The best approximation and coincidence theorems for composites of acyclic mappings

ＩｎｔｒｏｄｕｃｔｉｏｎＲｅｃｅｎｔｌｙｔｈｅｒｅｈａｖｅａｐｐｅａｒｅｄａｎｕｍｂｅｒｏｆｎｅｗｆｉｘｅｄｐｏｉｎｔｔｈｅｏｒｅｍｓａｎｄｃｏｉｎｃｉｄｅｎｃｅｔｈｅｏｒｅｍｓｉｎｖｏｌｖｉｎｇｓｏ＿ｃａｌｅｄＫａｋｕｔａｎｉｆａｃｔｏｒｉｚａｂｌ...     

NEW COLLECTIVELY FIXED POINT THEOREMS AND APPLICATIONS IN G-CONVEX SPACES

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ 1 991 ,Ｔａｒａｆｄａｒ[1]ｆｉｒｓｔｅｓｔａｂｌｉｓｈｅｄｔｈｅｆｏｌｌｏｗｉｎｇｃｏｌｌｅｃｔｉｖｅｌｙｆｉｘｅｄｐｏｉｎｔｔｈｅｏｒｅｍｏｎｔｈｅｐｒｏｄｕｃｔｓｐａｃｅｏｆｎｏｎｅｍｐｔｙｃｏｍｐａｃｔｃｏｎｖｅｘｓｕｂｓｅｔｓｏｆｔｏｐｏｌｏｇｉｃａｌｖｅｃｔｏｒｓｐａｃｅｓａｎｄｇａｖｅｉｔｓａｐｐｌｉｃａｔｉｏｎｓｔｏｔｈｅｅｘｉｓｔｅｎｃｅｏｆｅｑｕｉｌｉｂｒｉｕｍｐｏｉｎｔｓｆｏｒａｂｓｔｒａｃｔｅｃｏｎｏｍｉｅｓ.Ｔｈｅｏｒｅｍ 1　Ｌｅｔ Ｘｉ ｉ∈Ｉ…     

Lyapunov’s first and second instability theorems for Caputo fractional-order systems

As well as proving stability, Lyapunov functions can also be used to prove instability, for which there are two well-known theorems: Lyapunov’s first and second instability theorems, in the integer-order (ordinary differential equation) case. However, these instability theorems for Caputo fractional-order systems remain blank, due to the long lack of general results on continuation of solution and Caputo fractional derivative of Lyapunov functions along trajectories. In this paper, based on recent advances in these two aspects, the Lyapunov’s first and second instability theorems for Caputo fractional-order systems are presented with proofs and then illustrated by examples.

     

Fixed Points on Two Complete and Compact Metric Spaces

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｆｏｌｌｏｗｉｎｇｒｅｌａｔｅｄｆｉｘｅｄｐｏｉｎｔｔｈｅｏｒｅｍｗａｓｐｒｏｖｅｄｉｎ [1 ] .Ｔｈｅｏｒｅｍ 1　Ｌｅｔ(Ｘ ,ｄ)ａｎｄ (Ｙ ,ρ)ｂｅｃｏｍｐｌｅｔｅｍｅｔｒｉｃｓｐａｃｅｓ,ｌｅｔＴｂｅａｍａｐｐｉｎｇｏｆＸｉｎｔｏＹａｎｄｌｅｔＳｂｅａｍａｐｐｉｎｇｏｆＹｉｎｔｏＸｓａｔｉｓｆｙｉｎｇｔｈｅｉｎｅｑｕａｌｉｔｉｅｓρ(Ｔｘ,ＴＳｙ) ≤ｃｍａｘ ｄ(ｘ ,Ｓｙ) ,ρ(ｙ,Ｔｘ) ,ρ(ｙ,ＴＳｙ) ,ｄ(Ｓｙ ,ＳＴｘ) ≤ｃｍａｘ ρ(ｙ ,Ｔｘ) ,ｄ(ｘ,Ｓｙ) ,ｄ(ｘ ,ＳＴｘ)…     

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.     

GENERALIZED H-KKM TYPE THEOREMS IN H-METRIC SPACES WITH APPLICATIONS

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ 1 996,Ｋｈａｍｓｉ[1]ｅｓｔａｂｌｉｓｈｅｄｔｈｅｈｙｐｅｒｃｏｎｖｅｘｖｅｒｓｉｏｎｏｆｔｈｅｆａｍｏｕｓＦａｎ＿ＫＫＭｐｒｉｎｃｉｐｌｅｉｎｈｙｐｅｒｃｏｎｖｅｘｓｐａｃｅ .Ｙｕａｎ[2 ,3]ｏｂｔａｉｎｓｏｍｅｃｈａｒａｃｔｅｒｉｚａｔｉｏｎｏｆＫＫＭｐｒｉｎｃｉｐｌｅｉｎｈｙｐｅｒｃｏｎｖｅｘｓｐａｃｅｓ,ａｎｄａｓａｐｐｌｉｃａｔｉｏｎｓｏｆｔｈｅｉｒｒｅｓｕｌｔｓ,ｓｏｍｅｆｉｘｅｄｐｏｉｎｔｔｈｅｏｒｅｍｓａｎｄｍａｔｃｈｉｎｇｔｈｅｏｒｅｍｓｆｏｒｏｐｅｎａ…     

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

IntroductionThispaperisacontinuumoftheprecedingpaperofauthor[1] .Fortheconceptsandnotationsofgeneralizedconvex (orG_convex)space ,CG_convexspace,theclassB(Y ,X)ofbetteradmissiblemappings ,GB_mappings,GB_majorizedmappingsandtherelatednotions,thereadermayconsultRef.[1].Themainaimofthispaperistogivesomeapplicationsoftheexistencetheoremsofmaximalelementsobtainedbyauthor[1] .ByapplyingourresultsinRef.[1],wegivesomecomponentversionofcoincidencetheoremandFan_Browdertypefixedpointtheorems .Somee…     

Quasi-Equilibrium Problems and Constrained Multiobjective Games in Generalized Convex Space

ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＸａｎｄＹｂｅｎｏｎｅｍｐｔｙｓｅｔｓａｎｄ2 ＸｂｅｔｈｅｆａｍｉｌｙｏｆａｌｌｓｕｂｓｅｔｓｏｆＸ .ＬｅｔＴ :Ｘ→Ｙｂｅａｓｉｎｇｌｅ＿ｖａｌｕｅｄｍａｐｐｉｎｇ ,Ａ :Ｘ→ 2 Ｘｂｅａｓｅｔ＿ｖａｌｕｅｄｍａｐｐｉｎｇ ,ψ :Ｘ×Ｙ×Ｘ→Ｒ∪ ±∞ ａｎｄｆ:Ｘ×Ｙ→Ｒ∪ ±∞ ｂｅｔｗｏｆｕｎｃｔｉｏｎｓ.Ｔｈｅｇｅｎｅｒａｌｑｕａｓｉ＿ｅｑｕｉｌｉｂｒｉｕｍｐｒｏｂｌｅｍＧＱＥＰ (Ｔ ,Ａ ,ψ)ｉｓｔｏｆｉｎｄ ^ｘ∈Ｘｓｕｃｈｔｈａｔ^ｘ∈Ａ( ^ｘ) ,ψ( ^ｘ ,Ｔ^ｘ ,ｙ)≤ 0…     

事件空间中非完整有势系统的参数方程

本文首先在事件空间中建立非完整有势系统的广义方程,然后给出此空间中表示Nielsen算子和Euler算子之间关系的两个定理,最后由这些定理得到广义Nielsen方程。     

Some new results about fixed pansystems theorems

In this paper the fixed pansystems theorems concerning the composition-complement-operators are discussed.Some existence conditions of panchaos and strange panattractor are given.And using the results,some fixed point theorems for many-valued mappings are also proved,which complement and develop the results obtained by Kakutani.     

The extension theorems of cone linear operators

ＩｎｔｒｏｄｕｃｔｉｏｎＩｔｉｓｗｅｌｌ＿ｋｎｏｗｎｔｈａｔｔｈｅｅｘｔｅｎｓｉｏｎｔｈｅｏｒｅｍｏｆｔｈｅｌｉｎｅａｒｆｕｎｃｔｉｏｎａｌｉｓｏｎｅｏｆｔｈｅｂａｓｉｃｔｈｅｏｒｅｍｓｉｎｆｕｎｃｔｉｏｎａｌａｎａｌｙｓｉｓ.Ｉｔｈａｓｂｅｅｎｅｘｔｅｎｄｅｄｔｏｍａｎｙｆｏｒｍｓ,ａｎｄ ,ｏｆｃｏｕｒｓｅ,ｈａｓｆｏｕｎｄｍａｎｙｉｍｐｏｒｔａｎｔａｐｐｌｉｃａｔｉｏｎｉｎｓｕｃｈｆｉｅｌｄｓａｓｎｏｎｓｍｏｏｔｈａｎａｌｙｓｉｓ,ｏｐｔｉｍｉｚａｔｉｏｎａｎｄｖａｒｉａｔｉｏｎａｌｐｒｏｂｌｅ…     

Existence of solutions for generalized quasi-variational-like inequalities

ProjectsupportedbytheNationalNaturalScienceFoundationofChinaI.Introduction'LetEandFbetopologicalvectorspaceswithsamescalarfielddi(eithertherealfieldorthecomplexfield)andXbeanonempt}'subsetofE.Let<',.):FxE-dibeabilinearfunctional,j:X-Fbeasingle-valuedmappi…     

Nonempty intersection theorems in topological spaces with applications

In this paper, we establish some new nonempty intersection theorems for generalized L-KKM mappings and prove some new fixed point theorems for set-valued mappings under suitable conditions in topological spaces. As applications, an existence theorem for an equilibrium problem with lower and upper bounds and two existence theorems for a quasi-equilibrium problem with lower and upper bounds are obtained in topological spaces. Our results generalize some known results in the literature.     

Consistency between independence theorems and generalized self-consistent method

Recently Zheng & Hwang established a series of independence theorems concerning with planar effective elastic properties. It is manifested that the estimation of the effective elastic properties of microcracked solids through the generalized self-consistent method (GSCM) contradicts with these independence theorems. In this paper it is shown that such contradiction is actually caused by the approximate algorithm adopted, while the exact solution of GSCM is consistent with these rigorously established independence theorems. Since only an approximate algorithm in GCSM is available in dealing with problems involving non-circular inclusions or holes, an intrinsic GSCM is proposed, which can be performed based on an approximate algorithm and the corresponding estimations are consistent with the independence theorems.     

STABILITY OF NON-CONSERVATIVE LINEAR GYROSCOPIC SYSTEMS

ＳＴＡＢＩＬＩＴＹ　ＯＦ　ＮＯＮ－ＣＯＮＳＥＲＶＡＴＩＶＥ　ＬＩＮＥＡＲ　ＧＹＲＯＳＣＯＰＩＣ　ＳＹＳＴＥＭＳＬｉＪｕｎｆｅｎｇ（李俊峰）；ＷａｎｇＺｈａｏｌｉｎ（王照林）（ＲｅｃｅｉｖｅｄＮｏｖ．３，１９９５，ＲｅｖｉｓｅｄＡｐｒｉｌ２１，１９９６...     

Stochastic Three-Dimensional Rotating Navier–Stokes Equations: Averaging, Convergence and Regularity

We consider stochastic three-dimensional rotating Navier?CStokes equations and prove averaging theorems for stochastic problems in the case of strong rotation. Regularity results are established by bootstrapping from global regularity of the limit stochastic equations and convergence theorems.     

Quasi-equilibrium problems in noncompact generalized convex spaces

ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＸａｎｄＹｂｅｎｏｎｅｍｐｔｙｓｅｔｓａｎｄ2ＸｂｅｔｈｅｆａｍｉｌｙｏｆａｌｌｓｕｂｓｅｔｓｏｆＸ.ＬｅｔＴ:Ｘ→Ｙｂｅａｓｉｎｇｌｅ＿ｖａｌｕｅｄｍａｐｐｉｎｇ,Ａ:Ｘ→2Ｘｂｅａｓｅｔ＿ｖａｌｕｅｄｍａｐｐｉｎｇａｎｄｆ:Ｘ×Ｙ→Ｒ∪±∞ｂｅａｆｕｎｃｔｉｏｎ.Ｔｈｅｑｕａｓｉ＿ｅｑｕｉｌｉｂｒｉｕｍｐｒｏｂｌｅｍＱＥＰ(Ｔ,Ａ,ｆ)ｉｓｔｏｆｉｎｄ^ｘ∈Ｘｓｕｃｈｔｈａｔ^ｘ∈Ａ(^ｘ),ｆ(^ｘ,Ｔ^ｘ)≤ｆ(ｙ,Ｔ^ｘ),　　ｙ∈Ａ(^ｘ).(1)ＴｈｅＱＥＰ(Ｔ,Ａ,ｆ)ｗａｓｉｎｔｒｏｄ…     

Existence and comparison results of solutions for nonlinear random integral and differential equations relative to weak topology

In this paper, we prove several existence theorems of random solutions to nonlinear random Volterra integral equations under the weak topology of Banach spaces. Then, as applications, we obtain the existence theorems of weak random solutions to random differential equations. Existence of extremal random solutions and a random comparison theorem for these random equations are also obtained. Our theorems improve and extend the corresponding results in [4,5,10,11,12]. Projects supported by the Science Fund of the Chinese Academy of Sciences.     

Helmholtz方程的中值定理

本文提出并证明了二维和三维Ｈｅｌｍｈｏｌｔｚ方程的中值定理。令λ→０就得到二维和三维Ｌａｐｌａｃｅ方程的中值定理。     

Small elastoplastic strains of dielectrics

The theory of small elastoplastic strains of dielectrics in the presence of an electric field is developed in the work. An expression is obtained for the electric part of the stress tensor. Total free energy minimum theorems with constant temperature and simple proportional loading and unloading theorems are proved. Experiments to calculate the mass functions are discussed.