In this article, we extend the definition of uniformly starlike functions and uni- formly convex functions on the unit disk to the unit ball in C^n, give the discriminant criterions for them, and get some inequalities...In this article, we extend the definition of uniformly starlike functions and uni- formly convex functions on the unit disk to the unit ball in C^n, give the discriminant criterions for them, and get some inequalities for them.展开更多
Abstract In the present paper we introduce a random iteration scheme for three rondom operators defined on aclosed and convex subset of a uniformly convex Banach space and prove its convergence to a common fixedpoint ...Abstract In the present paper we introduce a random iteration scheme for three rondom operators defined on aclosed and convex subset of a uniformly convex Banach space and prove its convergence to a common fixedpoint of three random operators. The result is also an extension of a known theorem in the correspondingnon-random case.展开更多
In this paper we give a martingale representation in nearly uniformly convex Banach spaces. Our result generalizes the representation theorem established by Landers and Rogge.
In this article,we will investigate the properties of iterative sequence for non-expansive mappings and present several strong and weak convergence results of successive approximations to fixed points of non-expansive...In this article,we will investigate the properties of iterative sequence for non-expansive mappings and present several strong and weak convergence results of successive approximations to fixed points of non-expansive mappings in uniformly convex Banach spaces.The results presented in this article generalize and improve various ones concerned with constructive techniques for the fixed points of non-expansive mappings.展开更多
This paper shows that X is uniformly non-square iff P(η_o)】0 for someη_o∈(0,2).Thus X is super-reflexive if and only if for X there exists an equivalent normwhich meets the above condition.By virtue of the before ...This paper shows that X is uniformly non-square iff P(η_o)】0 for someη_o∈(0,2).Thus X is super-reflexive if and only if for X there exists an equivalent normwhich meets the above condition.By virtue of the before mentioned result,the author derives the necessary,and suffi-cient conditions for X and l^p(X_j)being uniformly non-square,respectively,and gives acharacterization of finite-dimensional spaces which are uniformly non-square.展开更多
Let X be a Banach space, S(X) be the unit sphere of X, φ be a function: S(X)→ S(X *) such that φ(x)∈ x, and v φ(ε) =inf 1-12x+y: x,y∈S(X), and 〈φ(x), x-y 〉≥ε, 0≤ε≤2, whe...Let X be a Banach space, S(X) be the unit sphere of X, φ be a function: S(X)→ S(X *) such that φ(x)∈ x, and v φ(ε) =inf 1-12x+y: x,y∈S(X), and 〈φ(x), x-y 〉≥ε, 0≤ε≤2, where x is the set of norm 1 supporting functionals of S(X) at x. A geometric concept, modulus of V convexity V(ε)= sup {V φ(ε), for all φ: S(X)→S(X *)}, is introduced; the properties of V(ε) and the relationship between V(ε) and other geometric concepts are discussed. The main result is that V12>0 implies normal structure.展开更多
Let d μ=ψ d ν be a complex valued measure where ν is a non negative measure and ψ is a complex valued function which satisfies b + p or b + ∞∩a 1 condition. We prove some basic martingale i...Let d μ=ψ d ν be a complex valued measure where ν is a non negative measure and ψ is a complex valued function which satisfies b + p or b + ∞∩a 1 condition. We prove some basic martingale inequalities such as B G inequalities, weak ( p,p) and strong (p,p) type inequalities for Banach space valued martingale with respect to complex measure μ .展开更多
This paper studies the convergence of the sequence defined by x0 ∈ C, xn+l =αnu+(1-αn)Txn, n=0, 1,2,..., where 0 ≤αn ≤ 1, limn→∞ αn = 0, ∑n=0^∞ αn = ∞, and T is a nonexpansive mapping from a nonempty...This paper studies the convergence of the sequence defined by x0 ∈ C, xn+l =αnu+(1-αn)Txn, n=0, 1,2,..., where 0 ≤αn ≤ 1, limn→∞ αn = 0, ∑n=0^∞ αn = ∞, and T is a nonexpansive mapping from a nonempty closed convex subset C of a Banach space X into itself. The iterative sequence {xn} converges strongly to a fixed point of T in the case when X is a uniformly convex Banach space with a uniformly Gateaux differentiable norm or a uniformly smooth Banach space only. The results presented in this paper extend and improve some recent results.展开更多
The purpose of this paper is to study and analyze an iterative method for finding a common element of the solution set ~ of the split feasibility problem and the set F(T) of fixed points of a right Bregman strongly ...The purpose of this paper is to study and analyze an iterative method for finding a common element of the solution set ~ of the split feasibility problem and the set F(T) of fixed points of a right Bregman strongly nonexpansive mapping T in the setting of p- uniformly convex Banach spaces which are also uniformly smooth. By combining Mann's iterative method and the Halpern's approximation method, we propose an iterative algorithm for finding an element of the set F(T)∩Ω moreover, we derive the strong convergence of the proposed algorithm under appropriate conditions and give numerical results to verify the efficiency and implementation of our method. Our results extend and complement many known related results in the literature.展开更多
The existence of common fixed points for a pair of Lipschitzian mappings in Banach spaces is proved. By using this result, some common fixed point theorems are also established for these mappings in Hilbert spaces, in...The existence of common fixed points for a pair of Lipschitzian mappings in Banach spaces is proved. By using this result, some common fixed point theorems are also established for these mappings in Hilbert spaces, in L p spaces, in Hardy spaces H p, and in Sobolev spaces H r,p , for 1<p<+∞ and r≥0.展开更多
We introduce a one-step implicit iterative method for two finite families of asymptotically nonexpansive mappings in a hyperbolic space and use it to approximate common fixed points of these families. The results pres...We introduce a one-step implicit iterative method for two finite families of asymptotically nonexpansive mappings in a hyperbolic space and use it to approximate common fixed points of these families. The results presented in this paper are new in the setting of hyperbolic spaces. On top, these are generalizations of several results in literature from Banach spaces to hyperbolic spaces. At the end of the paper, we give an example to validate our results.展开更多
The purpose of this paper is to prove a new weak convergence theorem for a finite family of asymptotically nonexpansive mappings in uniformly convex Banach space.
We establish the existence and multiplicity of weak solutions for equations which involve a uniformly convex elliptic operator in divergence form(in particular, a p-Laplacian operator), while the nonlinearity has a(p-...We establish the existence and multiplicity of weak solutions for equations which involve a uniformly convex elliptic operator in divergence form(in particular, a p-Laplacian operator), while the nonlinearity has a(p- 1)-superlinear growth at infinity. Our result completes and extends the relevant results of recent papers. The argument in the proof of our main result relies on the Z2-symmetric version of mountain pass lemma.展开更多
In the present paper, we study certain differential inequalities involving p-valent functions and obtain sufficient conditions for uniformly p-valent starlikeness and uniformly p-valent convexity. We also offer a corr...In the present paper, we study certain differential inequalities involving p-valent functions and obtain sufficient conditions for uniformly p-valent starlikeness and uniformly p-valent convexity. We also offer a correct version of some known criteria for uniformly p-valent starlike and uniformly p-valent convex functions.展开更多
Let C be a bounded convex subset in a uniformly convex Banach space X, x 0, u n∈C , then x n+1 =S nx n, where S n=α n0 I+α n1 T+α n2 T 2+…+α nk T k+γ nu n, α ni ≥0, 0<α≤α ...Let C be a bounded convex subset in a uniformly convex Banach space X, x 0, u n∈C , then x n+1 =S nx n, where S n=α n0 I+α n1 T+α n2 T 2+…+α nk T k+γ nu n, α ni ≥0, 0<α≤α n0 ≤b<1, ∑ki=0α ni +γ n=1, and n≥1. It is proved that x n converges to a fixed point on T if T is a nonexpansive mapping.展开更多
This paper through discussing subdifferentiability and convexity of convex functions shows that a Banach space admits an equivalent uniformly [locally uniformly, strictly] convex norm if and only if there exists a con...This paper through discussing subdifferentiability and convexity of convex functions shows that a Banach space admits an equivalent uniformly [locally uniformly, strictly] convex norm if and only if there exists a continuous uniformly [locally uniformly, strictly] convex function on some nonempty open convex subset of the space and presents some characterizations of super-reflexive Banach spaces.展开更多
This paper gives some relations and properties of several kinds of generalized convexity in Banach spaces. As a result, it proves that every kind of uniform convexity implies the Banach-Sakes property, and several not...This paper gives some relations and properties of several kinds of generalized convexity in Banach spaces. As a result, it proves that every kind of uniform convexity implies the Banach-Sakes property, and several notions of uniform convexity in literature are actually equivalent.展开更多
Let (Ω, F, P) be a probability space and L0(F,R) the algebra of equivalence classes of real- valued random variables on (Ω, F, P). When L0(F,R) is endowed with the topology of convergence in probability, we ...Let (Ω, F, P) be a probability space and L0(F,R) the algebra of equivalence classes of real- valued random variables on (Ω, F, P). When L0(F,R) is endowed with the topology of convergence in probability, we prove an intermediate value theorem for a continuous local function from L0(F, R) to L0(F,R). As applications of this theorem, we first give several useful expressions for modulus of random convexity, then we prove that a complete random normed module (S, ||·||) is random uniformly convex iff LP(S) is uniformly convex for each fixed positive number p such that 1 〈 p 〈 +∞.展开更多
In this paper, we will establish several strong convergence theorems for the approximation of common fixed points of r-strictly asymptotically pseudocontractive mappings in uniformly convex Banach spaces using the mod...In this paper, we will establish several strong convergence theorems for the approximation of common fixed points of r-strictly asymptotically pseudocontractive mappings in uniformly convex Banach spaces using the modiied implicit iteration sequence with errors, and prove the necessary and sufficient conditions for the convergence of the sequence. Our results generalize, extend and improve the recent work, in this topic.展开更多
We generalize Ekeland's Variational Principle for cyclic maps. We present applications of this version of the variational principle for proving of existence and uniqueness of best proximity points for different class...We generalize Ekeland's Variational Principle for cyclic maps. We present applications of this version of the variational principle for proving of existence and uniqueness of best proximity points for different classes of cyclic maps.展开更多
基金supported by the NNSF of China(11001074,11061015,11101124)the Foundation for University Young Key Teacher of Henan Province
文摘In this article, we extend the definition of uniformly starlike functions and uni- formly convex functions on the unit disk to the unit ball in C^n, give the discriminant criterions for them, and get some inequalities for them.
文摘Abstract In the present paper we introduce a random iteration scheme for three rondom operators defined on aclosed and convex subset of a uniformly convex Banach space and prove its convergence to a common fixedpoint of three random operators. The result is also an extension of a known theorem in the correspondingnon-random case.
文摘In this paper we give a martingale representation in nearly uniformly convex Banach spaces. Our result generalizes the representation theorem established by Landers and Rogge.
文摘In this article,we will investigate the properties of iterative sequence for non-expansive mappings and present several strong and weak convergence results of successive approximations to fixed points of non-expansive mappings in uniformly convex Banach spaces.The results presented in this article generalize and improve various ones concerned with constructive techniques for the fixed points of non-expansive mappings.
文摘This paper shows that X is uniformly non-square iff P(η_o)】0 for someη_o∈(0,2).Thus X is super-reflexive if and only if for X there exists an equivalent normwhich meets the above condition.By virtue of the before mentioned result,the author derives the necessary,and suffi-cient conditions for X and l^p(X_j)being uniformly non-square,respectively,and gives acharacterization of finite-dimensional spaces which are uniformly non-square.
文摘Let X be a Banach space, S(X) be the unit sphere of X, φ be a function: S(X)→ S(X *) such that φ(x)∈ x, and v φ(ε) =inf 1-12x+y: x,y∈S(X), and 〈φ(x), x-y 〉≥ε, 0≤ε≤2, where x is the set of norm 1 supporting functionals of S(X) at x. A geometric concept, modulus of V convexity V(ε)= sup {V φ(ε), for all φ: S(X)→S(X *)}, is introduced; the properties of V(ε) and the relationship between V(ε) and other geometric concepts are discussed. The main result is that V12>0 implies normal structure.
文摘Let d μ=ψ d ν be a complex valued measure where ν is a non negative measure and ψ is a complex valued function which satisfies b + p or b + ∞∩a 1 condition. We prove some basic martingale inequalities such as B G inequalities, weak ( p,p) and strong (p,p) type inequalities for Banach space valued martingale with respect to complex measure μ .
基金Supported by the Natural Science Foundation of the Educational Dept.of Zhejiang Province(20020868).
文摘This paper studies the convergence of the sequence defined by x0 ∈ C, xn+l =αnu+(1-αn)Txn, n=0, 1,2,..., where 0 ≤αn ≤ 1, limn→∞ αn = 0, ∑n=0^∞ αn = ∞, and T is a nonexpansive mapping from a nonempty closed convex subset C of a Banach space X into itself. The iterative sequence {xn} converges strongly to a fixed point of T in the case when X is a uniformly convex Banach space with a uniformly Gateaux differentiable norm or a uniformly smooth Banach space only. The results presented in this paper extend and improve some recent results.
文摘The purpose of this paper is to study and analyze an iterative method for finding a common element of the solution set ~ of the split feasibility problem and the set F(T) of fixed points of a right Bregman strongly nonexpansive mapping T in the setting of p- uniformly convex Banach spaces which are also uniformly smooth. By combining Mann's iterative method and the Halpern's approximation method, we propose an iterative algorithm for finding an element of the set F(T)∩Ω moreover, we derive the strong convergence of the proposed algorithm under appropriate conditions and give numerical results to verify the efficiency and implementation of our method. Our results extend and complement many known related results in the literature.
文摘The existence of common fixed points for a pair of Lipschitzian mappings in Banach spaces is proved. By using this result, some common fixed point theorems are also established for these mappings in Hilbert spaces, in L p spaces, in Hardy spaces H p, and in Sobolev spaces H r,p , for 1<p<+∞ and r≥0.
基金King Fahd University of Petroleum and Minerals for supporting the research project IN121055Higher Education Commission (HEC) of Pakistan for financial support
文摘We introduce a one-step implicit iterative method for two finite families of asymptotically nonexpansive mappings in a hyperbolic space and use it to approximate common fixed points of these families. The results presented in this paper are new in the setting of hyperbolic spaces. On top, these are generalizations of several results in literature from Banach spaces to hyperbolic spaces. At the end of the paper, we give an example to validate our results.
文摘The purpose of this paper is to prove a new weak convergence theorem for a finite family of asymptotically nonexpansive mappings in uniformly convex Banach space.
基金Supported by the NNSF of China(11101145)Supported by the NSF of Henan Province(102102210216)
文摘We establish the existence and multiplicity of weak solutions for equations which involve a uniformly convex elliptic operator in divergence form(in particular, a p-Laplacian operator), while the nonlinearity has a(p- 1)-superlinear growth at infinity. Our result completes and extends the relevant results of recent papers. The argument in the proof of our main result relies on the Z2-symmetric version of mountain pass lemma.
文摘In the present paper, we study certain differential inequalities involving p-valent functions and obtain sufficient conditions for uniformly p-valent starlikeness and uniformly p-valent convexity. We also offer a correct version of some known criteria for uniformly p-valent starlike and uniformly p-valent convex functions.
文摘Let C be a bounded convex subset in a uniformly convex Banach space X, x 0, u n∈C , then x n+1 =S nx n, where S n=α n0 I+α n1 T+α n2 T 2+…+α nk T k+γ nu n, α ni ≥0, 0<α≤α n0 ≤b<1, ∑ki=0α ni +γ n=1, and n≥1. It is proved that x n converges to a fixed point on T if T is a nonexpansive mapping.
文摘This paper through discussing subdifferentiability and convexity of convex functions shows that a Banach space admits an equivalent uniformly [locally uniformly, strictly] convex norm if and only if there exists a continuous uniformly [locally uniformly, strictly] convex function on some nonempty open convex subset of the space and presents some characterizations of super-reflexive Banach spaces.
基金Supported b-y National Natural Science Foundation of China (Grant No. 10926042 and 11001231), China Postdoctoral Science Foundation (Grant No. 20090460356), RFDP (Grant No. 200803841018)Acknowledgements The authors would like to thank Professor Cheng Lixin and Professor Bu Shangquan for many helpful conversations on this paper, and also thank the referee for many valuable suggestions.
文摘This paper gives some relations and properties of several kinds of generalized convexity in Banach spaces. As a result, it proves that every kind of uniform convexity implies the Banach-Sakes property, and several notions of uniform convexity in literature are actually equivalent.
基金Supported by National Natural Science Foundation of China (Grant No. 10871016)
文摘Let (Ω, F, P) be a probability space and L0(F,R) the algebra of equivalence classes of real- valued random variables on (Ω, F, P). When L0(F,R) is endowed with the topology of convergence in probability, we prove an intermediate value theorem for a continuous local function from L0(F, R) to L0(F,R). As applications of this theorem, we first give several useful expressions for modulus of random convexity, then we prove that a complete random normed module (S, ||·||) is random uniformly convex iff LP(S) is uniformly convex for each fixed positive number p such that 1 〈 p 〈 +∞.
基金Scientific Research Fund of Zhejiang Provincial Education Department(No.20051778 and No.20051760)Scientific Research Fund of Ningbo University(200542)
文摘In this paper, we will establish several strong convergence theorems for the approximation of common fixed points of r-strictly asymptotically pseudocontractive mappings in uniformly convex Banach spaces using the modiied implicit iteration sequence with errors, and prove the necessary and sufficient conditions for the convergence of the sequence. Our results generalize, extend and improve the recent work, in this topic.
基金The first author is partially supported by Scientific Research Fund of Sofia University,Contract 88/2014
文摘We generalize Ekeland's Variational Principle for cyclic maps. We present applications of this version of the variational principle for proving of existence and uniqueness of best proximity points for different classes of cyclic maps.