In this paper, we introduce and investigate some types of deductive systems in hyper EQ-algebras and discuss relationships among them. Especially, we focus on investigating two types of important deductive systems, na...In this paper, we introduce and investigate some types of deductive systems in hyper EQ-algebras and discuss relationships among them. Especially, we focus on investigating two types of important deductive systems, namely, （positive） implicative strong deductive systems, respectively. Moreover we give equivalent characterizations of them.展开更多
The whole of FORTRAN DO loops makes up an infinite set, wherein defining a meaningful 'order' is a meaningful job. In the note are proved the reflexivity, antisymmetry and transitivity of the weak-strong relat...The whole of FORTRAN DO loops makes up an infinite set, wherein defining a meaningful 'order' is a meaningful job. In the note are proved the reflexivity, antisymmetry and transitivity of the weak-strong relation among loops stated in [1], a partially ordered structure in loops being formed.展开更多
Let E be a real reflexive Banach space which admits a weakly sequentially continuous duality mapping from E to E^＊, and C be a nonempty closed convex subset of E. Let {T（t） ： t ≥ 0} be a nonexpansive semigroup on...Let E be a real reflexive Banach space which admits a weakly sequentially continuous duality mapping from E to E^＊, and C be a nonempty closed convex subset of E. Let {T（t） ： t ≥ 0} be a nonexpansive semigroup on C such that F ：=∩t≥0 Fix（T（t）） ≠ 0, and f ： C → C be a fixed contractive mapping. If {αn}, {βn}, {an}, {bn}, {tn} satisfy certain appropriate conditions, then we suggest and analyze the two modified iterative processes as：{yn=αnxn＋（1-αn）T（tn）xn,xn=βnf（xn）＋（1-βn）yn{u0∈C,vn=anun＋（1-an）T（tn）un,un＋1=bnf（un）＋（1-bn）vnWe prove that the approximate solutions obtained from these methods converge strongly to q ∈∩t≥0 Fix（T（t））, which is a unique solution in F to the following variational inequality：〈（I-f）q,j（q-u）〉≤0 u∈F Our results extend and improve the corresponding ones of Suzuki [Proc. Amer. Math. Soc., 131, 2133-2136 （2002）], and Kim and XU [Nonlear Analysis, 61, 51-60 （2005）] and Chen and He [Appl. Math. Lett., 20, 751-757 （2007）].展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11571281)Independent Innovation Project of Graduate Students in Northwestern University(Grant No.YZZ15069)Scientific Research Project of Xi'an Peihua University(Grant No.PHKT16075)
文摘In this paper, we introduce and investigate some types of deductive systems in hyper EQ-algebras and discuss relationships among them. Especially, we focus on investigating two types of important deductive systems, namely, （positive） implicative strong deductive systems, respectively. Moreover we give equivalent characterizations of them.
文摘The whole of FORTRAN DO loops makes up an infinite set, wherein defining a meaningful 'order' is a meaningful job. In the note are proved the reflexivity, antisymmetry and transitivity of the weak-strong relation among loops stated in [1], a partially ordered structure in loops being formed.
基金Supported by the National Natural Science Foundation of China (Grant No. 10771050)supported by the Higher Education Commission, Pakistan, through Research Grant No. 1-29/HEC/HRD/2005/90
文摘Let E be a real reflexive Banach space which admits a weakly sequentially continuous duality mapping from E to E^＊, and C be a nonempty closed convex subset of E. Let {T（t） ： t ≥ 0} be a nonexpansive semigroup on C such that F ：=∩t≥0 Fix（T（t）） ≠ 0, and f ： C → C be a fixed contractive mapping. If {αn}, {βn}, {an}, {bn}, {tn} satisfy certain appropriate conditions, then we suggest and analyze the two modified iterative processes as：{yn=αnxn＋（1-αn）T（tn）xn,xn=βnf（xn）＋（1-βn）yn{u0∈C,vn=anun＋（1-an）T（tn）un,un＋1=bnf（un）＋（1-bn）vnWe prove that the approximate solutions obtained from these methods converge strongly to q ∈∩t≥0 Fix（T（t））, which is a unique solution in F to the following variational inequality：〈（I-f）q,j（q-u）〉≤0 u∈F Our results extend and improve the corresponding ones of Suzuki [Proc. Amer. Math. Soc., 131, 2133-2136 （2002）], and Kim and XU [Nonlear Analysis, 61, 51-60 （2005）] and Chen and He [Appl. Math. Lett., 20, 751-757 （2007）].
