partially ordered cone metric spaces and coupled fixed point results bhaskar and lakshmikantham t g bhaskar v lakshmikantham fixed point theorems in partially ordered metric spaces and applications nonlinear anal 65 2006 1379 1393 studied the coupled coincidence point of a mapping f from xxx into x and a mapping g from x into x e karapinar e karapinar couple fixed point theorems for nonlinear contractions in cone metric spaces comput math appl 2010 doi 10 1016 j camwa 2010 03 062 proved some results of the coupled coincidence point of a mapping f from xxx into x and a mapping g from x into x over normal cones without regularity in the present paper we prove that coupled coincidence fixed point theorems over cone metric spaces are not necessarily normal our results generalize several well known comparable results in the literature

odd dimensional orthogonal groups as amalgams of unitary groups part 1 general simple connectedness we extend the phan theory described in c bennett r gramlich c hoffman s shpectorov curtis phan tits theory in a a ivanov m w liebeck j saxl eds groups combinatorics and geometry world scientific river edge 2003 pp 13 29 to the last remaining infinite series of classical chevalley groups over finite fields namely we prove that the twin buildings for the group spin 2n 1 q2 q odd admit a unique unitary flip and that the corresponding flipflop geometry is simply connected for almost all finite fields fq2 applying standard methods from amalgam theory this results in a characterization of central quotients of the group spin 2n 1 q by a phan system of rank one and rank two subgroups in the present first part of a series of two articles we present simple connectedness results for sufficiently large fields or sufficiently large rank to be precise the result stated in the present paper is proved for all cases but n 3 and q 3 5 7 9 the remaining cases are dealt with in the sequel r gramlich m horn w nickel odd dimensional orthogonal groups as amalgams of unitary groups part 2 machine computations submitted for publication computationally

kkm mappings in cone metric spaces and some fixed point theorems abstract in this paper we define kkm mappings in cone metric spaces and define n cone metric spaces to obtain some fixed point theorems and hence generalize the results obtained in a amini m fakhar j zafarani kkm mapping in metric spaces nonlinear anal 60 2005 1045 1052

boyd wong type common fixed point results in cone metric spaces abstract some common fixed point results in cone metric spaces of c di bari and p vetro c di bari p vetro pairs and common fixed points in cone metric spaces rend cir mat palermo 57 2008 279 285 as well as p raja and s m vaezpour p raja s m vaezpour some extensions of banach s contraction principle in complete metric spaces fixed point theory appl 2008 doi 10 1155 2008 768294 are extended using generalized contractive type conditions and cones which may be nonnormal cone metric versions of several well known results such as boyd wong s theorem d w boyd j s wong on nonlinear contractions proc amer math soc 20 1969 458 464 are obtained as special cases

common fixed points for maps on cone metric space the purpose of this paper is to generalize and to unify fixed point theorems of das and naik ciric jungck huang and zhang on complete cone metric space

cone metric spaces and fixed point theorems of contractive mappings in this paper we introduce cone metric spaces prove some fixed point theorems of contractive mappings on cone metric spaces

a phan type theorem for sp 2n q in 1977 kok wee phan published a theorem see 4 on generation of the special unitary group su n 1 q2 by a system of its subgroups isomorphic to su 3 q2 this theorem is similar in spirit to the famous curtis tits theorem in fact both the curtis tits theorem and phan s theorem were used as principal identification tools in the classification of finite simple groups the proof of phan s theorem given in his 1977 paper is somewhat incomplete this motivated bennett and shpectorov 1 to revise phan s paper and provide a new and complete proof of his theorem they used an approach based on the concepts of diagram geometries and amalgams of groups it turned out that phan s configuration arises as the amalgam of rank two parabolics in the flag transitive action of su n 1 q2 on the geometry of nondegenerate subspaces of the underlying unitary space this point of view leads to a twofold interpretation of phan s theorem its complete proof must include 1 a classification of related amalgams and 2 a verification that apart from some small exceptional cases the above geometry is simply connected these two parts are tied together by a lemma due to tits that implies that if a group g acts flag transitively on a simply connected geometry then the corresponding amalgam of maximal parabolics provides a presentation for g see proposition 7 1 the curtis tits theorem can also be restated in similar geometric terms let g be a chevalley group then g acts on a spherical building b and also on the corresponding twin building b b b d here b b b and d is a codistance between

the virasoro algebra three theroems are proved with suitable hypotheses in each case characterizations are found for the virasoro algebra for some of its representations and for the ramond neveu schwarz superalgebra built around the virasoro algebra

ordered cone metric spaces and fixed point results in this paper we introduce a partial order on a cone metric space and prove a caristi type theorem furthermore we prove fixed point theorems for single valued nondecreasing and weakly increasing mappings and multi valued mappings on an ordered cone metric space

a quasi curtis tits phan theorem for the symplectic group abstract we obtain the symplectic group sp v as the universal completion of an amalgam of low rank subgroups akin to levi components we let sp v act flag transitively on the geometry of maximal rank subspaces of v we show that this geometry and its rank 3 residues are simply connected with few exceptions the main exceptional residue is described in some detail the amalgamation result is then obtained by applying tits lemma this provides a new way of recognizing the symplectic groups from a small collection of small subgroups

curtis tits groups generalizing kac moody groups of type a n 1 abstract in 13 we define a curtis tits group as a certain generalization of a kac moody group we distinguish between orientable and non orientable curtis tits groups and identify all orientable curtis tits groups as kac moody groups associated to twin buildings in the present paper we construct all orientable as well as non orientable curtis tits groups with diagram a n 1 n 4 over a field k of size at least 4 the resulting groups are quite interesting in their own right the orientable ones are related to drinfeld s construction of vector bundles over a non commutative projective line and to the classical groups over cyclic algebras the non orientable ones are related to expander graphs 14 and have symplectic orthogonal and unitary groups as quotients

common fixed points under contractive conditions in cone metric spaces the aim of this paper is to present coincidence point result for two mappings in cone metric space which satisfy new contractive conditions our results generalize fixed point theorems of jungck g jungck commuting maps and fixed points amer math monthly 83 1976 261 263 abbas jungck m abbas g jungck common fixed point results for noncommuting mappings without continuity in cone metric spaces j math anal appl 341 2008 416 420 and fisher b fisher four mappings with a common fixed point arabic summary j univ kuwait sci 8 1981 131 139 in cone metric spaces to symmetric spaces

a note on cone metric fixed point theory and its equivalence abstract the main aim of this paper is to investigate the equivalence of vectorial versions of fixed point theorems in generalized cone metric spaces and scalar versions of fixed point theorems in general metric spaces in usual sense we show that the banach contraction principles in general metric spaces and in t v s cone metric spaces are equivalent our theorems also extend some results in huang and zhang 2007 l g huang x zhang cone metric spaces and fixed point theorems of contractive mappings j math anal appl 332 2007 1468 1476 rezapour and hamlbarani 2008 sh rezapour r hamlbarani some notes on the paper cone metric spaces and fixed point theorems of contractive mappings j math anal appl 345 2008 719 724 and others

a curtis tits phan theorem for the twin building of type a n 1 abstract the curtis tits phan theory as laid out originally by bennett and shpectorov describes a way to employ tits lemma to obtain presentations of groups related to buildings as the universal completion of an amalgam of low rank groups it is formulated in terms of twin buildings but all concrete results so far were concerned with spherical buildings only we describe an explicit flip flop geometry for the twin building of type a n 1 associated to k t t 1 on which a unitary group su n k t t 1 related to a certain non degenerate hermitian form acts flag transitively and obtain a presentation for this group in terms of a rank 2 amalgam consisting of unitary groups this is the most natural generalization of the original result by phan for the unitary groups

presentations of finite simple groups a quantitative approach there is a constant such that all nonabelian finite simple groups of rank over with the possible exception of the ree groups have presentations with at most generators and relations and total length at most as a corollary we deduce a conjecture of holt there is a constant such that for every finite simple group every prime and every irreducible module

the generalized additional symmetries of the two toda lattice hierarchy the generalized additional symmetries of the two toda lattice hierarchy are investigated in this paper the algebraic structure of this generalized additional symmetry is showed as w w and the actions of the generalized additional symmetries on function are also discussed by restricting the two toda lattice hierarchy to the semi infinite case

common fixed point results for noncommuting mappings without continuity in cone metric spaces the existence of coincidence points and common fixed points for mappings satisfying certain contractive conditions without appealing to continuity in a cone metric space is established these results generalize several well known comparable results in the literature

pair of non self mappings and common fixed points we study quasi contraction type non self mappings on takahashi convex metric spaces and common fixed point theorems for a pair of maps results generalizing and unifying fixed point theorems of imdad and kumar das and naik jungck ciric ume khan and pathak and ciric are established

on cone metric spaces a survey abstract using an old m krein s result and a result concerning symmetric spaces from s radenovic z kadelburg quasi contractions on symmetric and cone symmetric spaces banach j math anal 5 1 2011 38 50 we show in a very short way that all fixed point results in cone metric spaces obtained recently in which the assumption that the underlying cone is normal and solid is present can be reduced to the corresponding results in metric spaces on the other hand when we deal with non normal solid cones this is not possible in the recent paper m a khamsi remarks on cone metric spaces and fixed point theorems of contractive mappings fixed point theory appl 2010 7 pages article id 315398 doi 10 1115 2010 315398 the author claims that most of the cone fixed point results are merely copies of the classical ones and that any extension of known fixed point results to cone metric spaces is redundant also that underlying banach space and the associated cone subset are not necessary in fact khamsi s approach includes a small class of results and is very limited since it requires only normal cones so that all results with non normal cones which are proper extensions of the corresponding results for metric spaces cannot be dealt with by his approach

gauge theory of w symmetry the w algebra is a higher spin extension of the virasoro algebra in this paper we construct the gauge theory of w symmetry in terms of its representations

abstract metric spaces and sehgal guseman type theorems recently raja and vaezpour p raja and s m vaezpour some extensions of banach s contraction principle in complete cone metric spaces fixed point theory appl 2008 11 pages doi 10 1155 2008 768294 article id 768294 proved some results for sehgal guseman type theorems in the framework of abstract cone metric spaces over a normal solid cone the purpose of this paper is to present this in the framework of symmetric spaces which are associated with abstract cone metric spaces introduced by radenovic and kadelburg s radenovic z kadelburg quasi contractions on symmetric and cone symmetric spaces isi j bjma electronic in press our results extend and generalize sehgal guseman type theorems from metric and abstract metric spaces to some symmetric spaces examples are given to illustrate the results

weak phan systems of type c n abstract the present article provides a classification of noncollapsing phan amalgams of type c n and of shape s s 2 over finite fields of square order distinct from four together with the results of r gramlich c hoffman s shpectorov j algebra 264 2003 358 384 this completes the proof of a phan type theorem for the group sp 2 n q for sufficiently large n and q

even dimensional orthogonal groups as amalgams of unitary groups abstract this article is part of the program described in c d bennett r gramlich c hoffman s shpectorov curtis phan tits theory in a a ivanov et al eds groups combinatorics and geometry proceedings of the durham conference on groups and geometries 2001 world scientific singapore 2003 pp 13 29 we provide presentations of even dimensional orthogonal groups a characterization of even dimensional orthogonal groups by certain amalgams of subgroups isomorphic to su 2 q 2 su 3 q 2 and su 2 q 2 su 2 q 2 over any finite field and a classification of related amalgams the results are obtained by diagram geometry geometric covering theory and analysis of amalgams

the point of coincidence and common fixed point for a pair of mappings in cone metric spaces in this paper the existence of a point of coincidence and a common fixed point for two weakly compatible maps on a cone metric space has been established the two mappings are assumed to satisfy certain weak inequalities supporting examples are also given

fixed point theory in cone metric spaces obtained via the scalarization method motivated by the scalarization method in vector optimization theory we take a new approach to fixed point theory on cone metric spaces by using our method we prove some fixed point theorems and several common fixed point theorems on cone metric spaces in which the cone need not be normal our results improve and generalize many well known results from the literature