On self-mapping degrees of <Emphasis Type="Italic">S</Emphasis><Superscript>3</Superscript>-geometry manifolds

In this paper we determined all of the possible self-mapping degrees of the manifolds with S3-geometry, which are supposed to be all 3-manifolds with finite fundamental groups. This is a part of a project to determine all possible self-mapping degrees of all closed orientable 3-manifold in Thurston＇s picture.     

Homomorphisms in quasi-Banach algebras associated with a Pexiderized Cauchy-Jensen functional equation

In this paper, we prove the generalized Hyers-Ulam stability of homomorphisms in quasi- Banach algebras associated with the following Pexiderized Jensen functional equation
f（x＋y/2＋z）-g（x-y/2＋z）=h（y）.
This is applied to investigating homomorphisms between quasi-Banach algebras. The concept of the generalized Hyers-Ulam stability originated from Rassias＇ stability theorem that appeared in his paper： On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72, 297-300 （1978）.     

Viscosity methods for zeroes of accretive operators

This paper deals with the general iteration method , for calculating a particular zero of A, an m-accretive operator in a Banach space X, T_n being a sequence of nonexpansive self-mappings in X. Under suitable conditions on the parameters and X, we state strong and weak convergence results of (x_n). We also show how to compute a common zero of two m-accretive operators in X.     

Stability for parametric implicit vector equilibrium problems

In this paper, we consider a class of parametric implicit vector equilibrium problems in Hausdorff topological vector spaces where a mapping f and a set K are perturbed by parameters and λ, respectively. We establish sufficient conditions for the upper semicontinuity and lower semicontinuity of the solution set mapping S:Λ₁×Λ₂→2^X for such parametric implicit vector equilibrium problems.     

On a Cauchy-Jensen functional equation and its stability

In this paper, we obtain the general solution and stability of the Cauchy-Jensen functional equation

     

Solutions of nonlinear evolution inclusions

In this paper, the solution of the nonlinear evolution inclusion problem of the form u^′(t)+B(t,u(t))∋f(t) is studied. In this problem, the operators are of type (M) or type (S₊), which are different from those of pseudo-monotone operators that had been studied by many authors. At the same time, we study the perturbation problem. In fact, many kinds of evolution equations can be generalized by this problem. The former results are improved and generalized by our conclusions, and we will give more applications.     

Effectively open real functions

A function f is continuous iff the pre-image f^-1[V] of any open set V is open again. Dual to this topological property, f is called open iff the image f[U] of any open set U is open again. Several classical open mapping theorems in analysis provide a variety of sufficient conditions for openness.By the main theorem of recursive analysis, computable real functions are necessarily continuous. In fact they admit a well-known characterization in terms of the mapping Vf^-1[V] being effective: given a list of open rational balls exhausting V, a Turing Machine can generate a corresponding list for f^-1[V]. Analogously, effective openness requires the mapping Uf[U] on open real subsets to be effective.The present work combines real analysis with algebraic topology and Tarski's quantifier elimination to effectivize classical open mapping theorems and to establish several rich classes of real functions as effectively open.     

Ergodic Retraction Theorem and Weak Convergence Theorem for Reversible Semigroups of Non-Lipschitzian Mappings

Let G be a semitopological semigroup. Let C be a closed convex subset of a uniformly convex Banaeh space E with a Frechet differentiable norm, and T = {Tt ： t ∈ G} be a continuous representation of G as nearly asymptotically nonexpansive type mappings of C into itself such that the common fixed point set F（T） of T in C is nonempty. It is shown that if G is right reversible, then for each almost-orbit u（.） of T, ∩s∈G ^-CO{u（t） ： t ≥ s} ∩ F（T） consists of at most one point. Furthermore, ∩s∈G ^-CO{Ttx ： t ≥ s} ∩ F（T） is nonempty for each x ∈ C if and only if there exists a nonlinear ergodic retraction P of C onto F（T） such that PTs - TsP = P for all s ∈ G and Px ∈^-CO{Ttx ： s ∈ G} for each x ∈ C. This result is applied to study the problem of weak convergence of the net {u（t） ： t ∈ G} to a common fixed point of T.