We introduce the concepts of unitary, almost unitary and strongly almost unitary subset of an ordered semigroup. For the notions of almost unitary and strongly almost unitary subset of an ordered semigroup, we use the...We introduce the concepts of unitary, almost unitary and strongly almost unitary subset of an ordered semigroup. For the notions of almost unitary and strongly almost unitary subset of an ordered semigroup, we use the notion of translational hull of an ordered semigroup. If (S,⋅,≤) is an ordered semigroup having an element e such that e ≤ e<sup>2</sup> and U is a nonempty subset of S such that u ≤ eu, u ≤ ue for all u ∈ U, we show that U is almost unitary in S if and only if U is unitary in . Also if (S,⋅,≤) is an ordered semigroup, e ∉ S, U is a nonempty subset of S, S<sup>e</sup>:= S ∪ {e} and U<sup>e</sup>:= U ∪ {e}, we give conditions that an (“extension” of S) ordered semigroup and the subset U<sup>e</sup> of S<sup>e</sup> must satisfy in order for U to be almost unitary or strongly almost unitary in S (in case U is strongly almost unitary in S, then the given conditions are equivalent).展开更多
The α-times integrated C semigroups, α > 0, are introduced and analyzed. The Laplace inverse transformation for α-times integrated C semigroups is obtained, some known results are generalized.
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
Difficulties encountered in studying generators of semigroup of binary relations defined by a complete X -semilattice of unions D arise because of the fact that they are not regular as a rule, which makes their invest...Difficulties encountered in studying generators of semigroup of binary relations defined by a complete X -semilattice of unions D arise because of the fact that they are not regular as a rule, which makes their investigation problematic. In this work, for special D, it has been seen that the semigroup , which are defined by semilattice D, can be generated by the set .展开更多
On the base of the construction of abundant semigroups with a normal mallal idempotent[14], in this paper we consider a class of naturally ordered abundant semigroups which satisfies the regularity condition and conta...On the base of the construction of abundant semigroups with a normal mallal idempotent[14], in this paper we consider a class of naturally ordered abundant semigroups which satisfies the regularity condition and contains a greatest idempotent.Furthermore, we give a completely description of the overall structure of such ordered semigroups vis the algebraic structure of them, which generalizes known result obtainedby blyth and McFadden[3].展开更多
In this paper,we shall prove that for any positive interger n,there exists non-trivialcommutative finite semigroup of idempotent consisting of some n×n real quaternion matri-ces which is lower semilattice.In the ...In this paper,we shall prove that for any positive interger n,there exists non-trivialcommutative finite semigroup of idempotent consisting of some n×n real quaternion matri-ces which is lower semilattice.In the process of solving this problem we shall see thatmany properties of generalized inverses for complex matrices still hold for quaternions ma-展开更多
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
Throughout this paper, we introduce a new hybrid iterative algorithm for finding a common element of the set of common fixed points of a finite family of uniformly asymptotically nonexpansive semigroups and the set of...Throughout this paper, we introduce a new hybrid iterative algorithm for finding a common element of the set of common fixed points of a finite family of uniformly asymptotically nonexpansive semigroups and the set of solutions of an equilibrium problem in the framework of Hilbert spaces. We then prove the strong convergence theorem with respect to the proposed iterative algorithm. Our results in this paper extend and improve some recent known results.展开更多
In this paper we prove the analyticity of the semigroups generated by some singular differential matrix operators of the form in the Banach space with suitable boundary conditions. To illustrate the work an example is...In this paper we prove the analyticity of the semigroups generated by some singular differential matrix operators of the form in the Banach space with suitable boundary conditions. To illustrate the work an example is discussed.展开更多
In this paper we are interested in studying the dissipativity of degenerate mixed differential operators involving an interface point. We show that, under particular interface conditions, such operators generate analy...In this paper we are interested in studying the dissipativity of degenerate mixed differential operators involving an interface point. We show that, under particular interface conditions, such operators generate analytic semigroups on an appropriate Hilbert space . To illustrate the results an example is discussed.展开更多
The infinite generator of α-times Integrated C semigroups and the properties of resolvent are given. At the same time, we discuss the relationship between the existence of strong solution of a class of nonhomogeneous...The infinite generator of α-times Integrated C semigroups and the properties of resolvent are given. At the same time, we discuss the relationship between the existence of strong solution of a class of nonhomogeneous abstract Cauchy problem and α-times integrated C semigroups, and a sufficient and necessary condition is obtained.展开更多
In this paper,we introduce Lawson partial order ≤ w on wrpp semigroups.After obtaining some properties of ≤ w,we determine when ≤ w is(left;right) compatible with the multiplication.These results extend and enrich ...In this paper,we introduce Lawson partial order ≤ w on wrpp semigroups.After obtaining some properties of ≤ w,we determine when ≤ w is(left;right) compatible with the multiplication.These results extend and enrich the related results of Lawson and GuoLuo on abundant semigroups,of Guo-Shum on rpp semigroups and of Liu-Guo on wrpp semigroups.展开更多
Green's relations and generalized Green's relations play a fundamental role in the study of semigroups.GV-semigroups are the generalizations of completely regular semigroups in the range of π-regular semigrou...Green's relations and generalized Green's relations play a fundamental role in the study of semigroups.GV-semigroups are the generalizations of completely regular semigroups in the range of π-regular semigroups.In this paper,Green's relations and generalized Green's relations on GV-semigroups are considered by the structure of GV-semigroups.D=j and D C D* on GV-semigroups will be proved.展开更多
As we know if D is a complete X-semilattice of unions then semigroup Bx(D) possesses a right unit iff D is an XI-semilattice of unions. The investigation of those a-idempotent and regular elements of semigroups Bx(D) ...As we know if D is a complete X-semilattice of unions then semigroup Bx(D) possesses a right unit iff D is an XI-semilattice of unions. The investigation of those a-idempotent and regular elements of semigroups Bx(D) requires an investigation of XI-subsemilattices of semilattice D for which V(D,a)=Q∈∑2(X,8) . Because the semilattice Q of the class ∑2(X,8) are not always XI -semilattices, there is a need of full description for those idempotent and regular elements when V(D,a)=Q . For the case where X is a finite set we derive formulas by calculating the numbers of such regular elements and right units for which V(D,a)=Q .展开更多
This paper obtains a group of necessary and sufficient conditions which guarantee a closed linear operator A to be the complete infinitesimal generator of an analytic semigroup of growth order α.
In this paper,the definitions of fuzzy regular subsemigroup and fuzzy left(right,intra-)regular sub-semigroup in semigroups are introduced.Some characterizations of them are given.Proposition 2.1.A fuzzy set A in a se...In this paper,the definitions of fuzzy regular subsemigroup and fuzzy left(right,intra-)regular sub-semigroup in semigroups are introduced.Some characterizations of them are given.Proposition 2.1.A fuzzy set A in a semigroup S is a fuzzy subsemigroup iff for any λ∈[0,1],if A_λ={x∈S|A(x)≥λ}≠ ,then A_λ is a subsemigroup of S.Proposition 2.2.A fuzzy set A in a semigroup S is a fuzzy left(right)ideal iff for any λ∈(0,1],if A={x∈S|A(x)展开更多
Wlpp semigroups are generalizations of lpp semigroups and regular semigroups. In this paper, we consider some kinds of wlpp semigroups, namely right-e wlpp semigroups. It is proved that such a semigroup S, if and only...Wlpp semigroups are generalizations of lpp semigroups and regular semigroups. In this paper, we consider some kinds of wlpp semigroups, namely right-e wlpp semigroups. It is proved that such a semigroup S, if and only if S is the strong semilattice of L-right cancellative planks; also if and only if S is a spined product of a right-e wlpp semigroup and a left normal band.展开更多
In this paper, author abtains a group of characteristic conditions for the infinitesimal generators of positive contraction semigroups and stochastic semigroups.Furthermore, Applications of them to linear transport th...In this paper, author abtains a group of characteristic conditions for the infinitesimal generators of positive contraction semigroups and stochastic semigroups.Furthermore, Applications of them to linear transport theory are discussed.展开更多
文摘We introduce the concepts of unitary, almost unitary and strongly almost unitary subset of an ordered semigroup. For the notions of almost unitary and strongly almost unitary subset of an ordered semigroup, we use the notion of translational hull of an ordered semigroup. If (S,⋅,≤) is an ordered semigroup having an element e such that e ≤ e<sup>2</sup> and U is a nonempty subset of S such that u ≤ eu, u ≤ ue for all u ∈ U, we show that U is almost unitary in S if and only if U is unitary in . Also if (S,⋅,≤) is an ordered semigroup, e ∉ S, U is a nonempty subset of S, S<sup>e</sup>:= S ∪ {e} and U<sup>e</sup>:= U ∪ {e}, we give conditions that an (“extension” of S) ordered semigroup and the subset U<sup>e</sup> of S<sup>e</sup> must satisfy in order for U to be almost unitary or strongly almost unitary in S (in case U is strongly almost unitary in S, then the given conditions are equivalent).
文摘The α-times integrated C semigroups, α > 0, are introduced and analyzed. The Laplace inverse transformation for α-times integrated C semigroups is obtained, some known results are generalized.
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Difficulties encountered in studying generators of semigroup of binary relations defined by a complete X -semilattice of unions D arise because of the fact that they are not regular as a rule, which makes their investigation problematic. In this work, for special D, it has been seen that the semigroup , which are defined by semilattice D, can be generated by the set .
文摘On the base of the construction of abundant semigroups with a normal mallal idempotent[14], in this paper we consider a class of naturally ordered abundant semigroups which satisfies the regularity condition and contains a greatest idempotent.Furthermore, we give a completely description of the overall structure of such ordered semigroups vis the algebraic structure of them, which generalizes known result obtainedby blyth and McFadden[3].
文摘In this paper,we shall prove that for any positive interger n,there exists non-trivialcommutative finite semigroup of idempotent consisting of some n×n real quaternion matri-ces which is lower semilattice.In the process of solving this problem we shall see thatmany properties of generalized inverses for complex matrices still hold for quaternions ma-
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Throughout this paper, we introduce a new hybrid iterative algorithm for finding a common element of the set of common fixed points of a finite family of uniformly asymptotically nonexpansive semigroups and the set of solutions of an equilibrium problem in the framework of Hilbert spaces. We then prove the strong convergence theorem with respect to the proposed iterative algorithm. Our results in this paper extend and improve some recent known results.
文摘In this paper we prove the analyticity of the semigroups generated by some singular differential matrix operators of the form in the Banach space with suitable boundary conditions. To illustrate the work an example is discussed.
文摘In this paper we are interested in studying the dissipativity of degenerate mixed differential operators involving an interface point. We show that, under particular interface conditions, such operators generate analytic semigroups on an appropriate Hilbert space . To illustrate the results an example is discussed.
文摘The infinite generator of α-times Integrated C semigroups and the properties of resolvent are given. At the same time, we discuss the relationship between the existence of strong solution of a class of nonhomogeneous abstract Cauchy problem and α-times integrated C semigroups, and a sufficient and necessary condition is obtained.
基金Supported by the NNSF of China(10961014)Supported by the NSF of Jiangxi Province(2008GZ048)Supported by the SF of Education Department of Jiangxi Province(GJJZ[2007]134)
文摘In this paper,we introduce Lawson partial order ≤ w on wrpp semigroups.After obtaining some properties of ≤ w,we determine when ≤ w is(left;right) compatible with the multiplication.These results extend and enrich the related results of Lawson and GuoLuo on abundant semigroups,of Guo-Shum on rpp semigroups and of Liu-Guo on wrpp semigroups.
基金Supported by the NNSF of China(10961014)Supported by the NSF of Jiangxi ProvinceSupported by the SF of Education Department of Jiangxi Province(GJJ11388)
基金Leading Academic Discipline Project of SHNU,China (No.DZL803)Innovation Project of Shanghai Education Committee,China(No.12YZ081)+2 种基金General Scientific Research Project of SHNU,China (No.SK201121)National Natural Science Foundation of China(No.11001046)Fundamental Research Fundation for the Central Universities,China (No.11D10904)
文摘Green's relations and generalized Green's relations play a fundamental role in the study of semigroups.GV-semigroups are the generalizations of completely regular semigroups in the range of π-regular semigroups.In this paper,Green's relations and generalized Green's relations on GV-semigroups are considered by the structure of GV-semigroups.D=j and D C D* on GV-semigroups will be proved.
文摘As we know if D is a complete X-semilattice of unions then semigroup Bx(D) possesses a right unit iff D is an XI-semilattice of unions. The investigation of those a-idempotent and regular elements of semigroups Bx(D) requires an investigation of XI-subsemilattices of semilattice D for which V(D,a)=Q∈∑2(X,8) . Because the semilattice Q of the class ∑2(X,8) are not always XI -semilattices, there is a need of full description for those idempotent and regular elements when V(D,a)=Q . For the case where X is a finite set we derive formulas by calculating the numbers of such regular elements and right units for which V(D,a)=Q .
文摘This paper obtains a group of necessary and sufficient conditions which guarantee a closed linear operator A to be the complete infinitesimal generator of an analytic semigroup of growth order α.
文摘In this paper,the definitions of fuzzy regular subsemigroup and fuzzy left(right,intra-)regular sub-semigroup in semigroups are introduced.Some characterizations of them are given.Proposition 2.1.A fuzzy set A in a semigroup S is a fuzzy subsemigroup iff for any λ∈[0,1],if A_λ={x∈S|A(x)≥λ}≠ ,then A_λ is a subsemigroup of S.Proposition 2.2.A fuzzy set A in a semigroup S is a fuzzy left(right)ideal iff for any λ∈(0,1],if A={x∈S|A(x)
基金The NSF(11471255)of Chinathe Scientific Research Project(15JK1411)of Education Department of Shaanxi Provincial Governmentthe Scientific Research Project(17KY02)of College
文摘Wlpp semigroups are generalizations of lpp semigroups and regular semigroups. In this paper, we consider some kinds of wlpp semigroups, namely right-e wlpp semigroups. It is proved that such a semigroup S, if and only if S is the strong semilattice of L-right cancellative planks; also if and only if S is a spined product of a right-e wlpp semigroup and a left normal band.
文摘In this paper, author abtains a group of characteristic conditions for the infinitesimal generators of positive contraction semigroups and stochastic semigroups.Furthermore, Applications of them to linear transport theory are discussed.
