iterative construction of fixed points of asymptotically nonexpansive mappings abstract let t be a completely continuous and asymptotically nonexpansive self mapping of a nonempty closed bounded and convex subset of a hilbert space then under certain conditions the sequence defined by xn 1 ntn xn 1 n x n converges strongly to some fixed point of t a similar result is obtained for asymptotically pseudocontractive mappings whose iterates are lipschitz continuous with respect to some common lipschitz constant

indecomposable generalisations of the standard angular momentum representations of so 3 indecomposable representations of the lie algebra of the rotation group so 3 are studied on the heisenberg weyl basis which is the basis for a subspace of a quotient space of the space of the universal enveloping algebra of the heisenberg weyl algebra the author obtains an infinite dimensional indecomposable representation which induces the finite dimensional representation on certain quotient spaces and subduces the infinite dimensional indecomposable representations on invariant subspaces the standard angular momentum representations of so 3 are given as special cases

iterative processes with mixed errors for nonlinear equations with perturbed m accretive operators in banach spaces let x be a real uniformly smooth banach space of which the dual x has a frechet differentiable norm let a d a x 2 x be an m accretive operator with closed domain d a and bounded range r a and s x x a continuous and a strongly accretive operator with bounded range r i s it is proved that the ishikawa and mann iterative processes with mixed errors converge strongly to the unique solution of the equation z sx lax for given z x and l 0

complete real kahler submanifolds in codimension two minimal isometric immersions f m 2n rightarrow mathbb r 2n 2 in codimension two from a complete kahler manifold into euclidean space had been classified in dajczer and gromoll invent math 119 235 242 1995 for n 3 in this note we describe the non minimal situation showing that if f is real analytic but not everywhere minimal then f is a cylinder over a real kahler surface g n 4 rightarrow mathbb r 6 that is m 2n n 4 times mathbb c n 2 and f g id split where id mathbb c n 2 cong mathbb r 2n 4 is the identity map moreover g can be further described

tannaka krein duality for compact matrix pseudogroups twisted su n groups the notion of concrete monoidalw category is introduced and investigated a generalization of the tannaka krein duality theorem is proved it leads to new examples of compact matrix pseudogroups among them we have twistedsu n groups denoted bys u n it is shown that the representation theory fors u n is similar to that ofsu n irreducible representations are labeled by young diagrams and formulae for dimensions and multiplicity are the same as in the classical case

the quantum group suq 2 and a q analogue of the boson operators a new realisation of the quantum group suq 2 is constructed by means of a q analogue to the jordan schwinger mapping determining thereby both the complete representation structure and q analogues to the wigner and racah operators to achieve this realisation a new elementary object is defined a q analogue to the harmonic oscillator the uncertainty relation for position and momentum in a q harmonic oscillator is quite unusual

compact matrix pseudogroups the compact matrix pseudogroup is a non commutative compact space endowed with a group structure the precise definition is given and a number of examples is presented among them we have compact group of matrices duals of discrete groups and twisted deformed su n groups the representation theory is developed it turns out that the tensor product of representations depends essentially on their order the existence and the uniqueness of the haar measure is proved and the orthonormality relations for matrix elements of irreducible representations are derived the form of these relations differs from that in the group case this is due to the fact that the haar measure on pseudogroups is not central in general the corresponding modular properties are discussed the haar measures on the twistedsu 2 group and on the finite matrix pseudogroup are found

conformal hypersurfaces with the same gauss map in this paper we provide a complete classification of all hypersurfaces of euclidean space which admit conformal deformations other than the ones obtained through conformal diffeomorphisms of the ambient space preserving the gauss map elie cartan in one of his earlier papers in differential geometry classified all euclidean hypersurfaces of dimension at least five which admit conformal deformations other than the trivial ones obtained through compositions with conformal diffeomorphisms of the ambient space when all possible conformal deformations are trivial a hypersurface is called conformally rigid first cartan proved that a hypersurface is conformally rigid if at no point does there exist a principal curvature of multiplicity at least n 2 see ca cd2 or da using this he concluded that a conformally deformable hypersurface is either conformally flat or a 2 parameter envelope of spheres or planes of some very special type moreover the set of all conformal deformations is either a 1parameter family or there is just one other deformation in this paper we classify all euclidean hypersurfaces which admit nontrivial conformal deformations preserving the gauss map in the isometric case a complete classification for any codimension has been obtained by dajczer and gromoll dg2 while the conformal case but only for surfaces is due to vergasta ve2 theorem let f g mn rn 1 n 3 be conformal immersions of an ndimensional connected riemannian manifold with the same gauss map assume that on no open subset do they differ by a conformal diffeomorphism of rn l then f mn is part of one of the following examples while g mn is of the same type i a minimal real kaehler hypersurface ii a rotation hypersurface over a plane curve iii a rotation hypersurface over a minimal surface in r3 minimal real kaehler hypersurfaces have been completely classified by dajczer and gromoll in dg2 the assumption that f and g do not differ locally by a conformal deformation of the ambient space has been introduced in order to produce a global result without that assumption our proof shows that the only other possibility is to have an open subset where up to homothety received by the editors december 10 1993 1991 mathematics subject classification primary 53c42 1995 american mathematical society

convergence theorems of fixed points for asymptotically hemi pseudocontractive mappings in this paper the concept of asymptotically hemi pseudocontractive mapping in banach space which is a proper generalization of asymptotically pseudocontractive mapping with nonempty fixed point set as shown by an example is introduced some sufficient and necessary conditions on the strong convergence of the modified ishikawa and the modified mann iteration sequences with mean errors for uniformly l lipshitzian asymptotically hemi pseudocontractive mappings are presented

strong convergence of an implicit iteration process for a finite family of asymptotically quasi nonexpansive mappings in the present paper we prove that the modified implicit iteration sequence for a finite family of asymptotically quasi nonexpansive mappings converges strongly to a common fixed point of the family in a uniformly convex banach space requiring one member t in the family to be semi compact our results extend and improve some recent results

iterative solution of nonlinear equations with strongly accretive operators abstract let e be a real banach space with a uniformly convex dual suppose t e e is a strongly accretive map with bounded range such that for each e the equation tx has a solution in e it is proved that each of the two well known fixed point iteration methods the mann and ishikawa iteration methods under suitable conditions converges strongly to a solution of the equation tx furthermore our method shows that such a solution is necessarily unique explicit error estimates are given our results resolve in the affirmative an open problem j math anal appl 151 no 2 1990 460 and generalize important known results

set valued variational inclusions in banach spaces the purpose of this paper is to introduce and study a class of set valued variational inclusions without compactness condition in banach spaces by using michael s selection theorem and nadler s theorem an existence theorem and an iterative algorithm for solving this kind of set valued variational inclusions in banach spaces are established and suggested

boson realisation of virasoro and kac moody algebras and their indecomposable representations in this letter we give the boson realisation of virasoro and kac moody algebras without central terms and construct their indecomposable representations from some representations of the heisenberg weyl algebra the boson realisation of the kac moody algebra a 2 associated to the lie algebra su 2 is discussed in detail

convergence theorems for φ strongly accretive and φ hemicontractive operators suppose that x is an arbitrary real banach space and t x x is a continuous strongly accretive operator it is shown that the nonlinear equation tx f has a unique solution and under certain conditions both the mann and ishikawa iteration methods with errors introduced by y xu 1998 j math anal appl 224 91 101 converge strongly to the solution a related result deals with the approximation of fixed points of hemicontractive operators

approximating fixed points of a pair of contractive type mappings in generalized convex metric spaces in this paper we consider an ishikawa type iteration process with errors which converges to the unique common fixed point of a pair of contractive type mappings in complete generalized convex metric spaces furthermore we obtain the corresponding results in banach spaces our results extend and generalize many known results

an iterative process for nonlinear lipschitzian strongly accretive mappings in lp spaces abstract suppose x l p or l p p 2 let t x x be a lipschitzian and strongly accretive map with constant k 0 1 and lipschitz constant l define s x x by sx f tx x let c n n 1 be a real sequence satisfying 1 i 0 c n k p 1 l 2 2 k 1 1 for each n 2 ii n c n then for arbitrary x 0 x the sequence x n 1 1 c n x n c n sx n n 0 converges strongly to the unique solution of tx f moreover if c n k p 1 l 2 2 k 1 1 for each n then x n 1 q n 2 x 1 q where q denotes the solution of tx f and 1 k p 1 l 2 2 k 1 1 0 1 a related result deals with the iterative approximation of lipschitz strongly pseudocontractive maps in x

on chidume s open questions and approximate solutions of multivalued strongly accretive mapping equations in banach spaces abstract some new convergence theorems of the ishikawa iteration process for multi valued pseudo contractive mappings and multi valued accretive mappings are obtained which affirmatively answer the open questions put forth by 4

characteristic inequalities of uniformly convex and uniformly smooth banach spaces abstract let x be a real banach space with dual x and moduli of convexity and smoothness x e and x respectively for 1 p denotes the duality mapping from x into 2 x with gauge function t p 1 and j p denotes an arbitrary selection for j p let a r 0 0 t is strictly increasing and there exists c 0 such that t c x t 2 and f r 0 0 t is convex nondecreasing and there exists k 0 such that k x it is proved that x is uniformly convex if and only if there is a a such that x y p x p p j p x y x y x y x and x is uniformly smooth if and only if there is a f such that x y p x p p j p x y x y x y x where for given function f f x y is defined by f x y p 0 1 x ty x p t f t y x ty x dt these inequalities which have various applications can be regarded as general banach space versions of the well known polarization identity occurring in hilbert spaces

complete minimal hypersurfaces in the hyperbolic space mathbb h 4 with vanishing gauss kronecker curvature we investigate 3 dimensional complete minimal hypersurfaces in the hyperbolic space h 4 with gauss kronecker curvature identically zero more precisely we give a classification of complete minimal hypersurfaces with gauss kronecker curvature identically zero a nowhere vanishing second fundamental form and a scalar curvature bounded from below

boson fermion realisation of indecomposable representations for lie superalgebras lndecomposable representations of lie superalgebras are studied on quotient spaces of the universal enveloping algebra of the heisenberg weyl superalgebra b b f j e by boson fermion realisation these representations are constructed from certain types of indecomposable representations of the heisenberg weyl superalgebra and induce usual irreducible representations on invariant subspaces of a quotient space as a physically significant example the explicit form of the boson fermion realisation of indecomposable representations of the classical lie superalgebra su 211 are obtained and discussed in this paper

a q deformed osp 1 2 superalgebra and its two component coherent state representations a q deformed osp 1 2 superalgebra is defined by the use of a pair of q boson annihilation and creation operators a kind of two component coherent state representation of the q deformed superalgebra is found and a q differential realization of the q deformed osp 1 2 superalgebra is obtained

a deformed quantum su 2 superalgebra a quantum q deformation of the su 2 superalgebra is obtained which contains as an even part the quantum suq 2 algebra the finite dimensional irreducible representations of the deformed quantum superalgebra are found

the gauss map for kahlerian submanifolds of ⁿ we introduce a gauss map for kahler submanifolds of euclidean space and study its geometry in relation to that of the given immersion in particular we generalize a number of results of the classical theory of minimal surfaces in euclidean space

iterative approximations of fixed points and solutions for strongly accretive and strongly pseudo contractive mappings in banach spaces abstract in this article we prove some new convergence theorems of the ishikawa and mann iteration sequences for strongly accretive and strongly pseudo contractive mappings by using the new inequality and the new approximation methods our main results improve and extend the corresponding results of j math anal appl 151 1990 453 461 proc amer math soc 120 1994 545 551 j math appl 192 1995 502 518 j math anal appl 174 1993 441 449 acta appl math 32 1993 183 196 nonlinear anal tma 24 1995 981 987 j math anal appl 178 1993 9 21 proc amer math soc 125 6 1997 1705 1709

the q supercoherent states of the q deformed su 2 superalgebra the q supercoherent states associated with the q deformed su 2 superalgebra are constructed explicitly and their properties are investigated in detail the completeness relation of the q supercoherent states is proved by the use of the q integration

two parametric solution to graded yang baxter equation and two parametric uuvgl 1 mod 1 algebra as a hopf algebra the authors discuss a two parametric solution of the graded yang baxter equation ybe and perform the yang baxterization to obtain the solution to the quantum ybe in the formalism developed previously they present the two parametric quantized superalgebra uuvgl 1 mod 1 and prove that this algebra is a hopf algebra with the hopf operations explicitly provided