Fixed Point Theorem of {a,b,c} Contraction and Nonexpansive Type Mappings in Weakly Cauchy Normed Spaces

Let C be a closed convex weakly Cauchy subset of a normed space X. Then we define a new {a,b,c} type nonexpansive and {a,b,c} type contraction mapping T from C into C. These types of mappings will be denoted respectively by {a,b,c}-ntype and {a,b,c}-ctype. We proved the following： 1. If T is {a,b,c}-ntype mapping, then inf{ ｜｜ T（x）-x｜｜ ：x C C} =0, accordingly T has a unique fixed point. Moreover, any sequence {Xn}n∈NN in C with limn→∞｜｜T（xn） - Xn｜｜ = 0 has a subsequence strongly convergent to the unique fixed point of T. 2. If T is {a,b,c}-ctype mapping, then T has a unique fixed point. Moreover, for any x∈C the sequence of iterates {Tn （x）}n∈N has subsequence strongly convergent to the unique fixed point of T. This paper extends and generalizes some of the results given in [2,4, 7] and [13].     

Hyperbolic Mapping Classes and Their Lifts on the Bers Fiber Space

Let S be a Riemann surface with genus p and n punctures. Assume that 3p - 3 n ＞ 0 and n ≥ 1. Let a be a puncture of S and let (～S) = S ∪ {a}. Then all mapping classes in the mapping class group Mods that fixes the puncture a can be projected to mapping classes of Mod(～S) under the forgetful map. In this paper the author studies the mapping classes in Mods that can be projected to a given hyperbolic mapping class in Mod(～S).     

Convergence analysis of iterative sequences for a pair of mappings in Banach spaces

Let C be a nonempty closed convex subset of a real Banach space E. Let S ： C→ C be a quasi-nonexpansive mapping, let T ： C→C be an asymptotically demicontractive and uniformly Lipschitzian mapping, and let F ：= {x ∈C ： Sx = x and Tx = x}≠Ф Let {xn}n≥0 be the sequence generated irom an arbitrary x0∈Cby xn＋i=（1-cn）Sxn＋cnT^nxn, n≥0.We prove the necessary and sufficient conditions for the strong convergence of the iterative sequence {xn} to an element of F. These extend and improve the recent results of Moore and Nnoli.     

More on Fixed Point Theorem of {a, b, c}-Generalized Nonexpansive Mappings in Normed Spaces

Let X be a weakly Cauchy normed space in which the parallelogram law holds, C be a bounded closed convex subset of X with one contracting point and T be an {a, b, c}-generalized-nonexpansive mapping from C into C. We prove that the infimum of the set { ||x-T(x)|| } on C is zero, study some facts concerning the {a,b,c}-generalized-nonexpansive mapping and prove that the asymptotic center of any bounded sequence with respect to C is singleton. Depending on the fact that the {a,b,0}-generalized-nonexpansive mapping from C into C has fixed points, accordingly, another version of the Browder ’s strong convergence theorem for mappings is given.     

The Degree of Proper Holomorphic MappingsBetween Special Domains in C^n

Let Gi be closed Lie groups of U (n), Ω i be bounded Gi-invariant domains in C^n which contains 0, and O(C^n)^Gi = C, for i = 1, 2. It is known that if f : Ω 1 → Ω 2 is a proper holomorphic mapping, and f^-1{0} = {0}, then f is a polynomial mapping. In this paper, we provide an upper bound for the degree of such a polynomial mapping using the multiplicity of f .     

严格伪压缩映象的Ishikawa 迭代序列的收敛率估计

It is shown that any fixed point of each l.ipschitzian, strictly pseudocontractive mapping 7“ on a closed convex subset K of a Banach space X may be norm approximated by Ishikawa iterative procedure. The argument in this paper provides a convergence rate estimate.Moreover the result in this paper improves, generalizes and summarizes some important and elegant recent results.     

A new class of three-variable orthogonal polynomials and their recurrences relations

A new class of three-variable orthogonai polynomials,defined as eigenfunctions of a second order PDE operator,is studied.These polynomials are orthogonal over a curved tetrahedron region, which can be seen as a mapping from a traditional tetrahedron,and can be taken as an extension of the 2-D Steiner domain.The polynomials can be viewed as Jacobi polynomials on such a domain.Three- term relations are derived explicitly.The number of the individual terms,involved in the recurrences relations,are shown to be independent on the total degree of the polynomials.The numbers now are determined to be five and seven,with respect to two conjugate variables z,(?) and a real variable r, respectively.Three examples are discussed in details,which can be regarded as the analogues of the Chebyshev polynomials of the first and the second kinds,and Legendre polynomials.     

Self-normalized Cramer-type Moderate Deviations for Functionals of Markov Chain

Let{xn,n≥0}be a Markov chain with a countable state space S and let f(·)be a measurable function from S to R and consider the functionals of the Markov chain yn:=f(xn).We construct a new type of self-normalized sums based on the random-block scheme and establish a Crame′r-type moderate deviations for self-normalized sums of functionals of the Markov chain.     

CONVERGENCE OF CONTROLLED MODELS FOR CONTINUOUS-TIME MARKOV DECISION PROCESSES WITH CONSTRAINED AVERAGE CRITERIA

This paper attempts to study the convergence of optimal values and optimal policies of continuous-time Markov decision processes(CTMDP for short)under the constrained average criteria. For a given original model M_∞of CTMDP with denumerable states and a sequence {M_n} of CTMDP with finite states, we give a new convergence condition to ensure that the optimal values and optimal policies of {M_n} converge to the optimal value and optimal policy of M_∞as the state space Snof Mnconverges to the state space S_∞of M_∞, respectively. The transition rates and cost/reward functions of M_∞are allowed to be unbounded. Our approach can be viewed as a combination method of linear program and Lagrange multipliers.     

Dimension Results for Space-anisotropic Gaussian Random Fields

Let X = {X(t) ∈ R~d, t ∈ R~N} be a centered space-anisotropic Gaussian random field whose components satisfy some mild conditions. By introducing a new anisotropic metric in R~d, we obtain the Hausdorff and packing dimension in the new metric for the image of X. Moreover, the Hausdorff dimension in the new metric for the image of X has a uniform version.     

POSITIVE FIXED POINT THEOREMS FOR β-SEMIDIFFERENTIABLE κ -SET-CONTRACTIVE MAPPINGS WITH APPLICATION TO AN INFECTIOUS DISEASE MODEL

In this paper we define the new concept of β -semidifferentiability of a mapping and obtain the positive fixed point theorems for β -semidifferentiable k -set-contractive mappings. Then the theorems are ap-plied to the nonlinear integral equation, x(t) = (s,x(s))ds , which can be interpreted as a modelfor the spread of certain infectious diseases, and the existence theorems of the positive solutions and positive eigenvalues for the equation are obtained.     

Continuous Order Homomorphism and bi-continuous Mapping

The relation of LFtopology on set X to the classical topology is always important for us to understand LFtopology. In this paper, we construct a bitopological space from a LFtopologial space,and we show that for a continuous order homomorphism between two LFtopological spaces there is a correspondent bicontinuous mapping between the constructed bitopological spaces.Let X be a set,L be a fuzzy lattice,use L~x denote all the fuzzy subsets of X use π_x denote set X×{L\{ O, 1} }, P(πx) is power set of π_x. Now we first define mapping, a of π_x into itself as following:     

THE EMBEDDED THEOREM AND ITS APPLICATION TO STATISTICAL METRIC SPACE

We prove the following result in this paper: Let(X, ζ, △) be a T—complete Menger space. If {T_i, i=1, 2, …} are a sequence of the self mapping of the contractive type on X and {m_i(x), i=1, 2, …} are the functional sequence satisfying m_i(x)|m(T_i(x)), i=1, 2, …, then {T_i, i=1, 2, …} have a common fixed point.This result is a generalization to the result obtained in I. Istratescu [7, 14]. Other results are proved concerning the fixed point theorems for G valued metric space. The concept, the embedded theorem of S. M. space, is discussed and its relation to the existence of fixed point for above mapping is also discussed in S. M. space.     

Modified mann iterations for nonexpansive semigroups in Banach space

Let E be a real reflexive Banach space which admits a weakly sequentially continuous duality mapping from E to E^＊, and C be a nonempty closed convex subset of E. Let {T（t） ： t ≥ 0} be a nonexpansive semigroup on C such that F ：=∩t≥0 Fix（T（t）） ≠ 0, and f ： C → C be a fixed contractive mapping. If {αn}, {βn}, {an}, {bn}, {tn} satisfy certain appropriate conditions, then we suggest and analyze the two modified iterative processes as：{yn=αnxn＋（1-αn）T（tn）xn,xn=βnf（xn）＋（1-βn）yn
{u0∈C,vn=anun＋（1-an）T（tn）un,un＋1=bnf（un）＋（1-bn）vn
We prove that the approximate solutions obtained from these methods converge strongly to q ∈∩t≥0 Fix（T（t））, which is a unique solution in F to the following variational inequality：
〈（I-f）q,j（q-u）〉≤0 u∈F Our results extend and improve the corresponding ones of Suzuki [Proc. Amer. Math. Soc., 131, 2133-2136 （2002）], and Kim and XU [Nonlear Analysis, 61, 51-60 （2005）] and Chen and He [Appl. Math. Lett., 20, 751-757 （2007）].     

Positive eigenvalue-eigenvector of nonlinear positive mappings

We show that an （eventually） strongly increasing and positively homogeneous mapping T defined on a Banach space can be turned into an Edelstein contraction with respect to Hilbert＇s projective metric. By applying the Edelstein contraction theorem, a nonlinear version of the famous Krein- Rutman theorem is presented, and a simple iteration process {T^kx/｜｜T^kx｜｜} （ x ∈ P^＋） is given for finding a positive eigenvector with positive eigenvalue of T. In particular, the eigenvalue problem of a nonnegative tensor A can be viewed as the fixed point problem of the Edelstein contraction with respect to Hilbert＇s projective metric. As a result, the nonlinear Perron-Frobenius property of a nonnegative tensor A is reached easily.     

REGULARITY OF P-HARMONIC MAPPINGS INTO NPC SPACES

Let M be a C²-smooth Riemannian manifold with boundary and X be a metric space with non-positive curvature in the sense of Alexandrov.Let u:M→X be a Sobolev mapping in the sense of Korevaar and Schoen.In this short note,we introduce a notion of p-energy for u which is slightly different from the original definition of Korevaar and Schoen.We show that each minimizing p-harmonic mapping(p≥2)associated to our notion of p-energy is locally Holder continuous whenever its image lies in a compact subset of X.     

The Degree of Proper Holomorphic Mappings Between Special Domains in■

Let G_i be closed Lie groups of U(n),Ω_i be bounded G_i-invariant domains in ■which contains 0,and■,for i=1,2.It is known that if f:Ω_1→Ω_2 is a proper holomorphic mapping,and,then f is a polynomial mapping.In this paper,we provide an upper bound for the degree of such a polynomial mapping using the multiplicity of f.     

Projection on Segre varieties and determination of holomorphic mappings between real submanifolds Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

It is shown that a germ of a holomorphic mapping sending a real-analytic generic submanifold of finite type into another is determined by its projection on the Segre variety of the target manifold. A necessary and sufficient condition is given for a germ of a mapping into the Segre variety of the target manifold to be the projection of a holomorphic mapping sending the source manifold into the target. An application to the biholomorphic equivalence problem is also given.     

A note on extremal quasi-conformal mappings

An extremal quasi-conformal mapping f of a domain D is said to be of non-landslide type if the set Ef(δ):= {z∈D:|μf(z)|≤||μ|| ∞ -δ} has no interior points for any δ 0. In this paper,we construct a quasi-conformal mapping f of the unit disc D such that its Teichmu¨ller equivalence class [f] contains infinitely many extremal mappings of non-landslide type. The relation between extremal mappings of non-landslide type and locally extremal mappings is also discussed.     

A Class of Cone Bounded Quasiconvex Mappings in Topological Vector Spaces

Within the context of cone-ordered topological vector spaces, this paper introduces the concepts of cone bounded point and cone bounded set for vector set. With their aid, a class of new cone quasiconvex mappings in topological vector spaces is defined, and their fundamental properties are presented. The relationships between the cone bounded quasiconvex mapping defined in this paper and cone convex mapping, and other known cone quasiconvex mapping are also discussed.