THE BLOCH CONSTANT OF LOCALLY BIHOLOMORPHIC MAPPINGS ON BOUNDED SYMMETRIC DOMAINS

51.IntroductionIn[11,westudiedtheboundsofBlochconstantofholomorphicmappingsonirreducibleboundedsymmetricdomains.ThispaperisasuccessivepaPerof[1].WestudytheboundsoftheBlochconstantoflocallybiholomorphicmappingsonirreducibleboundedsymmetricdomains.AllthenotationsofthispaPerarethesameasthoseweusedin[1].LetDbeadomain,whichcontainstheorigin.AholomorphicmappingonDisdefinedasaBlochmappingifthefamilyofmappingsFj={g:g(z)=f(rk(z))-j(gh(o)),forallrkEAut(D)},isanormalfamily.TheBlochnormofaBlochmapp…     

THE GROWTH THEOREM FOR STARLIKE MAPPINGS ON BOUNDED STARLIKE CIRCULAR DOMAINS

1.IntroductionOnthegeometricfunctiontheoryofonecomplexvariable,thefollowinggrowthandi-coveringtheoremiswellknown(see[2]).TheoremA.Foreachno~alizedunivalentjunctionfontheunitdiscDCC,ESPecially,theleft-handsideOftheaboveinequalityimpliesf(D)2ID.ForeachzED,z/0,equalityoccursintheaboveinequalityifandonlyiffisKoe6efunctionK(z)=theoritsrotatione--"K(e"z).Itisnaturaltoextendthisandotherresultsonthegeometricfunctiontheoryofonevariablestoseveralvariables.Butasearlyasfiftyyearsago,H.Cartanpointe…     

ON A SURJECTIVITY FOR THE SUM OF TWO MAPPINGS OF MONOTONE TYPE

In this paper the sum(T+S)of two nonlinear mappings is considered,where T ismaximal monotone or generalized pseudomonotone and S is generalized pseudomonotone orof type(M).By using the concepts of T-boundedness,T-generalized pseudomonotonemappings and mappings of type T--(M) introduced by the author,it is proved that(T+S) is of type (M).A new surjectivity result for multivalued pseudo A-propermappings is given.As a consequence,it is obtained that the coercive mappings of type(M)whose effective domain contains a dense linear subspace are surjectivity. In particular,the author answers affirmatively a part of Browder's question(see[1],p.70).     

ON THE RATES OF CONVERGENCE FOR PROBABILITY TYPE OPERATORS SEQUENCE

Abstract. In this paper, the rates of convergence for some probability type operators sequence are obtained. The quantitative Poisson type limit theorem is established as an application.     

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 almost-orbits of this class of commutative semigroups. The author improves, extends and develops some recent and earlier results.     

THE SHARP ESTIMATE OF THE THIRD HOMOGENEOUS EXPANSION FOR A CLASS OF STARLIKE MAPPINGS OF ORDER α ON THE UNIT POLYDISK IN Cn

In this article,first,a sufficient condition for a starlike mapping of order α f(x) defined on the unit ball in a complex Banach space is given. Second,the sharp estimate of the third homogeneous expan...     

FEKETE AND SZEG INEQUALITY FOR A SUBCLASS OF STARLIKE MAPPINGS OF ORDER αON THE BOUNDED STARLIKE CIRCULAR DOMAIN IN C~n

In this article, first, we establish the Fekete and Szeg inequality for an interesting subclass of biholomorphic functions in the open unit disk U. Second, we generalize this result to the bounded starlike circular domain in C~n. The proofs of these results use some restrictive assumptions, which in the case of one complex variable are automatically satisfied.     

ON THE GLOBAL ALGORITHM FOR FINDING ZEROS OF GENERAL MAPPINGS OVER R~2

This paper presents a simplicial method for numerically approximating all zeros of a generic mapping over. R by use of the complex degree proposed by the authors . The detail of an algorithm, which can be implemented easily, is outlined sufficiently. Some numerical examples are given for further illustrating the convergence and the stability of the algorithm.     

ON THE SINGULAR CA UCHY PROBLEM FOR NONLINEAR EQUATION OF HYPERBOLIC TYPE

Denote Ω={(x,y)|x>y}. We consider in Ω the Cauchy problem for the nonlinear singular equation: