A New Kind of Pre-Mean-Type Mappings and Its Gauss Iteration

A function which is reflexive is called by pre-mean, a more generalized definition of a mean. In this paper, we define a new pre-mean and study its properties, and then using the given invariant curve we consider the problem of convergence of Gauss iteration of a kind of pre-mean type mappings generated by the exponential and logarithmic functions.

Convergence Theorems of φ-pseudo Contractive Type Mappings in Normed Linear Spaces

In this paper, by virtue of an inequality and sane analysis techniques, we prove sane convergence theorems cm the iterative process for nonlinear mappings of-pseudo contractive type in named linear spaces, which extend and improve the corresponding results obtained by others recently.

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.

Mapping Detailed Soil Property Using Small Scale Soil Type Maps and Sparse Typical Samples

Soil type maps at the scale of I Z 1 000 000 are used extensively to provide soil spatial distribution information for soil erosion assessment and watershed management models in China. However, the soil property maps produced through conventional direct linking method usually suffer low accuracy as well as the lack of spatial details within a soil type polygon. This paper presents an effective method to produce detailed soil property map based on representative samples which were extracted from each polygon on the 1 ： 1 000 000 soil type map. The representative sample of each polygon is defined as the location that can represent the largest area within the polygon. The representativeness of a candidate sample is determined by calculating the soil-forming environment condition similarities between the sample and other locations. Once the representative sample of each polygon has been chosen, the property values of the existing typical samples are assigned to the corresponding representative samples with the same soil type. Finally, based on these representative samples, the detailed soil property map could be produced by using existing digital soil mapping methods. The case study in XuanCheng City, Anhui Province of China, demonstrated the proposed method could produce soil property map at a higher level of spatial details and accuracy： 1） The soil organic matter （SOM） map produced based on the representative samples can not only depict the detailed spatial distribution of SOM within a soil type polygon but also largely reduce the abrupt change of soil property at the boundaries of two adjacent polygons. 2） The Root Mean Squared Error （RMSE） of the SOM map based on the representative samples is 1.61, and it is 1.37 for the SOM map produced by using conventional direct linking method. Therefore, the proposed method is an effective approach to produce spatial detailed soil property map with higher accuracy for environment simulation models.

ASYMPTOTIC BEHAVIOR FOR COMMUTATIVE SEMIGROUPS OF ALMOST ASYMPTOTICALLY NONEXPANSIVE TYPE MAPPINGS

This article introduces the concept of commutative semigroups of almost asymptotically nonexpansive-type mappings in a Banach space X which has the Opial property and whose norm is UKK, and establishes the weak convergence theorems for almostorbits of this class of commutative semigroups. The author improves, extends and develops some recent and earlier results.

ON THE CONVERGENCE PROBLEMS OF ISHIKAWA AND MANN ITERATIVE PROCESSES WITH ERROR FOR Φ-PSEUDO CONTRACTIVE TYPE MAPPINGS

The purpose of this paper is to introduce the concept of Φ_pseudo contractive type mapping and to study the convergence problem of Ishikawa and Mann iterative processes with error for this kind of mappings. The results presented in this paper improve and extend many authors'recent results.

INTERATIVE APPROXIMATION OF FIXED POINTS FOR ALMOST ASYMPTOTICALLY NONEXPANSIVE TYPE MAPPINGS IN BANACH SPACES

A new class of almost asymptotically nonexpansive type mappings in Banach spaces is introduced,which includes a number of known classes of nonlinear Lipschitzian mappings and non_Lipschitzian mappings in Banach spaces as special cases; for example,the known classes of nonexpansive mappings,asymptotically nonexpansive mappings and asymptotically nonexpansive type mappings.The convergence problem of modified Ishikawa iterative sequences with errors for approximating fixed points of almost asymptotically nonexpansive type mappings is considered.Not only S.S.Chang's inequality but also H.K.Xu's one for the norms of Banach spaces are applied to make the error estimate between the exact fixed point and the approximate one.Moreover,Zhang Shi_sheng's method(Applied Mathematics and Mechanics(English Edition),2001,22(1):25-34) for making the convergence analysis of modified Ishikawa iterative sequences with errors is extended to the case of almost asymptotically nonexpansive type mappings. The new convergence criteria of modified Ishikawa iterative sequences with errors for finding fixed points of almost asymptotically nonexpansive type mappings in uniformly convex Banach spaces are presented. Also,the new convergence criteria of modified Mann iterative sequences with errors for this class of mappings are immediately obtained from these criteria.The above results unify,improve and generalize Zhang Shi_sheng's ones on approximating fixed points of asymptotically nonexpansive type mappings by the modified Ishikawa and Mann iterative sequences with errors.

DEGREE THEORY FOR MULTIVALUED (S) TYPE MAPPINGS AND FIXED POINT THEOREMS

The main purpose of this paper is devoted to generalizing the results of Browder[1,2]This paper consists of four parts. In the first part, we introduce the concepts of multivalued (S) and (S), type mappings and the concepts of the limits of multivalued (S) and (S) + type mappings. These kinds of mappings contain many monotone type mappings, such as maximal monotone mapping, bounded pseudo-monotone mapping and bounded generalized pseudo-monotone mapping, as its special cases. In the second part we define the pseudo-degree for (S) type mapping and the degree for (S)+ type mapping. These two kinds of degrees are all the generalizations of the degree defined by Browder[1,2] As applications, we utilize the degree theory presented in part 2 to study the existence of solutions for the multivalued operator equations (see part 3) and to obtain some new fixed point theorems in part 4.

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].

Compilation of 1:50,000 vegetation type map with remote sensing images based on mountain altitudinal belts of Taibai Mountain in the North-South transitional zone of China

The compilation of 1:250,000 vegetation type map in the North-South transitional zone and 1:50,000 vegetation type maps in typical mountainous areas is one of the main tasks of Integrated Scientific Investigation of the North-South Transitional Zone of China.In the past,vegetation type maps were compiled by a large number of ground field surveys.Although the field survey method is accurate,it is not only time-consuming,but also only covers a small area due to the limitations of physical environment conditions.Remote sensing data can make up for the limitation of field survey because of its full coverage.However,there are still some difficulties and bottlenecks in the extraction of remote sensing information of vegetation types,especially in the automatic extraction.As an example of the compilation of 1:50,000 vegetation type map,this paper explores and studies the remote sensing extraction and mapping methods of vegetation type with medium and large scales based on mountain altitudinal belts of Taibai Mountain,using multi-temporal high resolution remote sensing data,ground survey data,previous vegetation type map and forest survey data.The results show that:1)mountain altitudinal belts can effectively support remote sensing classification and mapping of 1:50,000 vegetation type map in mountain areas.Terrain constraint factors with mountain altitudinal belt information can be generated by mountain altitudinal belts and 1:10,000 Digital Surface Model(DSM)data of Taibai Mountain.Combining the terrain constraint factors with multi-temporal and high-resolution remote sensing data,ground survey data and previous small-scale vegetation type map data,the vegetation types at all levels can be extracted effectively.2)The basic remote sensing interpretation and mapping process for typical mountains is interpretation of vegetation type-groups→interpretation of vegetation formation groups,formations and subformations→interpretation and classification of vegetation types&subtypes,which is a combination method of top-down method and bottom-up method,not the top-down or the bottom-up classification according to the level of mapping units.The results of this study provide a demonstration and scientific basis for the compilation of large and medium scale vegetation type maps.

Asymptotic Behavior of Asymptotically Nonexpansive Type Mappings in Banach Space

Let X be a uniformly convex Banach space X such that its dual X^＊ has the KK property. Let C be a nonempty bounded closed convex subset of X and G be a directed system. Let ={Tt ： t ∈ G} be a family of asymptotically nonexpansive type mappings on C. In this paper, we investigate the asymptotic behavior of {Ttx0 ： t∈ G} and give its weak convergence theorem.

A Remark on the Generalized Roper-Suffridge Extension Operator for Spirallike Mappings of Type β and Order α

Suppose f is a spirallike function of type β and order α on the unit disk D.Let Ωn,p1,p2,…,pn={z=（z2,z2,…,zn）′∈C^n：∑j=1^n｜zj）^Pj〈1},where 1≤p1≤2,pj≥1,j=2,…,n,are real numbers.In this paper,we will prove that Φn,β2,γ2,…βn,γn（f）（z）=（f（z1）, preserves spirallikeness of type β and order α on Ωn,p1,p2,…,Pn.

SHARP ESTIMATES OF ALL HOMOGENEOUS EXPANSIONS FOR A SUBCLASS OF QUASI-CONVEX MAPPINGS OF TYPE B AND ORDER α IN SEVERAL COMPLEX VARIABLES

In this article, first, the sharp estimates of all homogeneous expansions for a subclass of quasi-convex mappings of type B and order B on the unit ball in complex Ba- nach spaces are given. Second, the sharp estimates of all homogeneous expansions for the above generalized mappings on the unit polydisk in （in are also established. In particular, the sharp estimates of all homogeneous expansions for a subclass of quasi-convex mappings （include quasi-convex mappings of type A and quasi-convex mappings of type B） in several complex variables are get accordingly. Our results state that a weak version of the Bieber- bach conjecture for quasi-convex mappings of type B and order a in several complex variables is proved, and the derived conclusions are the generalization of the classical results in one complex variable.

Coupled Coincidence Points for F-Contractive Type Mappings in Partially Ordered Metric Spaces

In this article,some coupled coincidence point results for two mappings g:X→X and G:X×X→X satisfying F-contractive type conditions are obtained,and some coupled fixed point results are derived in partially ordered metric spaces.A sufficient condition for uniqueness of coupled point of coincidence are established for F type contraction,and a coupled common fixed point theorem is obtained.Some examples are given to support our results.

Monthly Mean Temperature Prediction Based on a Multi－level Mapping Model of Neural Network BP Type

In terms of 34-year monthly mean temperature series in 1946-1979,the multi-level maPPing model of neural netWork BP type was applied to calculate the system's fractual dimension Do=2'8,leading tO a three-level model of this type with ixj=3x2,k=l,and the 1980 monthly mean temperture predichon on a long-t6rm basis were prepared by steadily modifying the weighting coefficient,making for the correlation coefficient of 97% with the measurements.Furthermore,the weighhng parameter was modified for each month of 1980 by means of observations,therefore constrcuhng monthly mean temperature forecasts from January to December of the year,reaching the correlation of 99.9% with the measurements.Likewise,the resulting 1981 monthly predictions on a long-range basis with 1946-1980 corresponding records yielded the correlahon of 98% and the month-tO month forecasts of 99.4%.

Strong Convergence Theorems for Mixed Type Asymptotically Nonexpansive Mappings

The purpose of this paper is to study a new two-step iterative scheme with mean errors of mixed type for two asymptotically nonexpansive self-mappings and two asymptotically nonexpansive nonself-mappings and prove strong convergence theorems for the new two-step iterative scheme in uniformly convex Banach spaces.

THE INVARIANCE OF STRONG AND ALMOST SPIRALLIKE MAPPINGS OF TYPE β AND ORDER α

The invariance of strong and almost spirallike mappings of type β and order α is discussed in this paper. From the maximum modulus principle of holomorphic functions, we obtain that the generalized Roper-Suffridge operators preserve strong and almost spirallike-hess of type β and order α on the unit ball B^n in C^n and on bounded and complete Reinhardt domains. Therefore we obtain that the generalized Roper-Suffridge operators preserve strong spirllikeness of type β, strong and almost starlikeness of order α, strong starlikeness on the corresponding domains.Thus we can construct more subclasses of spirallike mappings in several complex variables.

SHARP ESTIMATES OF QUASI-CONVEX MAPPINGS OF TYPE B AND ORDER α

In this paper,we first establish several sharp inequalities of homogeneous expansion for biholomorphic quasi-convex mappings of type B and order a on the unit ball E in a complex Banach space X by applying the method and technique of complex analysis.Then,as the application of these sharp inequalities,we derive the sharp estimate of third homogeneous expansions for the above mappings defined on the unit polydisk U^n in C^n.

The Spirallike Mapping of Type a and the Generalized Roper-Suffridge Operator

In this paper, we get the fact that generalized Roper-Suffridge operators act on spirallike mapping of type α on different domains is invariable, these results include some results known.