In this paper, the notion of left weakly regular ordered semigroups is introduced. Furthermore, left weakly regular ordered semigroups are characterized by the properties of their left ideals, right ideals and （gener...In this paper, the notion of left weakly regular ordered semigroups is introduced. Furthermore, left weakly regular ordered semigroups are characterized by the properties of their left ideals, right ideals and （generalized） bi-ideals, and also by the properties of their fuzzy left ideals, fuzzy right ideals and fuzzy （generalized） bi-ideals.展开更多
In this works, by using the modified viscosity approximation method associated with Meir-Keeler contractions, we proved the convergence theorem for solving the fixed point problem of a nonexpansive semigroup and gener...In this works, by using the modified viscosity approximation method associated with Meir-Keeler contractions, we proved the convergence theorem for solving the fixed point problem of a nonexpansive semigroup and generalized mixed equilibrium problems in Hilbert spaces.展开更多
A normal orthodox semigroup is an orthodox semigroup whose idempotent elements form a normal band. We deal with congruences on a normal orthodox semigroup with an inverse transversal. A structure theorem for such semi...A normal orthodox semigroup is an orthodox semigroup whose idempotent elements form a normal band. We deal with congruences on a normal orthodox semigroup with an inverse transversal. A structure theorem for such semigroup is obtained. Munn(1966) gave a fundamental inverse semigroup. Following Munn's idea, we give a fundamental normal orthodox semigroup with an inverse transversal.展开更多
In this paper,we define intuitionistic fuzzy generalized bi-ideals in ordered semigroups and characterize regular and left weakly regular ordered semigroups in terms of intuitionistic fuzzy generalized bi-ideals.
The internal Zappa-Szép products emerge when a semigroup has the property that every element has a unique decomposition as a product of elements from two given subsemigroups. The external version constructed from...The internal Zappa-Szép products emerge when a semigroup has the property that every element has a unique decomposition as a product of elements from two given subsemigroups. The external version constructed from actions of two semigroups on one another satisfying axiom derived by G. Zappa. We illustrate the correspondence between the two versions internal and the external of Zappa-Szép products of semigroups. We consider the structure of the internal Zappa-Szép product as an enlargement. We show how rectangular band can be described as the Zappa-Szép product of a left-zero semigroup and a right-zero semigroup. We find necessary and sufficient conditions for the Zappa-Szép product of regular semigroups to again be regular, and necessary conditions for the Zappa-Szép product of inverse semigroups to again be inverse. We generalize the Billhardt λ-semidirect product to the Zappa-Szép product of a semilattice E and a group G by constructing an inductive groupoid.展开更多
The concepts of L*-inverse semigroups and left wreath products of semigroups are introduced. It is shown that the L*-inverse semigroup can be described as the left wreath product of a type A semigroupΓand a left regu...The concepts of L*-inverse semigroups and left wreath products of semigroups are introduced. It is shown that the L*-inverse semigroup can be described as the left wreath product of a type A semigroupΓand a left regular band B together with a mapping which maps the semigroupΓinto the endomorphism semigroup End(B). This result generalizes the structure theorem of Yamada for the left inverse semigroups in the class of regular semigroups. We shall also provide a constructed example for the L*-inverse semigroups by using the left wreath products.展开更多
Let T=(T(t))_(t≥0)be a bounded C-regularized semigroup generated by A on a Banach space X and R(C)be dense in X.We show that if there is a dense subspace Y of X such that for every x ∈ Y,σ_u(A,Cx),the set of all po...Let T=(T(t))_(t≥0)be a bounded C-regularized semigroup generated by A on a Banach space X and R(C)be dense in X.We show that if there is a dense subspace Y of X such that for every x ∈ Y,σ_u(A,Cx),the set of all points λ ∈ iR to which(λ-A)^(-1)Cx can not be extended holomorphically,is at most countable and σ_r(A)∩ iR=(?),then T is stable.A stability result for the case of R(C)being non-dense is also given.Our results generalize the work on the stability of strongly continuous semigroups.展开更多
基金The NSF(10961014) of Chinathe NSF(0501332) of Guangdong Province+1 种基金the Excellent Youth Talent Foundation(2009SQRZ149) of Anhui Provincethe Fuyang Normal College Youth Foundation (2008LQ11)
文摘In this paper, the notion of left weakly regular ordered semigroups is introduced. Furthermore, left weakly regular ordered semigroups are characterized by the properties of their left ideals, right ideals and （generalized） bi-ideals, and also by the properties of their fuzzy left ideals, fuzzy right ideals and fuzzy （generalized） bi-ideals.
文摘In this works, by using the modified viscosity approximation method associated with Meir-Keeler contractions, we proved the convergence theorem for solving the fixed point problem of a nonexpansive semigroup and generalized mixed equilibrium problems in Hilbert spaces.
文摘A normal orthodox semigroup is an orthodox semigroup whose idempotent elements form a normal band. We deal with congruences on a normal orthodox semigroup with an inverse transversal. A structure theorem for such semigroup is obtained. Munn(1966) gave a fundamental inverse semigroup. Following Munn's idea, we give a fundamental normal orthodox semigroup with an inverse transversal.
文摘In this paper,we define intuitionistic fuzzy generalized bi-ideals in ordered semigroups and characterize regular and left weakly regular ordered semigroups in terms of intuitionistic fuzzy generalized bi-ideals.
文摘The internal Zappa-Szép products emerge when a semigroup has the property that every element has a unique decomposition as a product of elements from two given subsemigroups. The external version constructed from actions of two semigroups on one another satisfying axiom derived by G. Zappa. We illustrate the correspondence between the two versions internal and the external of Zappa-Szép products of semigroups. We consider the structure of the internal Zappa-Szép product as an enlargement. We show how rectangular band can be described as the Zappa-Szép product of a left-zero semigroup and a right-zero semigroup. We find necessary and sufficient conditions for the Zappa-Szép product of regular semigroups to again be regular, and necessary conditions for the Zappa-Szép product of inverse semigroups to again be inverse. We generalize the Billhardt λ-semidirect product to the Zappa-Szép product of a semilattice E and a group G by constructing an inductive groupoid.
文摘The concepts of L*-inverse semigroups and left wreath products of semigroups are introduced. It is shown that the L*-inverse semigroup can be described as the left wreath product of a type A semigroupΓand a left regular band B together with a mapping which maps the semigroupΓinto the endomorphism semigroup End(B). This result generalizes the structure theorem of Yamada for the left inverse semigroups in the class of regular semigroups. We shall also provide a constructed example for the L*-inverse semigroups by using the left wreath products.
基金supported by the NSF of Chinasupported by TRAPOYT and the NSF of China(No.10371046)
文摘Let T=(T(t))_(t≥0)be a bounded C-regularized semigroup generated by A on a Banach space X and R(C)be dense in X.We show that if there is a dense subspace Y of X such that for every x ∈ Y,σ_u(A,Cx),the set of all points λ ∈ iR to which(λ-A)^(-1)Cx can not be extended holomorphically,is at most countable and σ_r(A)∩ iR=(?),then T is stable.A stability result for the case of R(C)being non-dense is also given.Our results generalize the work on the stability of strongly continuous semigroups.
