scholarly journals Approximation for the Hierarchical Constrained Variational Inequalities over the Fixed Points of Nonexpansive Semigroups

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Li-Jun Zhu
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Nonexpansive Mapping ◽  
Fixed Points ◽  
Linear Operators ◽  
Nonexpansive Semigroup ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Nonexpansive Semigroups

The purpose of the present paper is to study the hierarchical constrained variational inequalities of finding a pointx*such thatx*∈Ω,〈(A-γf)x*-(I-B)Sx*,x-x*〉≥0,  ∀x∈Ω, whereΩis the set of the solutions of the following variational inequality:x*∈Ϝ,〈(A-S)x*,x-x*〉≥0,  ∀x∈Ϝ, whereA,Bare two strongly positive bounded linear operators,fis aρ-contraction,Sis a nonexpansive mapping, andϜis the fixed points set of a nonexpansive semigroup{T(s)}s≥0. We present a double-net convergence hierarchical to some elements inϜwhich solves the above hierarchical constrained variational inequalities.

scholarly journals Some Results on the Approximation of Solutions of Variational Inequalities for Multivalued Maps on Banach Spaces

2021 ◽  
Vol 18 (4) ◽  
Author(s):  
Luigi Muglia ◽  
Giuseppe Marino
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Nonexpansive Mapping ◽  
Fixed Points ◽  
Banach Spaces ◽  
Unique Solution ◽  
Nonexpansive Mappings ◽  
Multivalued Maps ◽  
Demiclosedness Principle

AbstractMultivalued $$*$$ ∗ -nonexpansive mappings are studied in Banach spaces. The demiclosedness principle is established. Here we focus on the problem of solving a variational inequality which is defined on the set of fixed points of a multivalued $$*$$ ∗ -nonexpansive mapping. For this purpose, we introduce two algorithms approximating the unique solution of the variational inequality.

Cline’s formula for g-Drazin inverses in a ring

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2249-2255
Author(s):  
Huanyin Chen ◽  
Marjan Abdolyousefi
Keyword(s):  
Operator Theory ◽  
Spectral Properties ◽  
Associative Ring ◽  
Linear Operators ◽  
Drazin Inverse ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Cline’S Formula

It is well known that for an associative ring R, if ab has g-Drazin inverse then ba has g-Drazin inverse. In this case, (ba)d = b((ab)d)2a. This formula is so-called Cline?s formula for g-Drazin inverse, which plays an elementary role in matrix and operator theory. In this paper, we generalize Cline?s formula to the wider case. In particular, as applications, we obtain new common spectral properties of bounded linear operators.

Nonlocal fractional semilinear differential inclusions with noninstantaneous impulses and of order α ∈ (1, 2)

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
JinRong Wang ◽  
Ahmed G. Ibrahim ◽  
Donal O’Regan ◽  
Adel A. Elmandouh
Keyword(s):  
Differential Inclusions ◽  
Mild Solutions ◽  
Multivalued Function ◽  
Linear Operators ◽  
Solution Set ◽  
Cosine Family ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Noninstantaneous Impulses

AbstractIn this paper, we establish the existence of mild solutions for nonlocal fractional semilinear differential inclusions with noninstantaneous impulses of order α ∈ (1,2) and generated by a cosine family of bounded linear operators. Moreover, we show the compactness of the solution set. We consider both the case when the values of the multivalued function are convex and nonconvex. Examples are given to illustrate the theory.

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