The open question raised by Reich is studied in a Banach space with uniform normal structure, whose norm is uniformly Gateaux differentiable. Under more suitable assumptions imposed on an asymptotically nonexpansive m...The open question raised by Reich is studied in a Banach space with uniform normal structure, whose norm is uniformly Gateaux differentiable. Under more suitable assumptions imposed on an asymptotically nonexpansive mapping, an affirmative answer to Reich' s open question is given. The results presented extend and improve Zhang Shisheng' s recent ones in the following aspects : (i) Zhang' s stronger condition that the sequence of iterative parameters converges to zero is removed; (ii) Zhang' s stronger assumption that the asymptotically nonexpansive mapping has a fixed point is removed; (iii) Zhang' s stronger condition that the sequence generated by the Banach Contraction Principle is strongly convergent is also removed. Moreover, these also extend and improve the corresponding ones obtained previously by several authors including Reich, Shioji, Takahashi,Ueda and Wittmann.展开更多
In the paper, we use trace representations of Boolean functions to obtain that a class mappings including functionsF(x)=x d over field GF(2 n ), withW(d)=n?1, have desirable cryptographic properties. Therefore we gene...In the paper, we use trace representations of Boolean functions to obtain that a class mappings including functionsF(x)=x d over field GF(2 n ), withW(d)=n?1, have desirable cryptographic properties. Therefore we generalize an important result of Nyberg. As application, we use these conclusions to analyze cryptographic property of the S-box of AES (the Advanced Encryption Standard) and give its several equivalent representations, proving that the composition of inversion function of AES and any invertible affine transformations is impossible to satisfy strict avalanche criterion, any order propagation criteria and any order correlation immunity. Key words trace function - nonlinearity - differentially uniform - strict avalanche criterion CLC number TP 309 Foundation item: Supported by the National Natural Science Foundation of China (60373089, 60373041), Natural Science Foundation of Hubei Province (2002AB0037) and Chen-guang Plan of Wuhan City (20025001007).Biography: Zeng Xiang-yong (1973-), male, A postdoctoral fellow, research direction: cryptology and the representation theory of algebra.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
By the properties of the Musielak_Orlicz funciton's sequence, the necessary and sufficient condition for uniform Gateaux differential (UGD) property of Musielak_Orlicz sequence spaces equipped with the Luxemburg n...By the properties of the Musielak_Orlicz funciton's sequence, the necessary and sufficient condition for uniform Gateaux differential (UGD) property of Musielak_Orlicz sequence spaces equipped with the Luxemburg norm and a criterion for weakly uniform rotundity of Musielak_Orlicz sequence space with Orlicz norm are given.展开更多
It is our purpose in this paper to show that some results obtained in uniformly convex real Banach space with uniformly Gateaux differentiable norm are extendable to more general reflexive and strictly convex real Ban...It is our purpose in this paper to show that some results obtained in uniformly convex real Banach space with uniformly Gateaux differentiable norm are extendable to more general reflexive and strictly convex real Banach space with uniformly G&teaux differentiable norm. Demicompactness condition imposed in such results is dispensed with. Furthermore, Applications of our theorems to approximation of common fixed point of countable infinite family of continuous pseudocontractive mappings and approximation of common solution of countable infinite family of generalized mixed equilibrium problems are also discussed. Our theorems improve, generalize, unify and extend several recently announced results.展开更多
In this paper, the iteration xn+l =αny + (1 -αn)Ti(n)k(n)xn for a family of asymptotically nonexpansive mappings T1, T2, ..., TN is originally introduced in an uniformly convex Banach space. Motivated by rec...In this paper, the iteration xn+l =αny + (1 -αn)Ti(n)k(n)xn for a family of asymptotically nonexpansive mappings T1, T2, ..., TN is originally introduced in an uniformly convex Banach space. Motivated by recent papers, we prove that under suitable conditions the iteration scheme converges strongly to the nearest common fixed point of the family of asymptotically nonexpansive mappings. The results presented in this paper expand and improve correponding ones from Hilbert spaces to uniformly convex Banach spaces, or from nonexpansive mappings to asymptotically nonexpansive mappings.展开更多
We study the functions with low differential uniformity,and concentrates mainly on the properties of perfect nonlinear(PN) functions,including the properties of the derivative of the components of those functions.So...We study the functions with low differential uniformity,and concentrates mainly on the properties of perfect nonlinear(PN) functions,including the properties of the derivative of the components of those functions.Some sufficient and necessary conditions have been explored to judge when a function is a PN function.These conditions may be useful in constructing new PN functions.We also construct some functions with differential 4-uniformity that have rarely been studied in the literature.Some of the constructed functions with differential 4-uniformity have high nonlinearity as well.Finally,a class of functions with differential 4-uniformity which are not extended affine equivalent to any power functions are constructed.展开更多
Permutation polynomials with low differential uniformity and high nonlinearity are preferred in cryptographic systems. In 2018, Tu, Zeng and Helleseth constructed a new class of permutation quadrinomials over the fini...Permutation polynomials with low differential uniformity and high nonlinearity are preferred in cryptographic systems. In 2018, Tu, Zeng and Helleseth constructed a new class of permutation quadrinomials over the finite field F_(2 2m) for an odd integer m. In this paper, we aim to investigate the differential uniformity and nonlinearity of this class of permutation polynomials so as to find 4-uniform permutation polynomials with high nonlinearity.展开更多
文摘The open question raised by Reich is studied in a Banach space with uniform normal structure, whose norm is uniformly Gateaux differentiable. Under more suitable assumptions imposed on an asymptotically nonexpansive mapping, an affirmative answer to Reich' s open question is given. The results presented extend and improve Zhang Shisheng' s recent ones in the following aspects : (i) Zhang' s stronger condition that the sequence of iterative parameters converges to zero is removed; (ii) Zhang' s stronger assumption that the asymptotically nonexpansive mapping has a fixed point is removed; (iii) Zhang' s stronger condition that the sequence generated by the Banach Contraction Principle is strongly convergent is also removed. Moreover, these also extend and improve the corresponding ones obtained previously by several authors including Reich, Shioji, Takahashi,Ueda and Wittmann.
文摘In the paper, we use trace representations of Boolean functions to obtain that a class mappings including functionsF(x)=x d over field GF(2 n ), withW(d)=n?1, have desirable cryptographic properties. Therefore we generalize an important result of Nyberg. As application, we use these conclusions to analyze cryptographic property of the S-box of AES (the Advanced Encryption Standard) and give its several equivalent representations, proving that the composition of inversion function of AES and any invertible affine transformations is impossible to satisfy strict avalanche criterion, any order propagation criteria and any order correlation immunity. Key words trace function - nonlinearity - differentially uniform - strict avalanche criterion CLC number TP 309 Foundation item: Supported by the National Natural Science Foundation of China (60373089, 60373041), Natural Science Foundation of Hubei Province (2002AB0037) and Chen-guang Plan of Wuhan City (20025001007).Biography: Zeng Xiang-yong (1973-), male, A postdoctoral fellow, research direction: cryptology and the representation theory of algebra.
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By the properties of the Musielak_Orlicz funciton's sequence, the necessary and sufficient condition for uniform Gateaux differential (UGD) property of Musielak_Orlicz sequence spaces equipped with the Luxemburg norm and a criterion for weakly uniform rotundity of Musielak_Orlicz sequence space with Orlicz norm are given.
文摘It is our purpose in this paper to show that some results obtained in uniformly convex real Banach space with uniformly Gateaux differentiable norm are extendable to more general reflexive and strictly convex real Banach space with uniformly G&teaux differentiable norm. Demicompactness condition imposed in such results is dispensed with. Furthermore, Applications of our theorems to approximation of common fixed point of countable infinite family of continuous pseudocontractive mappings and approximation of common solution of countable infinite family of generalized mixed equilibrium problems are also discussed. Our theorems improve, generalize, unify and extend several recently announced results.
基金The Found(2011Z05)of the Key Project of Yibin University
文摘In this paper, the iteration xn+l =αny + (1 -αn)Ti(n)k(n)xn for a family of asymptotically nonexpansive mappings T1, T2, ..., TN is originally introduced in an uniformly convex Banach space. Motivated by recent papers, we prove that under suitable conditions the iteration scheme converges strongly to the nearest common fixed point of the family of asymptotically nonexpansive mappings. The results presented in this paper expand and improve correponding ones from Hilbert spaces to uniformly convex Banach spaces, or from nonexpansive mappings to asymptotically nonexpansive mappings.
基金Supported by the National Natural Science Foundation of China (60673068)the Fundamental Research Funds for the Central Universities (2009B27414)the Natural Science Foundation of Hohai University (2084/409270)
文摘We study the functions with low differential uniformity,and concentrates mainly on the properties of perfect nonlinear(PN) functions,including the properties of the derivative of the components of those functions.Some sufficient and necessary conditions have been explored to judge when a function is a PN function.These conditions may be useful in constructing new PN functions.We also construct some functions with differential 4-uniformity that have rarely been studied in the literature.Some of the constructed functions with differential 4-uniformity have high nonlinearity as well.Finally,a class of functions with differential 4-uniformity which are not extended affine equivalent to any power functions are constructed.
基金This work was supported by the Application Foundation Frontier Project of Wuhan Science and Technology Bureau(No.2020010601012189)the National Natural Science Foundation of China(Nos.61761166010,62072162).
文摘Permutation polynomials with low differential uniformity and high nonlinearity are preferred in cryptographic systems. In 2018, Tu, Zeng and Helleseth constructed a new class of permutation quadrinomials over the finite field F_(2 2m) for an odd integer m. In this paper, we aim to investigate the differential uniformity and nonlinearity of this class of permutation polynomials so as to find 4-uniform permutation polynomials with high nonlinearity.