In this paper, we prove a common fixed point theorem in Intuitionistic fuzzy metric space by using pointwise R-weak commutativity and reciprocal continuity of mappings satisfying contractive conditions.
Let G be a generalized matrix algebra over a commutative ring R and Z（G） be the center of G. Suppose that F, T ：G→G are two co-commuting R-linear mappings, i.e., F（x）x = xT（x） for all x ∈ G. In this note, we ...Let G be a generalized matrix algebra over a commutative ring R and Z（G） be the center of G. Suppose that F, T ：G→G are two co-commuting R-linear mappings, i.e., F（x）x = xT（x） for all x ∈ G. In this note, we study the question of when co-commuting mappings on G are proper.展开更多
A map φ on a Lie algebra g is called to be commuting if [φ(x), x] = 0 for all x ∈ g. Let L be a finite-dimensional simple Lie algebra over an algebraically closed field F of characteristic 0, P a parabolic subalgeb...A map φ on a Lie algebra g is called to be commuting if [φ(x), x] = 0 for all x ∈ g. Let L be a finite-dimensional simple Lie algebra over an algebraically closed field F of characteristic 0, P a parabolic subalgebra of L. In this paper, we prove that a linear mapφon P is commuting if and only if φ is a scalar multiplication map on P.展开更多
Let R be an arbitrary commutative ring with identity, and let Nn（R） be the set consisting of all n × n strictly upper triangular matrices over R. In this paper, we give an explicit description of the maps（with...Let R be an arbitrary commutative ring with identity, and let Nn（R） be the set consisting of all n × n strictly upper triangular matrices over R. In this paper, we give an explicit description of the maps（without linearity or additivity assumption） φ ： Nn（R） → Nn（R）satisfying φ（xy） = φ（x）y ＋ xφ（y）. As a consequence, additive derivations and derivations of Nn（R） are also described.展开更多
In this paper,we first give the general forms of skew commuting maps and skew anti-commuting maps by the Peirce decomposition on a unital ring with a nontrivial idempotent,respectively,and then,as applications,we obta...In this paper,we first give the general forms of skew commuting maps and skew anti-commuting maps by the Peirce decomposition on a unital ring with a nontrivial idempotent,respectively,and then,as applications,we obtain the concrete characterizations of all nonadditive skew(anti-)commuting maps on some operator algebras.展开更多
Let N be a nest on a Banach space X, and AlgN be the associated nest algebra. It is shown that, if there exists a non-trivial element N in N which is complemented in X and dim N ≠ 1, then every additive biderivation ...Let N be a nest on a Banach space X, and AlgN be the associated nest algebra. It is shown that, if there exists a non-trivial element N in N which is complemented in X and dim N ≠ 1, then every additive biderivation from AlgN into itself is an inner biderivation. Based on this result, we give characterizations of centralizing （commuting） maps, cocentraliz-ing derivations, and cocommuting generalized derivations on nest algebras.展开更多
In the present paper, we show that there exists a unique common fixed point for four self maps in a fuzzy metric space where two of the maps are reciprocally continuous and the other two maps are z-asymptotically comm...In the present paper, we show that there exists a unique common fixed point for four self maps in a fuzzy metric space where two of the maps are reciprocally continuous and the other two maps are z-asymptotically commuting.展开更多
Our purpose is to determine skew-symmetric biderivations Bider s(L,V)and commuting linear maps Com(L,V)on a multiplicative Hom-Lie algebra(L,α)having their ranges in an(L,α)-module(V,ρ,β),which are both closely re...Our purpose is to determine skew-symmetric biderivations Bider s(L,V)and commuting linear maps Com(L,V)on a multiplicative Hom-Lie algebra(L,α)having their ranges in an(L,α)-module(V,ρ,β),which are both closely related to Cent(L,V),the centroid of(L,α)on(V,ρ,β).We give the relationship between biderivations and commuting linear maps on a regular Hom-Lie algebra and those on the related Lie algebra.Under appropriate assumptions,we also prove that everyδin Bider_(s)(L,V)is of the formδ(x,y)=β^(−1)γ([x,y])for someγ∈Cent(L,V),and Com(L,V)coincides with Cent(L,V).Besides,we give the algorithms for describing Bider s(L,V)and Com(L,V).展开更多
文摘In this paper, we prove a common fixed point theorem in Intuitionistic fuzzy metric space by using pointwise R-weak commutativity and reciprocal continuity of mappings satisfying contractive conditions.
文摘Let G be a generalized matrix algebra over a commutative ring R and Z（G） be the center of G. Suppose that F, T ：G→G are two co-commuting R-linear mappings, i.e., F（x）x = xT（x） for all x ∈ G. In this note, we study the question of when co-commuting mappings on G are proper.
基金Supported by the National Natural Science Foundation of China（Ill01084） Supported by the Fujian Province Natural Science Foundation of China
文摘A map φ on a Lie algebra g is called to be commuting if [φ(x), x] = 0 for all x ∈ g. Let L be a finite-dimensional simple Lie algebra over an algebraically closed field F of characteristic 0, P a parabolic subalgebra of L. In this paper, we prove that a linear mapφon P is commuting if and only if φ is a scalar multiplication map on P.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1117134311426121)+1 种基金the Science Foundation of Jiangxi University of Science and Technology(Grant Nos.NSFJ2014–K12NSFJ2015–G24)
文摘Let R be an arbitrary commutative ring with identity, and let Nn（R） be the set consisting of all n × n strictly upper triangular matrices over R. In this paper, we give an explicit description of the maps（without linearity or additivity assumption） φ ： Nn（R） → Nn（R）satisfying φ（xy） = φ（x）y ＋ xφ（y）. As a consequence, additive derivations and derivations of Nn（R） are also described.
基金supported by the National Natural Science Foundation of China (Nos.12171290,12301152)the Natural Science Foundation of Shanxi Province (No.202203021222018)。
文摘In this paper,we first give the general forms of skew commuting maps and skew anti-commuting maps by the Peirce decomposition on a unital ring with a nontrivial idempotent,respectively,and then,as applications,we obtain the concrete characterizations of all nonadditive skew(anti-)commuting maps on some operator algebras.
基金Supported by the National Natural Science Foundation of China(Grant No.11101250)Youth Foundation ofShanxi Province(Grant No.2012021004)
文摘Let N be a nest on a Banach space X, and AlgN be the associated nest algebra. It is shown that, if there exists a non-trivial element N in N which is complemented in X and dim N ≠ 1, then every additive biderivation from AlgN into itself is an inner biderivation. Based on this result, we give characterizations of centralizing （commuting） maps, cocentraliz-ing derivations, and cocommuting generalized derivations on nest algebras.
文摘In the present paper, we show that there exists a unique common fixed point for four self maps in a fuzzy metric space where two of the maps are reciprocally continuous and the other two maps are z-asymptotically commuting.
基金supported by NSF of Jilin Province(YDZJ202301ZYTS381)NSF of China(11901057)+5 种基金SRF of Jilin Provincial Education Department(JJKH20220821KJ)NSF of Changchun Normal Universitysupported by NSF of China(11801066,11771410)and CSC of China(202106625001)supported by NSF of Jilin Province(YDZJ202201ZYTS589)NSF of China(12271085,12071405)the Fundamental Research Funds for the Central Universities.
文摘Our purpose is to determine skew-symmetric biderivations Bider s(L,V)and commuting linear maps Com(L,V)on a multiplicative Hom-Lie algebra(L,α)having their ranges in an(L,α)-module(V,ρ,β),which are both closely related to Cent(L,V),the centroid of(L,α)on(V,ρ,β).We give the relationship between biderivations and commuting linear maps on a regular Hom-Lie algebra and those on the related Lie algebra.Under appropriate assumptions,we also prove that everyδin Bider_(s)(L,V)is of the formδ(x,y)=β^(−1)γ([x,y])for someγ∈Cent(L,V),and Com(L,V)coincides with Cent(L,V).Besides,we give the algorithms for describing Bider s(L,V)and Com(L,V).
