共查询到20条相似文献,搜索用时 31 毫秒
1.
Let E be a real uniformly convex Banach space whose dual space E∗ satisfies the Kadec-Klee property, K be a closed convex nonempty subset of E. Let be asymptotically nonexpansive mappings of K into E with sequences (respectively) satisfying kin→1 as n→∞, i=1,2,…,m, and . For arbitrary ?∈(0,1), let be a sequence in [?,1−?], for each i∈{1,2,…,m} (respectively). Let {xn} be a sequence generated for m?2 by
2.
C.E. Chidume 《Journal of Mathematical Analysis and Applications》2007,326(2):960-973
Let E be a real uniformly convex Banach space, K be a closed convex nonempty subset of E which is also a nonexpansive retract with retraction P. Let be asymptotically nonexpansive mappings of K into E with sequences (respectively) satisfying kin→1 as n→∞, i=1,2,…,m, and . Let be a sequence in [?,1−?],?∈(0,1), for each i∈{1,2,…,m} (respectively). Let {xn} be a sequence generated for m?2 by
3.
Let K be a nonempty closed convex subset of a real Banach space E which has a uniformly Gâteaux differentiable norm and be a nonexpansive mapping with F(T):={x∈K:Tx=x}≠∅. For a fixed δ∈(0,1), define by Sx:=(1−δ)x+δTx, ∀x∈K. Assume that {zt} converges strongly to a fixed point z of T as t→0, where zt is the unique element of K which satisfies zt=tu+(1−t)Tzt for arbitrary u∈K. Let {αn} be a real sequence in (0,1) which satisfies the following conditions: ; . For arbitrary x0∈K, let the sequence {xn} be defined iteratively by
xn+1=αnu+(1−αn)Sxn. 相似文献
4.
Giuseppe Marino 《Journal of Mathematical Analysis and Applications》2006,318(1):43-52
Let H be a real Hilbert space. Consider on H a nonexpansive mapping T with a fixed point, a contraction f with coefficient 0<α<1, and a strongly positive linear bounded operator A with coefficient . Let . It is proved that the sequence {xn} generated by the iterative method xn+1=(I−αnA)Txn+αnγf(xn) converges strongly to a fixed point which solves the variational inequality for x∈Fix(T). 相似文献
5.
Strong and weak convergence theorems for common fixed points of nonself asymptotically nonexpansive mappings 总被引:1,自引:0,他引:1
Lin Wang 《Journal of Mathematical Analysis and Applications》2006,323(1):550-557
Suppose that K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E. Let be two nonself asymptotically nonexpansive mappings with sequences {kn},{ln}⊂[1,∞), limn→∞kn=1, limn→∞ln=1, , respectively. Suppose {xn} is generated iteratively by
6.
Let be the polynomial whose zeros are the j-invariants of supersingular elliptic curves over . Generalizing a construction of Atkin described in a recent paper by Kaneko and Zagier (Computational Perspectives on Number Theory (Chicago, IL, 1995), AMS/IP 7 (1998) 97-126), we define an inner product on for every . Suppose a system of orthogonal polynomials {Pn,ψ(x)}n=0∞ with respect to exists. We prove that if n is sufficiently large and ψ(x)Pn,ψ(x) is p-integral, then over . Further, we obtain an interpretation of these orthogonal polynomials as a p-adic limit of polynomials associated to p-adic modular forms. 相似文献
7.
Let K be a nonempty closed convex subset of a reflexive and strictly convex Banach space E with a uniformly Gâteaux differentiable norm, and a nonexpansive self-mappings semigroup of K, and a fixed contractive mapping. The strongly convergent theorems of the following implicit and explicit viscosity iterative schemes {xn} are proved.
xn=αnf(xn)+(1−αn)T(tn)xn, 相似文献
8.
Tian-Xiao Pang Zheng-Yan Lin 《Journal of Mathematical Analysis and Applications》2007,334(2):1246-1259
Let be a sequence of independent and identically distributed positive random variables, which is in the domain of attraction of the normal law, and tn be a positive, integer random variable. Denote , , where denotes the sample mean. Then we show that the self-normalized random product of the partial sums, , is still asymptotically lognormal under a suitable condition about tn. 相似文献
9.
Let C be a closed convex subset of a uniformly smooth Banach space E and let T:C→C be a nonexpansive mapping with a nonempty fixed points set. Given a point u∈C, the initial guess x0∈C is chosen arbitrarily and given sequences , and in (0,1), the following conditions are satisfied:
- (i)
- ;
- (ii)
- αn→0, βn→0 and 0<a?γn, for some a∈(0,1);
- (iii)
- , and . Let be a composite iteration process defined by
10.
Julian Edward 《Journal of Mathematical Analysis and Applications》2006,324(2):941-954
For complex valued sequences of the form ωn=an+ibn with an∈R and bn?0, we prove inequalities of the form , for all sequences {xn} with . We apply these to prove exact null-controllability for a class of hinged beam equations with mild internal damping with either boundary control or internal control. 相似文献
11.
Bebe Prunaru 《Journal of Functional Analysis》2008,254(6):1626-1641
Let H be a complex Hilbert space and let {Tn}n?1 be a sequence of commuting bounded operators on H such that . Let denote the space of all operators X in B(H) for which and suppose that . We will show that there exists a triple {K,Γ,{Un}n?1} where K is a Hilbert space, Γ:K→H is a bounded operator and {Un}n?1⊂B(K) is a sequence of commuting normal operators with such that TnΓ=ΓUn for n?1, and for which the mapping Y?ΓYΓ∗ is a complete isometry from the commutant of {Un}n?1 onto the space . Moreover we show that the inverse of this mapping can be extended to a ∗-homomorphism
12.
An implicit iteration process for nonexpansive semigroups 总被引:1,自引:0,他引:1
Duong Viet Thong 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(17):6116-6120
13.
Ji Gao 《Journal of Mathematical Analysis and Applications》2007,334(1):114-122
Let X be a normed linear space and be the unit sphere of X. Let , , and J(X)=sup{‖x+y‖∧‖x−y‖}, x and y∈S(X) be the modulus of convexity, the modulus of smoothness, and the modulus of squareness of X, respectively. Let . In this paper we proved some sufficient conditions on δ(?), ρX(?), J(X), E(X), and , where the supremum is taken over all the weakly null sequence xn in X and all the elements x of X for the uniform normal structure. 相似文献
14.
C.E Chidume 《Journal of Mathematical Analysis and Applications》2004,296(2):410-421
Let K be a nonempty closed convex and bounded subset of a real Banach space E. Let be a strongly continuous uniformly asymptotically regular and uniformly L-Lipschitzian semi-group of asymptotically pseudocontractive mappings from K into K. Then for a given u∈K there exists a sequence {yn}∈K satisfying the equation yn=(1−αn)(T(tn))nyn+αnu for each , where αn∈(0,1) and tn>0 satisfy appropriate conditions. Suppose further that E is uniformly convex and has uniformly Gâteaux differentiable norm, under suitable conditions on the mappings T, the sequence {yn} converges strongly to a fixed point of . Furthermore, an explicit sequence {xn} generated from x1∈K by xn+1:=(1−λn)xn+λn(T(tn))nxn−λnθn(xn−x1) for all integers n?1, where {λn}, {θn} are positive real sequences satisfying appropriate conditions, converges strongly to a fixed point of . 相似文献
15.
16.
Let , B and Aj () be real nonsingular n×n matrices, λk () be real numbers. In this paper we present a sufficient condition for the system to be a frame for . This sufficient condition also shows the stability of the system with respect to the perturbation of matrix dilation parameters and the perturbation of translation parameters . 相似文献
17.
Strong convergence theorem for uniformly L-Lipschitzian asymptotically pseudocontractive mapping in real Banach space 总被引:1,自引:0,他引:1
E.U. Ofoedu 《Journal of Mathematical Analysis and Applications》2006,321(2):722-728
Let E be a real Banach space. Let K be a nonempty closed and convex subset of E, a uniformly L-Lipschitzian asymptotically pseudocontractive mapping with sequence {kn}n?0⊂[1,+∞), limn→∞kn=1 such that F(T)≠∅. Let {αn}n?0⊂[0,1] be such that ∑n?0αn=∞, and ∑n?0αn(kn−1)<∞. Suppose {xn}n?0 is iteratively defined by xn+1=(1−αn)xn+αnTnxn, n?0, and suppose there exists a strictly increasing continuous function , ?(0)=0 such that 〈Tnx−x∗,j(x−x∗)〉?kn‖x−x∗‖2−?(‖x−x∗‖), ∀x∈K. It is proved that {xn}n?0 converges strongly to x∗∈F(T). It is also proved that the sequence of iteration {xn} defined by xn+1=anxn+bnTnxn+cnun, n?0 (where {un}n?0 is a bounded sequence in K and {an}n?0, {bn}n?0, {cn}n?0 are sequences in [0,1] satisfying appropriate conditions) converges strongly to a fixed point of T. 相似文献
18.
Y. Ben Cheikh 《Journal of Mathematical Analysis and Applications》2007,331(2):1200-1229
In this paper, we use some integral transforms to derive, for a polynomial sequence {Pn(x)}n?0, generating functions of the type , starting from a generating function of type , where {γn}n?0 is a real numbers sequence independent on x and t. That allows us to unify the treatment of a generating function problem for many well-known polynomial sequences in the literature. 相似文献
19.
Let D be a bounded n-dimensional domain, ∂D be its boundary, be its closure, T be a positive real number, B be an n-dimensional ball {x∈D:|x−b|<R} centered at b∈D with a radius R, be its closure, ∂B be its boundary, ν denote the unit inward normal at x∈∂B, and χB(x) be the characteristic function. This article studies the following multi-dimensional parabolic first initial-boundary value problem with a concentrated nonlinear source occupying :
20.
Jiang Ye 《Journal of Mathematical Analysis and Applications》2007,327(1):695-714
Let be a sequence of i.i.d. random variables with EX=0 and EX2=σ2<∞. Set , Mn=maxk?n|Sk|, n?1. Let r>1, then we obtain