Inclusion properties for certain classes of meromorphic functions associated with the Choi–Saigo–Srivastava operator

The purpose of the present paper is to introduce several new classes of meromorphic functions defined by using a meromorphic analogue of the Choi–Saigo–Srivastava operator for analytic functions and investigate various inclusion properties of these classes. Some interesting applications involving these and other classes of integral operators are also considered.     

Algebraic and topological closure conditions for classes of pseudo-Boolean functions

We examine classes of real-valued functions of 0-1 variables closed under algebraic operations as well as topological convergence, and having a certain local characteristic (requiring that any function not in the class should have a k-variable minor not belonging to this class). It is shown that for k=2, the only 4 maximal classes with these properties are those of submodular, supermodular, monotone increasing and monotone decreasing functions. All the 13 locally defined closed classes are determined and shown to be intersections of the 4 maximal ones. All maximal classes for k≥3 are determined and characterized by the sign of higher order derivatives of the functions in the class.     

Bounded iteration and unary functions

The set of unary functions of complexity classes defined by using bounded primitive recursion is inductively characterized by means of bounded iteration. Elementary unary functions, linear space computable unary functions and polynomial space computable unary functions are then inductively characterized using only composition and bounded iteration. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

用S\v{a}l\v{a}gean算子定义的某些新多叶亚纯函数类的优化性质

In the present paper, we investigate the majorization property for certain new class of multivalent meromorphic analytic functions defined by Salagean operator. Moreover, we point out some new and interesting applications of our main result to the other classes of multivalent meromorphic functions.     

某些一致倒结构的亚纯多叶函数类的系数估计

利用从属关系定义了某些新的一致倒结构的星象,凸象,近于凸和拟凸函数类,并得到了相应函数类的系数估计.其结果改进并推广了一些已有结论.     

Salagean算子定义的双单叶函数子类的系数估计

In this paper, a new subclass N_Σ~(h,p)(m, λ, μ) of analytic and bi-univalent functions in the open unit disk U is defined by salagean operator. We obtain coefficients bounds |a_2| and |a_3| for functions of the class. Moreover, we verify Brannan and Clunie's conjecture |a_2| ≤2~(1/2)for some of our classes. The results in this paper extend many results recently researched by many authors.     

由从属关系刻画的多叶调和函数新子类

本文引入了由广义Dziok-Srivastava算子定义的多叶调和函数新子类, 给出了该类中函数的系数不等式, 偏差估计和极值点等性质.     

Minimal convex majorants of functions and Demyanov–Rubinov exhaustive super(sub)differentials

ABSTRACT

The primary goal of the paper is to establish characteristic properties of (extended) real-valued functions defined on normed vector spaces that admit the representation as the lower envelope (the pointwise infimum) of their minimal (with respect of the pointwise ordering) convex majorants. The results presented in the paper generalize and extend the well-known Demyanov-Rubinov characterization of upper semicontinuous positively homogeneous functions as the lower envelope of exhaustive families of continuous sublinear functions to larger classes of (not necessarily positively homogeneous) functions defined on arbitrary normed spaces. As applications of the above results, we introduce, for nonsmooth functions, a new notion of the Demyanov-Rubinov exhaustive subdifferential at a given point, and show that it generalizes a number of known notions of subdifferentiability, in particular, the Fenchel-Moreau subdifferential of convex functions, the Dini-Hadamard (directional) subdifferential of directionally differentiable functions, and the Φ-subdifferential in the sense of the abstract convexity theory. Some applications of Demyanov-Rubinov exhaustive subdifferentials to extremal problems are considered.     

Ultra‐differentiable classes and intersection theorems

The aim of the paper is to study the relation between ultra‐differentiable classes of functions defined in terms of estimates on derivatives on one hand and in terms of growth properties of Fourier transforms of suitably localized functions in the class on the other hand. We establish this relation for the ultra‐differentiable classes introduced in 6 , 16 , and show that the classes of 6 , 16 , can be regarded as inhomogeneous Gevrey classes in the sense of 22 . We also discuss a number of properties of the weight functions used to define the respective classes and of their Young conjugates.     

A UNIFIED CLASS OF ANALYTIC FUNCTIONS WITH FIXED ARGUMENT OF COEFFICIENTS

In this paper we introduce new classes of analytic functions with fixed argument of coefficients defined by subordination. Coefficient estimates, distortion theorems, integral means inequalities, and the radii of convexity and starlikeness are investigated. Convolution properties are also pointed out.     

Optimal Recovery of Isotropic Classes of rth Differentiable Functions on ℝ d

We consider the optimal recovery problem of isotropic classes of r-th differentiable multivariate functions defined on ? ^d , and obtain some asymptotically optimal results. It turns out that this optimal recovery problem is intimately related to the optimal covering problem of ? ^d by equal balls in discrete geometry.     

强预拟不变凸函数与强拟不变凸函数

本文提出了两类新的广义凸函数—强预拟不变凸函数与强拟不变凸函数.讨论了强预拟不变凸函数与强拟不变凸函数间的关系,强拟不变凸函数与强伪不变凸函数间的关系.研究了强预拟不变凸函数在多目标优化中的应用.     

由广义微分算子定义的某些解析函数类的优化性质

本文首先引入了由广义微分算子定义的某些$p$叶解析函数新子类$S_{p,q,\lambda}^{m,j,l}[A,B;\gamma]$ 和 $H_{p,q,\lambda}^{m,j,l}(\alpha,\beta)$, 然后研究了该子类的优化性质, 所得结果推广了某些已知结论.     

Characterizing Translations on Groups by Cosets of Their Subgroups

On a group, constant functions and left translations by group elements map left cosets into left cosets for every subgroup. We determine classes of groups for which this property of preserving cosets characterizes constants and translations, e.g., finite non-abelian groups that are perfect, partitioned, primitive, or generated by elements of prime order p. For certain classes of groups we construct other coset-preserving functions, in particular, power endomorphisms and functions defined in terms of the subgroup lattice.     

Generalized Tricomi and Hermite-Tricomi functions

General classes of Tricomi and Hermite-Tricomi functions are introduced by exploiting properties of an iterated isomorphism, related to the so-called Laguerre-type exponentials, and we mainly consider the properties of the general classes of 3-variable 2-index Tricomi functions and 2-index 4-variable 1-parameter Hermite-Tricomi functions.     

Normality and boundary behaviour of arbitrary and meromorphic functions along simple curves and applications

In this paper, we establish some theorems giving necessary and sufficient conditions for an arbitrary function defined in the unit disc of the complex plane to have boundary values along classes of an equivalence relation over simple curves. Our results generalize the well-known theorems on asymptotic and angular boundary behaviours of meromorphic functions (Lindelölf-, Lehto–Virtanen- and Seidel–Walsh-type theorems). The obtained results are applied to the study of boundary behaviour of meromorphic functions along curves using P-sequences, as well as in the proof of the uniqueness theorem similar to ?aginjan’s one. The constructed examples of functions show that the results cannot be improved.     

On the fractional chromatic number of monotone self-dual Boolean functions

We compute the exact fractional chromatic number for several classes of monotone self-dual Boolean functions. We characterize monotone self-dual Boolean functions in terms of the optimal value of an LP relaxation of a suitable strengthening of the standard IP formulation for the chromatic number. We also show that determining the self-duality of a monotone Boolean function is equivalent to determining the feasibility of a certain point in a polytope defined implicitly.     

Polyanalytic Hardy decomposition of higher order Lipschitz functions

This paper is concerned with the problem of decomposing a higher order Lipschitz function on a closed Jordan curve Γ into a sum of two polyanalytic functions in each open domain defined by Γ. Our basic tools are the Hardy projections related to a singular integral operator arising in polyanalytic function theory, which, as it is proved here, represents an involution operator on the higher order Lipschitz classes. Our result generalizes the classical Hardy decomposition of Hölder continuous functions on the boundary of a domain.     

Pseudocontinuity in Optimization and Nonzero-Sum Games

We enlarge the class of sufficient conditions which guarantee, on the one hand, the sequential closedness of set-valued functions defined by minimum points and by social Nash equilibria and, on the other hand, the existence of solutions for MinSup problems, using new classes of functions, called sequentially lower pseudocontinuous and sequentially upper pseudocontinuous functions. Properties and characterizations of such classes are investigated.     

由卷积和从属关系刻画的单叶调和函数某些子类

Let SH be the class of functions f = h + ˉg that are harmonic univalent and sensepreserving in the open unit disk U = {z ∈ C : |z| 1} for which f(0) = f′(0)-1 = 0. In the present paper, we introduce some new subclasses of SH consisting of univalent and sensepreserving functions defined by convolution and subordination. Sufficient coefficient conditions,distortion bounds, extreme points and convolution properties for functions of these classes are obtained. Also, we discuss the radii of starlikeness and convexity.