Criteria for the existence of solutions to random integral and differential equations

In [1], we proved a general rondom fixed point theorem and gave some applications. In this paper, we shall give further applications of the theorem. We first obtain a rondom Darbo’s fixed point theorem, using the theorem, we give the criteria for the existence of solutions under compactness hypotheses to nonlinear rondom volterra integral equations and the Cauchy problem of nonlinear rondom differential equations. Our theorems improve andgeneralize some main results of Lakshmikanthem^[2], Vaughn^[3,4] as well as De Blasi and Myjak^[5].     

Fixed point theorems of random set-valued mappings and their applications

In this paper, first we show several new random fixed point theorems for random set-valued mappings and for a system of random set-valued mappings. Then, some applications of our results are given for the existence and uniqueness of random solution for a system of nonlinear random integral and differential equations. Our theorems improved and generalize many recent findings in [4–7, 9, 11–17].     

GENERAL RANDOM FIXED POINT THEOREM AND ITS APPLICATIONS

In this paper,we obtain a general random fixed point theorem which generalizes the main results of Engle[4,7] and Bocsan[8]. The usefulness of this theorem seems to lie in the fact that unlike many random fixed point theorems obtained by using special methods[1,4,5-13] can be proved by using out general theorem (Theorem 1 and Corollaries 1 and 2). Finally,we indicate some possible applications of our results to nonlinear random integral and differential equations.     

Minimal and maximal fixed point theorems and iterative technique for nonlinear operators in product spaces

In this paper, we study minimal and maximal fixed point theorems and iterative technique for nonlinear operators in product spaces. As a corollary of our result, some coupled fixed point theorems are obtained, which generalize the coupled fixed point theorems obtained by Guo Da-jun and Lankshmikanthamt and the results obtained by Lan in, and.     

Random common fixed point theorems of set-valued mappings

In this paper, we prove several random common fixed point theorems to general setvalued contractive mappings. These theorems improve and generalize the corresponding results in [1–18].     

Fixed point theorems for fuzzy mappings

Fixed point theorems for fuzzy mappings are of fundamental importance in fuzzy mathematical theory and application investigation. This paper pressents some new fixed point theorems for fuzzy mapping, whose results generalize and improve the results of [3] and give a partial answer to the unsolved problem suggested in [1].     

Some coincidence theorems of set-valued mappings

Browder^[1] obtained the sharpened forms of the Schauder fixed point theorem. Many authors generalized Browder’s results in several aspects. Recently, H.M. Ko and K.K. Tan^[2,3] generalized Browder’s theorems to the coincidence theorems of set-valued mappings. In this paper, we also show some coincidence theorems oj set-valued mappings. They improve and generalize the important results in [1,2,3].     

Fixed point index of uniform limit of set-Valued strict set-contractive mappings and its applications

In this paper,the class of uniform limit mappings of set-valued,strick set-contractivemappings is discussed.Furthermore,the fixed point index theory for the uniform limitmappings is established.Using the fixed point index theory,some positive fixed pointtheorems are proved.Our theorems generalize some results in[1,4,5,7].     

Random directional contractors and their applications

In this paper, as the generalizations of Altman’s directional contractors[4,5] and Lee and Padgett’s random contractors[1,2] we introduce the concept of random directional contractors for set-valued random operators. Using the new concept and transfinite induction, we show several existence theorems to solutions of nonlinear set-valued random operator equations. Our theorems improve and generalize the corresponding results in [1,2,4,5,11]. Next, some applications of our results to nonlinear random integral and differential equations are given.     

FIXED POINT THEOREMS FOR FUZZY MAPPINGS IN PROBABILISTIC METRIC SPACES

ＦＩＸＥＤ　ＰＯＩＮＴ　ＴＨＥＯＲＥＭＳ　ＦＯＲ　ＦＵＺＺＹ　ＭＡＰＰＩＮＧＳ　ＩＮ　ＰＲＯＢＡＢＩＬＩＳＴＩＣ　ＭＥＴＲＩＣ　ＳＰＡＣＥＳＺｈａｎｇＳｈｉｓｈｅｎｇ（张石生）；ＺｈａｎｇＹｉｎｇ（张颖）；ＹｕａｎＪｉａｗｅｉ（袁家玮）（Ｒｅｃｅｉｖ...     

Some new fixed point theorems in probabilistic metric spaces

ＳＯＭＥＮＥＷＦＩＸＥＤＰＯＩＮＴＴＨＥＯＲＥＭＳＩＮＰＲＯＢＡＢＩＬＩＳＴＩＣＭＥＴＲＩＣＳＰＡＣＥＳｚｈｕＣｈｕａｎ－ｘｉ（朱传喜）（ＭａｔｈｅｍａｔｉｅｓＤｉｖｉｓｉｏｎ,Ｎａｎｃｈａｎｇ．Ｕｎｉｖｅｒｓｉｔｙ,Ｎａｎｃｈａｎｇ）（Ｒｅｃｅｉｖ...     

An Improvement in the Static Method for Limit Analysis of Structures with Stochastic Strength Variations

On the basis of the static and kinematic theorems of probabilistic limit analysis [1-3], a new procedure to study the random strength of rigid-plastic structures is developed. This procedure leads to upper bounds to the failure probability, which show a remarkable improvement when compared with similar results so far obtained from “static” considerations. As an example, extensive numerical calculations carried out for a simple portal frame with random limit moments are presented and some observations are formulated.     

EXISTENCE OF POSITIVE FIXED POINTS FOR SEMIDIFFERENTIABLE SEMICOMPACT 1-SET-CONTRACTIONS

This paper obtains some fixed point theorems of semidifferentiable semmicompacl l-set-contraction maps, which extend some known results in [1, 2, 4, 5, 7].     

Fixed point theorems for fuzzy mappings (II)

This paper presents some new fixed point theorems for fuzzy mappings. The results given in this paper improve and extend some recent results of [1, 4, 5].Communicated by Zhou Mo-ren     

Topological version of section theorems with applications

ＴＯＰＯＬＯＧＩＣＡＬＶＥＲＳＩＯＮＯＦＳＥＣＴＩＯＮＴＨＥＯＲＥＭＳＷＩＴＨＡＰＰＬＩＣＡＴＩＯＮＳＺｈａｎｇＳｈｉ－ｓｈｅｎｇ（张石生）（ＳｉｃｈｕａｎＵｎｉｖｅｒｓｉｔｙ,Ｃｈｅｎｇｄｕ）ＷｕＸｉａｎ（吴鲜）（ＺｈａｏｔｏｎｇＴｅａｃｈｅｒ’ｓ...     

The description of the characteristics of the structure and the quantity in fixed pansystems theorems

Pansymmetry is the abstract of symetry, stability and other concepts in physics and so on. Fixed pansystems theorems portray a typical pansymmetry of systemic structure. The present paper complements and extends the Work in concerned in fixed pansystems theorems. It gives in finite case the structural character of fixed subsets; the criterion of existence of the least fixed subset, and the numbering formula of fixed subsets and minimal fixed subsets.     

Fixed point index of ultimately compact set-valued mappings in Hausdorff locally convex spaces and its applications

The author defines a concept of fixed point index of ultimately compact set-valued mappings in Hausdorff locally convex spaces. Using this concept, the author establishes several nonzero fixed point theorems of set-valued -condensing mappings. These theorems extend some known results in [1,2,7,8,9].Projects Supported by the Science Fund of the Chinese Academy of Sciences     

NEW VERSION OF KKMTHEOREM IN PROBABILISTIC METRIC SPACES WITH APPLICATIONS

ＮＥＷＶＥＲＳＩＯＮＯＦＫＫＭＴＨＥＯＲＥＭＩＮＰＲＯＢＡＢＩＬＩＳＴＩＣＭＥＴＲＩＣＳＰＡＣＥＳＷＩＴＨＡＰＰＬＩＣＡＴＩＯＮＳＺｈａｎｇＳｈｉｓｈｅｎｇ（张石生）ＹｅｏｌＪｅＣｈｏ（赵烈济）ＷｕＸｉａｎｇ（吴鲜）（ＲｅｃｅｉｖｅｄＭａｙ７，１９９...     

Coincidence point theorems in probabilistic metric spaces with a convex structures

ＣＯＩＮＣＩＤＥＮＣＥＰＯＩＮＴＴＨＥＯＲＥＭＳｉＮＰＲＯＢＡＢＩＬＩＳＴＩＣＭＥＴＲＩＣＳＰＡＣＥＳＷＩＴＨＡＣＯＮＶＥＸＳＴＲＵＣＴＵＲＥＳＷｅｅＴａｅＰａｒｋ（朴渭汰）ＫｅｕｎＳａｅｎｇＰａｒｋ（朴根生）ＹｅｏｌＪｅＣｈｏ（赵烈济）（Ｄｅｐａｒ...     

HARMONIC SOLUTIONS OF SOME SECOND-ORDER NONLINEAR EQUATIONS UNDER A PERIODIC FORCE

In this paper we prove some theorems on the existence of harmonic solutions of somesecond-order nonlinear equations under a periodic force.These theorems extend relevantresults in refs.[1]-[8].