This paper deals with a new class of nonlinear set valued implicit variational inclusion problems involving （A, η）-monotone mappings in 2-uniformly smooth Banach spaces. Semi-inner product structure has been used t...This paper deals with a new class of nonlinear set valued implicit variational inclusion problems involving （A, η）-monotone mappings in 2-uniformly smooth Banach spaces. Semi-inner product structure has been used to study the （A, η）-monotonicity. Using the generalized resolvent operator technique and the semi-inner product structure, the approximation solvability of the proposed problem is investigated. An iterative algorithm is constructed to approximate the solution of the problem. Convergence analysis of the proposed algorithm is investigated. Similar results are also investigated for variational inclusion problems involving （H, η）-monotone mappings.展开更多
Define two operators In and It,the inner product operator In(g)(x) := j∈Zs(g,f(·-j))f(x-j) and the interpolation operator It(g)(x) := j∈Zs g(j)f(x-j),where f belongs to some space and integer s 1.We call f the ...Define two operators In and It,the inner product operator In(g)(x) := j∈Zs(g,f(·-j))f(x-j) and the interpolation operator It(g)(x) := j∈Zs g(j)f(x-j),where f belongs to some space and integer s 1.We call f the generator of the operators In and It.It is well known that there are many results on operators In and It.But there remain some important problems to be further explored.For application we first need to find the available generators (that can recover polynomials as It(p) = p or In(p) = p,p ∈Πm-1) for constructing the relative operators.In this paper,we focus on the available generator in the class of spline functions.We shall see that not all spline functions can be used to construct available generators.Fortunately,we do find a spline function in S,of degree m-1,where m is even and S is a class of splines.But for odd m the problem is still open.Results on spline functions in this paper are new.展开更多
文摘This paper deals with a new class of nonlinear set valued implicit variational inclusion problems involving （A, η）-monotone mappings in 2-uniformly smooth Banach spaces. Semi-inner product structure has been used to study the （A, η）-monotonicity. Using the generalized resolvent operator technique and the semi-inner product structure, the approximation solvability of the proposed problem is investigated. An iterative algorithm is constructed to approximate the solution of the problem. Convergence analysis of the proposed algorithm is investigated. Similar results are also investigated for variational inclusion problems involving （H, η）-monotone mappings.
基金supported by National Natural Science Foundation of China (Grant No.10671062,60972126)
文摘Define two operators In and It,the inner product operator In(g)(x) := j∈Zs(g,f(·-j))f(x-j) and the interpolation operator It(g)(x) := j∈Zs g(j)f(x-j),where f belongs to some space and integer s 1.We call f the generator of the operators In and It.It is well known that there are many results on operators In and It.But there remain some important problems to be further explored.For application we first need to find the available generators (that can recover polynomials as It(p) = p or In(p) = p,p ∈Πm-1) for constructing the relative operators.In this paper,we focus on the available generator in the class of spline functions.We shall see that not all spline functions can be used to construct available generators.Fortunately,we do find a spline function in S,of degree m-1,where m is even and S is a class of splines.But for odd m the problem is still open.Results on spline functions in this paper are new.
