HB-Continuous Mappings in L-Topological Space

In this paper, we introduce and study the notion of HB-closed sets in L-topological space. Then, HB-convergence theory for L-molecular nets and L-ideals is established in terms of HB-closedness. Finally, we give a new definition of fuzzy H-continuous [1] which is called HB-continuity on the basis of the notion of H-bounded L-subsets in L-topological space. Then we give characterizations and properties by making use of HB-converges theory of L-molecular nets and L-ideals.

A Normalizing Flow-Based Bidirectional Mapping Residual Network for Unsupervised Defect Detection

Unsupervised methods based on density representation have shown their abilities in anomaly detection,but detection performance still needs to be improved.Specifically,approaches using normalizing flows can accurately evaluate sample distributions,mapping normal features to the normal distribution and anomalous features outside it.Consequently,this paper proposes a Normalizing Flow-based Bidirectional Mapping Residual Network(NF-BMR).It utilizes pre-trained Convolutional Neural Networks(CNN)and normalizing flows to construct discriminative source and target domain feature spaces.Additionally,to better learn feature information in both domain spaces,we propose the Bidirectional Mapping Residual Network(BMR),which maps sample features to these two spaces for anomaly detection.The two detection spaces effectively complement each other’s deficiencies and provide a comprehensive feature evaluation from two perspectives,which leads to the improvement of detection performance.Comparative experimental results on the MVTec AD and DAGM datasets against the Bidirectional Pre-trained Feature Mapping Network(B-PFM)and other state-of-the-art methods demonstrate that the proposed approach achieves superior performance.On the MVTec AD dataset,NF-BMR achieves an average AUROC of 98.7%for all 15 categories.Especially,it achieves 100%optimal detection performance in five categories.On the DAGM dataset,the average AUROC across ten categories is 98.7%,which is very close to supervised methods.

THE FEKETE-SZEG?INEQUALITY AND SUCCESSIVE COEFFICIENTS DIFFERENCE FOR A SUBCLASS OF CLOSE-TO-STARLIKE MAPPINGS IN COMPLEX BANACH SPACES

Let C be the familiar class of normalized close-to-convex functions in the unit disk.In[17],Koepf demonstrated that,as to a function■in the class C,■By applying this inequality,it can be proven that‖a3|-|a2‖≤1 for close-to-convex functions.Now we generalized the above conclusions to a subclass of close-to-starlike mappings defined on the unit ball of a complex Banach space.

The Local Theory of Completely 1-Summing Mapping Spaces

In this paper, we investigate local properties in the system of completely 1-summing mapping spaces. We introduce notions of injectivity, local reflexivity, exactness, nuclearity and finite-representability in the system of completely 1-summing mapping spaces. First we obtain that if V has WEP, V is locally reflexive in the system (Ⅱ1(⋅,⋅), π1(⋅)) if and only if it is locally reflexive in the system (Ⅰ(⋅,⋅), t(⋅)). Furthermore we prove that an operator space V ⊆ B(H) is exact in the system (Ⅱ1(⋅,⋅), π1(⋅)) if and only if V is finitely representable in {Mn}n∈N in the system (Ⅱ1(⋅,⋅), π1(⋅)). At last, we show that an operator space V is finitely representable in {Mn}n∈N in the system (Ⅱ1(⋅,⋅), π1(⋅)) if and only if V = C.

CONVERGENT PROBLEM OF ITERATIVE SEQUENCES FOR NONLINEAR MAPPINGS WITH ERROR MEMBERS IN BANACH SPACES

In this paper,the approximation problems of Ishikawa iteration with errors of fixed points for asymptotically nonexpansive mappings and asymptotically pseudocontractive mappings in arbitrary real Banach spaces are investigated.Some necessary condition and sufficient condition for the convergence of iterative sequences are given respectively.The results thus extend and improve some recent corresponding results.

Some New Theorems of Lipschitz Type Mappings in Cone Metric Spaces

In this paper, some new existence and uniqueness of common fixed points for three mappings of Lipschitz type are obtained. The conditions are greatly weaker than the classic conditions in cone metric spaces. These results improve and generalize several wellknown comparable results in the literature. Moreover, our results are supported by some examples.

NEW FIXED POINT THEOREMS OF CONDENSING MAPPINGS SATISFYING THE INTERIOR CONDITION IN BANACH SPACES

In this paper, based on a basic result on condensing mappings satisfying the interior condition, some new fixed point theorems of the condensing mappings of this kind are obtained. As a result, the famous Altman＇s theorem, Roth＇s theorem and Petryshyn＇s theorem are extended to condensing mappings satisfying the interior condition.

Generalized contraction mapping principle in intuitionistic Menger spaces and application to differential equations

Using the idea of Atanassov, we define the notion of intuitionistic Menger spaces as a netural generalizations of Menger spaces due to Menger. We also obtain a new generalized contraction mapping and utilize this contraction mapping to prove the existance theorems of solutions to differential equations in intuitionistic Menger spaces.

CONVERGENCE OF ISHIKAWA TYPE ITERATIVE SEQUENCE WITH ERRORS FOR QUASI-CONTRACTIVE MAPPINGS IN CONVEX METRIC SPACES

Some convergence theorems of Ishikawa type iterative sequence with errors for nonlinear general quasi-contractive mapping in convex metric spaces are proved. The results not only extend and improve the corresponding results of L. B. Ciric, Q. H. Liu, H. E. Rhoades and H. K. Xu, et al., but also give an affirmative answer to the open question of Rhoades-Naimpally- Singh in convex metric spaces.

APPROXIMATION OF FIXED POINTS AND VARIATIONAL SOLUTIONS FOR PSEUDO-CONTRACTIVE MAPPINGS IN BANACH SPACES

Let K be a nonempty, closed and convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. Assume that every nonempty closed con- vex and bounded subset of K has the fixed point property for nonexpansive mappings. Strong convergence theorems for approximation of a fixed point of Lipschitz pseudo-contractive map- pings which is also a unique solution to variational inequality problem involving φ-strongly pseudo-contractive mappings are proved. The results presented in this article can be applied to the study of fixed points of nonexpansive mappings, variational inequality problems, con- vex optimization problems, and split feasibility problems. Our result extends many recent important results.

STRONG CONVERGENCE OF APPROXIMATED SEQUENCES FOR NONEXPANSIVE MAPPINGS IN BANACH SPACES

This paper studies the convergence of the sequence defined by x0 ∈ C, xn＋l =αnu＋（1-αn）Txn, n=0, 1,2,..., where 0 ≤αn ≤ 1, limn→∞ αn = 0, ∑n=0^∞ αn = ∞, and T is a nonexpansive mapping from a nonempty closed convex subset C of a Banach space X into itself. The iterative sequence {xn} converges strongly to a fixed point of T in the case when X is a uniformly convex Banach space with a uniformly Gateaux differentiable norm or a uniformly smooth Banach space only. The results presented in this paper extend and improve some recent results.

GENERAL SPLIT FEASIBILITY PROBLEMS FOR TWO FAMILIES OF NONEXPANSIVE MAPPINGS IN HILBERT SPACES

The purpose of this article is to introduce a general split feasibility problems for two families of nonexpansive mappings in Hilbert spaces. We prove that the sequence generated by the proposed new algorithm converges strongly to a solution of the general split feasibility problem. Our results extend and improve some recent known results.

DISTORTION THEOREMS FOR CLASSES OF g-PARAMETRIC STARLIKE MAPPINGS OF REAL ORDER IN C^(n)

In this paper,we define the class S_(g)^(BX)of g-parametric starlike mappings of real order γ on the unit ball BX in a complex Banach space X,where g is analytic and satisfies certain conditions.By establishing the distortion theorem of the Fr´echet-derivative type of S_(g)^(BX)with a weak restrictive condition,we further obtain the distortion results of the Jacobi-determinant type and the Fr´echet-derivative type for the corresponding classes(compared with S_(g)^(BX))defined on the unit polydisc(resp.unit ball with the arbitrary norm)in the space of n-dimensional complex variables,n≥2.Our results extend the classic distortion theorem of holomorphic functions from the case in one-dimensional complex space to the case in the higher dimensional complex space.The main theorems also generalize and improve some recent works.

MAXIMAL ELEMENTS FOR G_B-MAJORIZED MAPPINGS IN PRODUCT G_CONVEX SPACES AND APPLICATIONS (Ⅱ)

A new family of set_valued mappings from a topological space into generalized convex spaces was introduced and studied. By using the continuous partition of unity theorem and Brouwer fixed point theorem, several existence theorems of maximal elements for the family of set_valued mappings were proved under noncompact setting of product generalized convex spaces. These theorems improve, unify and generalize many important results in recent literature.

MAXIMAL ELEMENTS FOR G_B-MAJORIZED MAPPINGS IN PRODUCT G-CONVEX SPACES AND APPLICATIONS (Ⅰ)

A new family of set_valued mappings from a topological space into generalized convex spaces was introduced and studied. By using the continuous partition of unity theorem and Brouwer fixed point theorem, several existence theorems of maximal elements for the family of set_valued mappings were proved under noncompact setting of product generalized convex spaces. These theorems improve, unify and generalize many important results in recent literature.

A novel three-step implicit iteration process for threeΦ-hemicontractive mapping in the intermediate sense

In this paper,we introduce a three-step composite implicit iteration process for approximating the common fixed point of three uniformly continuous and asymptotically generalizedΦ-hemicontractive mappings in the intermediate sense.We prove that our proposed iteration process converges to the common fixed point of three finite family of asymptotically generalizedΦ-hemicontractive mappings in the intermediate sense.Our results extends,improves and complements several known results in literature.

Common Fixed Point Theorems for Weakly Compatible Mappings in Fuzzy Metric Spaces Using (JCLR) Property

In this paper, we prove a common fixed point theorem for a pair of weakly compatible mappings in fuzzy metric space using the joint common limit in the range property of mappings called (JCLR) property. An example is also furnished which demonstrates the validity of main result. We also extend our main result to two finite families of self mappings. Our results improve and generalize results of Cho et al. [Y. J. Cho, S. Sedghi and N. Shobe, “Generalized fixed point theorems for compatible mappings with some types in fuzzy metric spaces,” Chaos, Solitons & Fractals, Vol. 39, No. 5, 2009, pp. 2233-2244.] and several known results existing in the literature.

SUMS OF DUAL TOEPLITZ PRODUCTS ON THE ORTHOGONAL COMPLEMENTS OF FOCK-SOBOLEV SPACES

We consider dual Toeplitz operators on the orthogonal complements of the FockSobolev spaces of all nonnegative real orders.First,for symbols in a certain class containing all bounded functions,we study the problem of when an operator which is finite sums of the dual Toeplitz products is compact or zero.Next,for bounded symbols,we construct a symbol map and exhibit a short exact sequence associated with the C^(*)-algebra generated by all dual Toeplitz operators with bounded symbols.

DENSITY PROPERTIES OF MAPPING SPACES FOR OPERATOR SPACES

In this article, we give the sufficient and necessary conditions for which several important mapping spaces are weak＊ dense in the corresponding completely bound mapping spaces.

On new chaotic mappings in symbol space

A well known chaotic mapping in symbol space is a shift mapping.However,other chaotic mappings in symbol space exist too.The basic change is to consider the process not only at a set of times which are equally spaced,say at unit time apart（a shift mapping）,but at a set of times which are not equally spaced,say if the unit time can not be fixed.The increasing mapping as a generalization of the shift mapping and the k-switch mapping are introduced.The increasing and k-switch mappings are chaotic.