point Theorem ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Almost Automorphic ◽  
Composition Theorem

We consider a class of nonautonomous stochastic evolution equations in real separable Hilbert spaces. We establish a new composition theorem for square-mean almost automorphic functions under non-Lipschitz conditions. We apply this new composition theorem as well as intermediate space techniques, Krasnoselskii fixed point theorem, and Banach fixed point theorem to investigate the existence of square-mean almost automorphic mild solutions. Some known results are generalized and improved.

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