关于sn度量空间的注记

The main purpose of this paper is to establish the mapping relation between metric spaces and sn-metric spaces.     

Minimax Theorems Involving Two Functions and Strictly Monotone Transformations of Their Values

Two two-function minimax theorems are proved.The concavity-convexity conditions of the twofunctions involve strictly monotone transformations and mixing of the values of the two functions,and aredescribed by the inequalities as upward and weakly downward conditions.     

Common fixed point theorem for hybrid generalized multi-valued contraction mappings

In this paper, we introduce the notion of a hybrid generalized multi-valued contraction mapping and establish the common fixed point theorem for this mapping. Our results generalize, unify, extend and complement several common fixed point theorems of many authors in the literature.     

Hamiltonian control used to improve the beam stability in particle accelerator models

We derive a Hamiltonian control theory which can be applied to a 4D symplectic map that models a ring particle accelerator composed of elements with sextupole nonlinearity. The controlled system is designed to exhibit a more regular orbital behavior than the uncontrolled one. Using the Smaller Alignment Index (SALI) chaos indicator, we are able to show that the controlled system has a dynamical aperture up to 1.7 times larger than the original model.     

On some auxiliary mappings generated by nonexpansive and strictly pseudo-contractive mappings

Starting by a finite family of mappings, we define the concept of procedure with Lipschitzian dependence of the coefficients. We give seven concrete examples of such procedures and prove the strong convergence of two viscosity methods.     

An iterative scheme for equilibrium problems and fixed point problems of strict pseudo-contraction mappings

In this paper, we propose an iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a strict pseudo-contraction mapping in the setting of real Hilbert spaces. We establish some weak and strong convergence theorems of the sequences generated by our proposed scheme. Our results combine the ideas of Marino and Xu’s result [G. Marino, H.K. Xu, Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces, J. Math. Anal. Appl. 329 (2007) 336–346], and Takahashi and Takahashi’s result [S. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2007) 506–515]. In particular, necessary and sufficient conditions for strong convergence of our iterative scheme are obtained.     

Refined functional equations stemming from cubic,quadratic and additive mappings

Let n ≥ 2 be an integer. In this paper, we investigate the generalized Hyers-Ulam stability problem for the following functional equation f（n-1∑j=1 xj＋2xn）＋f（n-1∑j=1 xj-2xn）＋8 n-1∑j=1f（xj）=2f（n-1∑j=1 xj） ＋4 n-1∑j=1[f（xj＋xn）＋f（xj-xn）] which contains as solutions cubic, quadratic or additive mappings.     

Uniformly nonsquare Banach spaces have the fixed point property for nonexpansive mappings

It is shown that if the modulus Γ_X of nearly uniform smoothness of a reflexive Banach space satisfies , then every bounded closed convex subset of X has the fixed point property for nonexpansive mappings. In particular, uniformly nonsquare Banach spaces have this property since they are properly included in this class of spaces. This answers a long-standing question in the theory.     

Convergence theorems for implicit iteration process for a finite family of continuous pseudocontractive mappings

In this paper, a necessary and sufficient conditions for the strong convergence to a common fixed point of a finite family of continuous pseudocontractive mappings are proved in an arbitrary real Banach space using an implicit iteration scheme recently introduced by Xu and Ori [H.K. Xu, R.G. Ori, An implicit iteration process for nonexpansive mappings, Numer. Fuct. Anal. Optim. 22 (2001) 767-773] in condition αn∈(0,1], and also strong and weak convergence theorem of a finite family of strictly pseudocontractive mappings of Browder-Petryshyn type is obtained. The results presented extend and improve the corresponding results of M.O. Osilike [M.O. Osilike, Implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps, J. Math. Anal. Appl. 294 (2004) 73-81].