This paper proposes a new hybrid variant of extragradient methods for finding a common solution of an equilibrium problem and a family of strict pseudo-contraction mappings. We present an algorithmic scheme that combi...This paper proposes a new hybrid variant of extragradient methods for finding a common solution of an equilibrium problem and a family of strict pseudo-contraction mappings. We present an algorithmic scheme that combine the idea of an extragradient method and a successive iteration method as a hybrid variant. Then, this algorithm is modified by projecting on a suitable convex set to get a better convergence property. The convergence of two these algorithms are investigated under certain assumptions.展开更多
In this article, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems, the set of common fixed point for a family of infinite k-strict pseu...In this article, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems, the set of common fixed point for a family of infinite k-strict pseudo-contractive mappings, and the set of solutions of the variational inclusion problem with multi-valued maximal monotone mappings and inverse-strongly monotone mappings in Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extends the recent results in G.L.Acedo and H.K.Xu [2], Zhang, Lee and Chan [8], Wakahashi and Toyoda [9], Takahashi and Takahashi [I0] and S. S. Chang, H. W. Joseph Lee and C. K. Chan [II], S.Takahashi and W.Takahashi [12]. Moreover, the method of proof adopted in this article is different from those of [4] and [12].展开更多
Let K be a nonempty, closed and convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. Assume that every nonempty closed con- vex and bounded subset of K has the fixed poin...Let K be a nonempty, closed and convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. Assume that every nonempty closed con- vex and bounded subset of K has the fixed point property for nonexpansive mappings. Strong convergence theorems for approximation of a fixed point of Lipschitz pseudo-contractive map- pings which is also a unique solution to variational inequality problem involving φ-strongly pseudo-contractive mappings are proved. The results presented in this article can be applied to the study of fixed points of nonexpansive mappings, variational inequality problems, con- vex optimization problems, and split feasibility problems. Our result extends many recent important results.展开更多
Some necessary and sufficient conditions for convergence of Ishikawa Mann and steepest descent iterative sequence for accretive and pseudo-contractive type mapping in Banach spaces were obtained. The results improve, ...Some necessary and sufficient conditions for convergence of Ishikawa Mann and steepest descent iterative sequence for accretive and pseudo-contractive type mapping in Banach spaces were obtained. The results improve, extend and include some recent results.展开更多
This paper obtains a strong convergence theorem for k-strictly pseudo-contractive mapping under the framework of Hilbert spaces using CQ method. Due to the fact that non-expansive mapping is only O-strictly pseudo-con...This paper obtains a strong convergence theorem for k-strictly pseudo-contractive mapping under the framework of Hilbert spaces using CQ method. Due to the fact that non-expansive mapping is only O-strictly pseudo-contractive, the main result obtained in this paper extends the corresponding main result of Nakajo-Takahashi from non-expansive mapping to k-strictly pseudo-contractive one, where k∈ [0,1）.展开更多
A specific uniform map is constructed as a homeomorphism mapping chaotic time series into [0,1] to obtain sequences of standard uniform distribution. With the uniform map, a chaotic orbit and a sequence orbit obtained...A specific uniform map is constructed as a homeomorphism mapping chaotic time series into [0,1] to obtain sequences of standard uniform distribution. With the uniform map, a chaotic orbit and a sequence orbit obtained are topologically equivalent to each other so the map can preserve the most dynamic properties of chaotic systems such as permutation entropy. Based on the uniform map, a universal algorithm to generate pseudo random numbers is proposed and the pseudo random series is tested to follow the standard 0-1 random distribution both theoretically and experimentally. The algorithm is not complex, which does not impose high requirement on computer hard ware and thus computation speed is fast. The method not only extends the parameter spaces but also avoids the drawback of small function space caused by constraints on chaotic maps used to generate pseudo random numbers. The algorithm can be applied to any chaotic system and can produce pseudo random sequence of high quality, thus can be a good universal pseudo random number generator.展开更多
In this paper, by virtue of an inequality and sane analysis techniques, we prove sane convergence theorems cm the iterative process for nonlinear mappings of-pseudo contractive type in named linear spaces, which exten...In this paper, by virtue of an inequality and sane analysis techniques, we prove sane convergence theorems cm the iterative process for nonlinear mappings of-pseudo contractive type in named linear spaces, which extend and improve the corresponding results obtained by others recently.展开更多
The purpose of this paper is to introduce the concept of Φ_pseudo contractive type mapping and to study the convergence problem of Ishikawa and Mann iterative processes with error for this kind of mappings. The resul...The purpose of this paper is to introduce the concept of Φ_pseudo contractive type mapping and to study the convergence problem of Ishikawa and Mann iterative processes with error for this kind of mappings. The results presented in this paper improve and extend many authors'recent results.展开更多
In this paper, first we introduce notions of (α, Ψ)-contractive and (α)-admissible for a pair of map and prove a coupled coincidence point theorem for compatible mappings using these notions. Our work extends and g...In this paper, first we introduce notions of (α, Ψ)-contractive and (α)-admissible for a pair of map and prove a coupled coincidence point theorem for compatible mappings using these notions. Our work extends and generalizes the results of Mursaleen et al. [1]. At the end, we will provide an example in support of our result.展开更多
The purpose of this paper is to study the weak convergence problems of the implicity iteration process for Lipschitzian pseudocontractive semi-groups in the general Banach spaces. The results presented in this paper e...The purpose of this paper is to study the weak convergence problems of the implicity iteration process for Lipschitzian pseudocontractive semi-groups in the general Banach spaces. The results presented in this paper extend and improve the corresponding results of some people.展开更多
The composite implicit iteration process introduced by Su and Li [J. Math. Anal. Appl. 320 (2006) 882-891] is modified. A strong convergence theorem for approximation of common fixed points of finite family of k-stric...The composite implicit iteration process introduced by Su and Li [J. Math. Anal. Appl. 320 (2006) 882-891] is modified. A strong convergence theorem for approximation of common fixed points of finite family of k-strictly asymptotically pseudo-contractive mappings is proved in Banach spaces using the modified iteration process.展开更多
Some properties of the pseudo umbilical surface M in R 4 are discussed and thus the lower for the tolal mean curvature of M is estimated. On the basis of the estimation and by using the Gauss map of M...Some properties of the pseudo umbilical surface M in R 4 are discussed and thus the lower for the tolal mean curvature of M is estimated. On the basis of the estimation and by using the Gauss map of M , a sufficient condition is given for M as a flat torus in R 4 .展开更多
The purpose of this paper is to study necessary and su？cient condition for the strong convergence of a new parallel iterative algorithm with errors for two finite families of uniformly L-Lipschitzian mappings in Bana...The purpose of this paper is to study necessary and su？cient condition for the strong convergence of a new parallel iterative algorithm with errors for two finite families of uniformly L-Lipschitzian mappings in Banach spaces. The results presented in this paper improve and extend the recent ones announced by [2–7].展开更多
In a recent decade, many DNA sequencing projects are developed on cells, plants and animals over the world into huge DNA databases. Researchers notice that mammalian genomes encoding thousands of large noncoding RNAs ...In a recent decade, many DNA sequencing projects are developed on cells, plants and animals over the world into huge DNA databases. Researchers notice that mammalian genomes encoding thousands of large noncoding RNAs (lncRNAs), interact with chromatin regulatory complexes, and are thought to play a role in localizing these complexes to target loci across the genome. It is a challenge target using higher dimensional tools to organize various complex interactive properties as visual maps. In this paper, a Pseudo DNA Variant MapPDVM is proposed following Cellular Automata to represent multiple maps that use four Meta symbols as well as DNA or RNA representations. The system architecture of key components and the core mechanism on the PDVM are described. Key modules, equations and their I/O parameters are discussed. Applying the PDVM, two sets of real DNA sequences from both the sample human (noncoding DNA) and corn (coding DNA) genomes are collected in comparison with two sets of pseudo DNA sequences generated by a stream cipher HC-256 under different modes to show their intrinsic properties in higher levels of similar relationships among relevant DNA sequences on 2D maps. Sample 2D maps are listed and their characteristics are illustrated under a controllable environment. Various distributions can be observed on both noncoding and coding conditions from their symmetric properties on 2D maps.展开更多
The purpose of this paper is to introduce the concept of accretive mapping in probabilistic normed space (PN space, in short) and to study the existence problem of solutions for equations with accretive mappings in PN...The purpose of this paper is to introduce the concept of accretive mapping in probabilistic normed space (PN space, in short) and to study the existence problem of solutions for equations with accretive mappings in PN space and some existence theorems are shown.展开更多
New high throughput DNA technologies resulted in a disproportion between the high number of scored markers for the mapping populations and relatively small sizes of the genotyped populations. Correspondingly, the numb...New high throughput DNA technologies resulted in a disproportion between the high number of scored markers for the mapping populations and relatively small sizes of the genotyped populations. Correspondingly, the number of markers may, by orders of magnitude, exceed the threshold of recombination resolution achievable for a given population size. Hence, only a small part of markers can be genuinely ordered in the map. The question is how to choose the most informative markers for building such a reliable “skeleton” map. We believe that our approach provides a solution to this difficult problem due to: a) powerful tools of discrete optimization for multilocus ordering;b) a verification procedure, which is impossible without fast and high-quality optimization, to control the map quality based on re-sampling techniques;c) an interactive algorithm of marker clustering in complicated situations caused by significant deviation of recombination rates between markers of non-homologous chromosomes from the expected 50% (referred to as quasi-linkage or pseudo-linkage);and d) an algorithm for detection and removing excessive markers to increase the stability of multilocus ordering.展开更多
Using the new analysis techniques, the problem of iterative approximation of solutions of the equation for Lipschitz phi-strongly accretive operators and of fixed points for Lipschitz phi-strongly pseudo-contractive m...Using the new analysis techniques, the problem of iterative approximation of solutions of the equation for Lipschitz phi-strongly accretive operators and of fixed points for Lipschitz phi-strongly pseudo-contractive mappings are discussed. The main results of this paper improve and extend the corresponding results obtained by Chang, Chidume, Deng, Ding, Tan-Xu and Osilike.展开更多
文摘This paper proposes a new hybrid variant of extragradient methods for finding a common solution of an equilibrium problem and a family of strict pseudo-contraction mappings. We present an algorithmic scheme that combine the idea of an extragradient method and a successive iteration method as a hybrid variant. Then, this algorithm is modified by projecting on a suitable convex set to get a better convergence property. The convergence of two these algorithms are investigated under certain assumptions.
基金supported by Scientific Research Fund of Sichuan Provincial Education Department (09ZB102)Scientific Research Fund of Science and Technology Deportment of Sichuan Provincial (2011JYZ011)
文摘In this article, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems, the set of common fixed point for a family of infinite k-strict pseudo-contractive mappings, and the set of solutions of the variational inclusion problem with multi-valued maximal monotone mappings and inverse-strongly monotone mappings in Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extends the recent results in G.L.Acedo and H.K.Xu [2], Zhang, Lee and Chan [8], Wakahashi and Toyoda [9], Takahashi and Takahashi [I0] and S. S. Chang, H. W. Joseph Lee and C. K. Chan [II], S.Takahashi and W.Takahashi [12]. Moreover, the method of proof adopted in this article is different from those of [4] and [12].
文摘Let K be a nonempty, closed and convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. Assume that every nonempty closed con- vex and bounded subset of K has the fixed point property for nonexpansive mappings. Strong convergence theorems for approximation of a fixed point of Lipschitz pseudo-contractive map- pings which is also a unique solution to variational inequality problem involving φ-strongly pseudo-contractive mappings are proved. The results presented in this article can be applied to the study of fixed points of nonexpansive mappings, variational inequality problems, con- vex optimization problems, and split feasibility problems. Our result extends many recent important results.
文摘Some necessary and sufficient conditions for convergence of Ishikawa Mann and steepest descent iterative sequence for accretive and pseudo-contractive type mapping in Banach spaces were obtained. The results improve, extend and include some recent results.
文摘This paper obtains a strong convergence theorem for k-strictly pseudo-contractive mapping under the framework of Hilbert spaces using CQ method. Due to the fact that non-expansive mapping is only O-strictly pseudo-contractive, the main result obtained in this paper extends the corresponding main result of Nakajo-Takahashi from non-expansive mapping to k-strictly pseudo-contractive one, where k∈ [0,1）.
基金supported by the National Natural Science Foundation of China (Grant No.10871168)
文摘A specific uniform map is constructed as a homeomorphism mapping chaotic time series into [0,1] to obtain sequences of standard uniform distribution. With the uniform map, a chaotic orbit and a sequence orbit obtained are topologically equivalent to each other so the map can preserve the most dynamic properties of chaotic systems such as permutation entropy. Based on the uniform map, a universal algorithm to generate pseudo random numbers is proposed and the pseudo random series is tested to follow the standard 0-1 random distribution both theoretically and experimentally. The algorithm is not complex, which does not impose high requirement on computer hard ware and thus computation speed is fast. The method not only extends the parameter spaces but also avoids the drawback of small function space caused by constraints on chaotic maps used to generate pseudo random numbers. The algorithm can be applied to any chaotic system and can produce pseudo random sequence of high quality, thus can be a good universal pseudo random number generator.
文摘In this paper, by virtue of an inequality and sane analysis techniques, we prove sane convergence theorems cm the iterative process for nonlinear mappings of-pseudo contractive type in named linear spaces, which extend and improve the corresponding results obtained by others recently.
文摘The purpose of this paper is to introduce the concept of Φ_pseudo contractive type mapping and to study the convergence problem of Ishikawa and Mann iterative processes with error for this kind of mappings. The results presented in this paper improve and extend many authors'recent results.
文摘In this paper, first we introduce notions of (α, Ψ)-contractive and (α)-admissible for a pair of map and prove a coupled coincidence point theorem for compatible mappings using these notions. Our work extends and generalizes the results of Mursaleen et al. [1]. At the end, we will provide an example in support of our result.
基金supported by the Natural Science Foundation of Yibin University (No. 2007Z3)
文摘The purpose of this paper is to study the weak convergence problems of the implicity iteration process for Lipschitzian pseudocontractive semi-groups in the general Banach spaces. The results presented in this paper extend and improve the corresponding results of some people.
文摘The composite implicit iteration process introduced by Su and Li [J. Math. Anal. Appl. 320 (2006) 882-891] is modified. A strong convergence theorem for approximation of common fixed points of finite family of k-strictly asymptotically pseudo-contractive mappings is proved in Banach spaces using the modified iteration process.
文摘Some properties of the pseudo umbilical surface M in R 4 are discussed and thus the lower for the tolal mean curvature of M is estimated. On the basis of the estimation and by using the Gauss map of M , a sufficient condition is given for M as a flat torus in R 4 .
基金supported by the National Natural Science Foun-dation of China (11071169)the Natural Science Foundation of Zhejiang Province (Y6110287)
文摘The purpose of this paper is to study necessary and su？cient condition for the strong convergence of a new parallel iterative algorithm with errors for two finite families of uniformly L-Lipschitzian mappings in Banach spaces. The results presented in this paper improve and extend the recent ones announced by [2–7].
文摘In a recent decade, many DNA sequencing projects are developed on cells, plants and animals over the world into huge DNA databases. Researchers notice that mammalian genomes encoding thousands of large noncoding RNAs (lncRNAs), interact with chromatin regulatory complexes, and are thought to play a role in localizing these complexes to target loci across the genome. It is a challenge target using higher dimensional tools to organize various complex interactive properties as visual maps. In this paper, a Pseudo DNA Variant MapPDVM is proposed following Cellular Automata to represent multiple maps that use four Meta symbols as well as DNA or RNA representations. The system architecture of key components and the core mechanism on the PDVM are described. Key modules, equations and their I/O parameters are discussed. Applying the PDVM, two sets of real DNA sequences from both the sample human (noncoding DNA) and corn (coding DNA) genomes are collected in comparison with two sets of pseudo DNA sequences generated by a stream cipher HC-256 under different modes to show their intrinsic properties in higher levels of similar relationships among relevant DNA sequences on 2D maps. Sample 2D maps are listed and their characteristics are illustrated under a controllable environment. Various distributions can be observed on both noncoding and coding conditions from their symmetric properties on 2D maps.
文摘The purpose of this paper is to introduce the concept of accretive mapping in probabilistic normed space (PN space, in short) and to study the existence problem of solutions for equations with accretive mappings in PN space and some existence theorems are shown.
文摘New high throughput DNA technologies resulted in a disproportion between the high number of scored markers for the mapping populations and relatively small sizes of the genotyped populations. Correspondingly, the number of markers may, by orders of magnitude, exceed the threshold of recombination resolution achievable for a given population size. Hence, only a small part of markers can be genuinely ordered in the map. The question is how to choose the most informative markers for building such a reliable “skeleton” map. We believe that our approach provides a solution to this difficult problem due to: a) powerful tools of discrete optimization for multilocus ordering;b) a verification procedure, which is impossible without fast and high-quality optimization, to control the map quality based on re-sampling techniques;c) an interactive algorithm of marker clustering in complicated situations caused by significant deviation of recombination rates between markers of non-homologous chromosomes from the expected 50% (referred to as quasi-linkage or pseudo-linkage);and d) an algorithm for detection and removing excessive markers to increase the stability of multilocus ordering.
文摘Using the new analysis techniques, the problem of iterative approximation of solutions of the equation for Lipschitz phi-strongly accretive operators and of fixed points for Lipschitz phi-strongly pseudo-contractive mappings are discussed. The main results of this paper improve and extend the corresponding results obtained by Chang, Chidume, Deng, Ding, Tan-Xu and Osilike.
