On Induced Mappings

ＯｎＩｎｄｕｃｅｄＭａｐｐｉｎｇｓＣｕｉＨｏｎｇｂｉｎＦａｎＬｅｉＺｈｅｎｇＣｈｏｎｇｙｏｕ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＣａｐｉｔａｌＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉｊｉｎｇ，１０００３７）ＡｂｓｔｒａｃｔＬｅｔＸｂｅ...     

On the Fekete and Szeg? Problem for Starlike Mappings of Order α

Let S_α~*be the familiar class of normalized starlike functions of order α in the unit disk. In this paper, we establish the Fekete and Szeg? inequality for the class S_α~*, and then we generalize this result to the unit ball in a complex Banach space or on the unit polydisk in C~n.     

On Strong Sequence-Covering Compact Mappings

ＯｎＳｔｒｏｎｇＳｅｑｕｅｎｃｅ┐ＣｏｖｅｒｉｎｇＣｏｍｐａｃｔＭａｐｐｉｎｇｓＹａｎＰｅｎｇｆｅｉ（燕鹏飞）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＡｎｈｕｉＵｎｉｖｅｒｓｉｔｙ，Ｈｅｆｅｉ，２３００３９）ＡｂｓｔｒａｃｔＩｎｔｈｉｓｐａ...     

On α-Relation and Transitivity Conditions of α

The main tools in the theory of hyperstructurs are the fundamental relations. The fundamental relation on hyperring was introduced by Vougiouklis at the fourth AHA congress (1990). The fundamental relation on a hyperring is defined as the smallest equivalence relation so that the quotient would be the ring. Note that, generally, the commutativity in the ring are not assumed. In this article, we introduce a new strongly regular equivalence relation on hyperring so that the quotient is a commutative ring. Also we state the condition that is equivalent with the transitivity of this relation and finally we characterize the complete hyperring (with the fundamental relation as commutative).     

On Positive Eigenvalues and Positive Fixed Points of Multivalued Condensing Mappings

In this paper,we discuss the calculations of fixed point indexs for multivalued condensing mappings and k-set-contraction mappings,obtain some theorems on the eigenvalues and the fixed points under the suitable conditions. Our conclusions improve and generalize some well-known results.     

On Ekeland's Variational Principle for Set-Valued Mappings

In this paper,we derive a general vector Ekeland variational principle for set-valued mappings,which has a closed relation to εk~O-efficient points of set-valued optimization problems.The main result presentedin this paper is a generalization of the corresponding result in[3].     

On Generalized Jordan Triple (α, β)*-Derivations and Related Mappings

Let R be a 2-torsion free semiprime *-ring and let α, β be surjective endomorphisms of R. The aim of the paper is to show that every generalized Jordan triple (α, β)*-derivation on R is a generalized Jordan (α, β)*-derivation. This result makes it possible to prove that every generalized Jordan triple (α, β)*-derivation on a semisimple H*- algebra is a generalized Jordan (α, β)*-derivation. Finally, we prove that every Jordan triple left α*-centralizer on a 2-torsion free semiprime ring is a Jordan left α*-centralizer.     

On a Non-linear Open Mapping Theorem

Let c be a positive number.A continuous linear map F from a Banachspace X into a Banach space Y is said to be c-open if Y_1 F(X_c)where Y_1denotes the closed unit ball in Y and X_c the closed ball in X with centre at ori-gin and radius c.This is equivalent to require that the equation F_x=y has a so-lution x with ||x||≤||y|| whenever y∈Y. F is c-open for some c>0 if and only ifit is an open map.In this note we concern with a non-linear situation.Thus let     

On Ekeland＇s Variational Principle for Set-Valued Mappings

In this paper, we derive a general vector Ekeland variational principle for set-valued mappings, which has a dosed relation to εk^0 -efficient points of set-valued optimization problems. The main result presented in this paper is a generalization of the corresponding result in [3].     

On Fixed Point and Almost Fixed Point Problems of Lower Semicontinuous Type Multivalued Mappings

In the present paper, some new almost fixed point theorems and fixed point theorems for lower semicontinuous type multivalued mappings are obtained in metrizable H-spaces.     

On Weighted α-Besov Spaces and α-Bloch Spaces of Quaternion-Valued Functions

In this paper, we give the definitions of weighted α-Besov-type spaces and α-Bloch spaces of quaternion-valued functions, then we obtain characterizations of these quaternion α-Bloch spaces by quaternion α-Besov-type spaces. Relations between Q _p norms and weighted α-Besov norms are also considered. The role of ρ?^α sequences in securing non-Bloch functions is highlighted in quaternion sense.     

On α-quasi-irresolute functions

Joseph and Kwack [9] introduced the notion of (θ,s)-continuous functions in order to investigateS-closed spaces due to Thompson [32]. In [26], the present authors investigated further properties of (θ,s)-continuous functions. In this paper, we introduce a new class of functions called α-quasi-irresolute functions which is weaker than (θ,s)-continuous and improve some results established in [26].     

On α-accessible domains

The class A _ρ ^α of domains D ? ?ⁿ which are α-accessible with respect to the origin, α ∈ [0, 1], and have the property \(\rho = \mathop {\min }\limits_{\rho \in \partial D} ||p||\), where ρ ∈ (0, +∞) is a fixed number, is considered. Such domains satisfy the so-called cone condition, i.e., are conically accessible from the interior. The maximal set of points a such that all domains D ∈ A _ρ ^α are β-accessible with respect to a, 0 ≤ β ≤ α, is found, which solves a problem posed by Professor S.I. Dudov. This set is proved to be the open ball of radius ρ centered at 0 if α = 1 and β = 0 and the closed ball of radius \(\rho \sin \frac{{\left( {\alpha - \beta } \right)\pi }}{2}|\) centered at 0 otherwise. An answer to a question of Professor S. R. Nasyrov is also given. For domains D ? ? ⁿ α-accessible with respect to the origin, α ∈ (0, 1], a sharp upper bound for \(\rho = \mathop {\max }\limits_{\rho \in \partial D} ||p||/\rho = \mathop {\min }\limits_{\rho \in \partial D} ||p||\) is found.     

On α-close-to-convex functions

LetP(α) denote the class of functionsf analytic in the unit discE, withf(0)=0,f(z)≠0 (0<|z|<1) andf′(z)≠0 inE, satisfying the condition $$\int\limits_{\theta _1 }^{\theta _2 } {\operatorname{Re} } \left\{ {a\left( {1 + \frac{{zf''\left( z \right)}}{{f'\left( z \right)}}} \right) + \left( {1 - a} \right)\frac{{zf'\left( z \right)}}{{f\left( z \right)}}} \right\}d\theta > - \pi $$ whenever 0≤θ₁≤θ₂≤θ₁+2π,z=re^iθ r<1 and α is any positive real number. The functions inP(α) unify the classes of close-to-starlike (α=0) and close-to-convex (α=1) functions. We callf∈P(α) and α-close-to-convex function. In this paper we investigate certain properties of the classP(α).     

On an Open Problem on Permutation Polynomials

ＯｎａｎＯｐｅｎＰｒｏｂｌｅｍｏｎＰｅｒｍｎｔａｔｉｏｎＰｏｌｙｎｏｍｉａｌｓＺｈａｎｇＱｉｆａｎ（张起帆）（ＳｉｃｈｕａｎＵｎｉｖｅｒｓｉｔｙ，Ｃｈｅｎｇｄｕ，Ｓｉｃｈｕａｎ，６１００６４）ＣｏｍｍｕｎｉｃａｔｅｄｂｙＫｅＺｈａｏＲｅｃｅｉｖｅｄＪ...     

On the Generalized Topological Degree for Perturbed Maximal Monotone Mappings

In recent years, F.E. Browder has constructed the topological degree for nonlinear monotone mappings.In the paper[1], we have introduced the classes of mappings of type (S)_ ~* and of type quasi-(S)_ ~* and the concept of weakly-demicontinuity and we have constructed the generalized topological degree for these classes of mappings. Some important results in [2] and [3] have