Showing papers in "Filomat in 2009"
TL;DR: In this article, it was shown that quasiconformal harmonic mappings on the proper domains in R 2 are bi-Lipschitz with respect to the quasihyperbolic metric.
Abstract: We show that quasiconformal harmonic mappings on the proper domains in R 2 are bi-Lipschitz with respect to the quasihyperbolic metric.
61 citations
TL;DR: For the holomorphic and harmonic version of the Hardy-Stein identity, Zhu et al. as mentioned in this paper showed that if f is holomorphic on the unit disk D, then Hp is the p-Hardy space, which improves a result of Yamashita [Proc. Amer. Math.
Abstract: This is a collection of some known and some new facts on the holomorphic and the harmonic version of the Hardy-Stein identity as well as on their extensions to the real and the complex ball. For example, we prove that if f is holomorphic on the unit disk D, then ׀׀f ׀׀Hp = ׀f(0)׀p + ∫D׀f'(z)׀ p-2 ׀f'(z)׀2(1-׀z׀) dA(z), (†) where Hp is the p-Hardy space, which improves a result of Yamashita [Proc. Amer. Math. Soc. 75 (1979), no. 1, 69-72]. An extension of (†) to the unit ball of Cn improves results of Beatrous an Burbea [Kodai Math. J. 8 (1985), 36-51], and of Stoll [J. London Math. Soc. (2) 48 (1993), no. 1, 126-136]. We also prove the analogous result for the harmonic Hardy spaces. The proofs of known results are shorter and more elementary then the existing ones, see Zhu [Spaces of holomorphic functions in the unit ball, Graduate Texts in Mathematics, vol. 226, Springer-Verlag, New York, 2005, Ch. IV]. We correct some constants in that book and in a paper of Jevtic and Pavlovic [Publ. Inst. Math. (Beograd) (N.S.) 64(78) (1998), 36-52].
30 citations
TL;DR: In this article, the Wiener-type invariants of some graph operations are computed and the formulae for reciprocal Wiener index, Harary index, hyperWiener index and Tratch-Stankevich-Zefirov index are calculated.
Abstract: Let d(G, k) be the number of pairs of vertices of a graph G that are at distance k, λ ar eal number, andWλ(G )= � k≥1 d(G, k)k λ . Wλ(G) is called the Wiener-type invariant of G associated to real number λ. In this paper, the Wiener-type invariants of some graph operations are computed. As immediate consequences, the formulae for reciprocal Wiener index, Harary index, hyperWiener index and Tratch-Stankevich-Zefirov index are calculated. Some upper and lower bounds are also presented.
25 citations
TL;DR: In this paper, the achromatic number of central graph, middle graph and total graph of star graph has been found, denoted by C(K1,n), M(K 1,n) and T(K 2,n) respectively.
Abstract: In this paper, we find the achromatic number of central graph, middle graph and total graph of star graph, denoted by C(K1,n), M(K1,n) and T(K1,n) respectively.
22 citations
TL;DR: In this article, the authors give sufficient conditions for general two integral operators to be univalent in the open unit disk, and they give a proof of the existence of such conditions.
Abstract: In this paper, we give some sufficient conditions for general two integral operators to be univalent in the open unit disk.
20 citations
TL;DR: In this paper, Jensen's type inequalities for two differentiable functions of selfadjoint boolean operators in Hilbert spaces under suitable assumptions for the involved boolean operators are given and applications for particular cases of interest are also provided.
Abstract: Some Jensen’s type inequalities for twice differentiable functions of selfadjoint
operators in Hilbert spaces under suitable assumptions for the involved
operators are given. Applications for particular cases of interest are also provided.
15 citations
TL;DR: Some inequalities for convex functions of selfadjoint operators in Hilbert spaces under suitable assumptions for the involved operators are given in this paper, where applications for particular cases of interest are also provided.
Abstract: Some inequalities for convex functions of selfadjoint operators in Hilbert spaces under suitable assumptions for the involved operators are given. Applications for particular cases of interest are also provided.
15 citations
TL;DR: In this paper, an order relation on uniform spaces was introduced and utilized to prove fixed point theorems for single and multi-valued mappings in ordered uniform spaces, where the relation was used to prove a fixed point theorem for fixed point mappings.
Abstract: In this paper, we introduce an order relation on uniform spaces and utilize this relation to prove some fixed point theorems for single and multi valued mappings in ordered uniform spaces.
14 citations
TL;DR: In this paper, it was shown that for any n 2 N, there exists a set of n graphs with O(n) vertices having equal oriented incidence energy, where n is the number of vertices in the graph.
Abstract: Let G be a simple graph with n vertices and m edges. Let edges of G be given an arbitrary orientation, and let Q be the vertex-edge incidence matrix of such oriented graph. The oriented incidence energy of G is then the sum of singular values of Q. We show that for any n 2 N, there exists a set of n graphs with O(n) vertices having equal oriented incidence energy.
14 citations
TL;DR: In this article, it was shown that every connected Cayley graph of an abelian group of odd order which is not a cycle is 1 1 -extendable, and this result was then used to classify 2-extendably connected Cayleys of generalized dihedral groups.
Abstract: A connected graph i of even order is n-extendable, if it contains a matching of size n and if every such matching is contained in a perfect matching of i. Furthermore, a connected graph i of odd order is n 1 -extendable, if for every vertex v of i the graph i i v is n-extendable. It is proved that every connected Cayley graph of an abelian group of odd order which is not a cycle is 1 1 -extendable. This result is then used to classify 2-extendable connected Cayley graphs of generalized dihedral groups.
10 citations
TL;DR: In this paper, the authors studied several classes of polynomials, which are related to the Chebyshev, Morgan-Voyce, Horadam and Jacobsthal classes.
Abstract: We study several classes of polynomials, which are related to the Chebyshev, Morgan-Voyce, Horadam and Jacobsthal polynomials. Thus, we unify some of well-known results.
TL;DR: In this paper, the mixed and componentwise condition numbers for the weighted Moore-Penrose inverse of a matrix A, as well as for the solution and residue of a weighted linear least squares problem were given.
Abstract: Condition numbers play an important role in numerical analysis. Classical condition numbers are normwise: they measure both input perturbations and output errors with norms. To take into account the relative scaling of data components or a possible sparseness, componentwise condition numbers have been increasingly considered. In this paper, we give explicit expressions for the mixed and componentwise condition numbers for the weighted Moore-Penrose inverse of a matrix A, as well as for the solution and residue of a weighted linear least squares problem kW 1 2(Axib)k2 = minv2Rn kW 1 2(Avib)k2, where the matrix A with full column rank.
TL;DR: For a class of moduli functions ω(δ) = δα (0 < α ≤ 1), this article showed that for any moduli function ω (δ), 0 ≤ δ ≤ 2, the property πφ(ξ) - φ (η) ׀≤ ωξ - η׀, ξ, ηЄ Sn-1 implies the corresponding property u(x)-u(y) δ, x, y Є Bn; for u =
Abstract: We show that, for a class of moduli functions ω(δ), 0 ≤ δ ≤ 2, the property ׀φ(ξ) - φ(η) ׀≤ ω (׀ξ - η׀), ξ, ηЄ Sn-1 implies the corresponding property ׀u(x)-u(y) ׀≤ Cω(׀x-y׀) x, y Є Bn; for u = P[φ], provided u is a quasiregular mapping. Our class of moduli functions includes φ(δ) = δα (0 < α ≤ 1), so our result generalizes earlier results on Holder continuity (see [1]) and Lipschitz continuity (see [2]).
TL;DR: In this article, the hypercyclic and chaotic properties of C-distribution semigroups and global integrated C-semigroups were analyzed and the results were incorporated in the study of the dynamics of the backwards L p heat semigroup (p > 2) on symmetric spaces of non-compact type.
Abstract: We introduce and analyze hypercyclic and chaotic properties of C-distribution semigroups and global integrated C-semigroups. The obtained results are incorporated in the study of the dynamics of the backwards L p heat semigroups (p > 2) on symmetric spaces of non-compact type.
TL;DR: In this article, two sequences of polynomials, denoted by {Un(k),m} and {Vn(k,m}, where k, m, n are nonnegative integers, and m ≥ 2.
Abstract: In this note we consider two sequences of polynomials, which are denoted by {Un(k),m} and {Vn(k),m}, where k, m, n are nonnegative integers, and m ≥ 2. These sequences represent generalizations of the well-known Fibonacci and Lucas polynomials. For example, if m = 2, then we obtain exactly the Fibonacci and Lucas polynomials. If m = 3, then polynomials Un(k),3 and Vn (k),3 were considered in papers (G. B. Đorđevic, Fibonacci Quart. 39.2(2001), and G. B. Đordjevic, Fibonacci Quart. 43.4(2005)).
TL;DR: This work studies identities for the antisymmetriy with respect to two indices, the cyclic symmetry, the symmetry with respect of pairs of indices for curvature tensors in the generalized Finsler space GFN.
Abstract: In the some previous works we have obtained several curvature tensors in the generalized Finsler space GFN (the space with non-symmetric basic tensor and non-symmetric connection in Rund’s sence). In this work we study identities for the mentioned tensors (the antisymmetriy with respect of two indices, the cyclic symmetry, the symmetry with respect of pairs of indices).
TL;DR: In this paper, the authors studied the existence and uniqueness of solutions for a general stochastic integrodierentia l equation of the Ito type, by using the concept of non-linear bounded random integral contractors, which includes the Lipschitz condition as a special case.
Abstract: The aim of this paper is to study the existence and uniqueness of solutions for a general stochastic integrodierentia l equation of the Ito type, by using the concept of non-linear bounded random integral contractors, which includes the Lipschitz condition as a special case The method applied in this consideration follows partially the basic ideas of the contractor theory introduced earlier by Altman [1, 2] and Kuo [6] It is also shown that the Lipschitz condition and the condition based on a bounded random integral contractor for the coecients of the considered equation, in general, cannot be compared
TL;DR: Some common fixed point theorems for any even number of compatible mappings in complete L-fuzzy metric spaces are proved.
Abstract: In this paper, we prove some common fixed point theorems for any even number of compatible mappings in complete L-fuzzy metric spaces. Our main results extend and generalize some known results in fuzzy metric spaces, intuitionistic metric spaces and L-fuzzy metric spaces.
TL;DR: In this article, the authors introduced two new classes of complex valued harmonic multivalent functions of the form f = h+g, where h and g are analytic in the unit disk ¢ = fz : jzj < 1g and f(z) satisfying the condition Re (1 i ) D v v f
Abstract: In this paper we have introduced two new classes HRp(fl;‚;k;v);HRp(fl;‚;k;v) of complex valued harmonic multivalent functions of the form f = h+g, where h and g are analytic in the unit disk ¢ = fz : jzj < 1g and f(z) satisfying the condition Re (1 i ‚) D v f
TL;DR: In this paper, CurveBend, a tool for graphical presentation of non-rigid curves is presented, and the influence of infinitesimal bending field on curves is discussed and visualized by the tool.
Abstract: An infinitesimal bending of the curve at E 3 is considered and the infinitesimal bending field is determined and discussed. CurveBend, tool for graphical presentation of non rigid curves is presented. Influence of infinitesimal bending field on curves is discussed and visualized by the tool.
TL;DR: In this paper, the authors introduced the concept of normalized duality mapping on normed linear spaces and normed algebra and extended the usual definitions of the numerical range from one operator to two operators.
Abstract: Introducing the concept of the normalized duality mapping on normed linear space and normed algebra, we extend the usual definitions of the numerical range from one operator to two operators. In this note we study the convexity of these types of numerical ranges in normed algebras and linear spaces. We establish some Birkho-James orthogonality results in terms of the algebra numerical range V (T)A which generalize those given by J.P. William and J.P. Stamplfli. Finally, we give a positive answer of the Mathieu’s question.
TL;DR: In this paper graphical presentation some of the constant mean curvature surfaces (CMC surfaces) obtained using Mathematica computer program are given.
Abstract: In this paper graphical presentation some of the constant mean curvature surfaces (CMC surfaces) is given. This work is an extension of the results [3]. Interesting shapes and complicate structures of CMC surfaces obtained using Mathematica computer program are given.
TL;DR: An algorithm for unconstrained optimization based on the reduction of the modified Newton method with line search into a gradient descent method based on approximation of Hessian by a diagonal matrix is introduced.
Abstract: We introduced an algorithm for unconstrained optimization based on the reduction of the modified Newton method with line search into a gradient descent method. Main idea used in the algorithm construction is approximation of Hessian by a diagonal matrix. The step length calculation algorithm is based on the Taylor's development in two successive iterative points and the backtracking line search procedure.
TL;DR: In this article, the authors present some possibilities how dieren t areas of visual mathematics (symmetry in art and science, isometric symmetry groups, similarity symmetry, modularity, antisymmetry, tessellations) can be used as a tool of visual communication.
Abstract: In this paper we present some possibilities how dieren t areas of visual mathematics (symmetry in art and science, isometric symmetry groups, similarity symmetry, modularity, antisymmetry, tessellations, theory of proportions, theory of visual perception, perspective, anamorphoses, visual illusions, ethnomathematics, mirror curves, op-tiles, fractal structures) can be used as a tool of visual communication. The paper also contains (in parts) a description of the course "Visual Mathematics and Design" organized at the Faculty of Information Technologies (Belgrade).
TL;DR: In this article, the existence and uniqueness of the solution for a system of variational inclusions with (A;·)-monotone mappings was examined. But the solution was not shown to be unique.
Abstract: This paper deals with existence and uniqueness of the solution for a system of variational inclusions with (A;·)-monotone mappings.
TL;DR: In this article, a generalized Kahlerian space GK 2 N of the second kind is defined, as a GRN with almost complex structure F h i, that is covariantly constant with respect to the covariant derivative (equation (2.3)).
Abstract: Starting from the definition of generalized Riemannian space (GRN) (1), in which a non-symmetric basic tensor gij is introduced, in the present paper a generalized Kahlerian space GK 2 N of the second kind is defined, as a GRN with almost complex structure F h i , that is covariantly constant with respect to the second kind of covariant derivative (equation (2.3)). Several theorems are proved. These theorems are generalizations of the corresponding theorems relating to KN. The relations between F h i and four curvature tensors from GRN are obtained.
TL;DR: In this paper, the authors studied the boundedness and compactness of integral type and composition operators from general weighted Bloch space to F(p, q, s) space, where α > 0.
Abstract: Products of integral-type and composition operators has been recently introduced by Li and Stevic and studied in a series of their papers. In this note we study the boundedness and compactness of these products from generally weighted Bloch space to F(p; q; s) space, where 0 -2; α > 0.
TL;DR: By means of Ruscheweyh derivative operator, this paper introduced and investigated two new subclasses of p-valent analytic functions, and various results obtained here for each of these function class include coecient bounds and distortion inequalities.
Abstract: By means of Ruscheweyh derivative operator , we introduced and investigated two new subclasses of p-valent analytic functionsThe various results obtained here for each of these function class include coecient bounds and distortion inequalities, associated inclusion relations for the (n;µ)-neighborhoods of subclasses of analytic and multivalent functions with negative coecients, which are defined by means of non-homogenous dierential equation
TL;DR: The length of the cycle of unicyclic simple graphs with seven loaded vertices was shown to be at most 10 in this article, and all such graphs with the length of cycle 10, 9 and 8 were found.
Abstract: A simple graph is reflexive if the second largest eigenvalue of its (0, 1)- adjacency matrix does not exceed 2. A vertex of the cycle of unicyclic simple graph is said to be loaded if its degree is greater than 2. In this paper we establish that the length of the cycle of unicyclic reflexive graph with seven loaded vertices is at most 10 and find all such graphs with the length of the cycle 10, 9 and 8.
TL;DR: In this article, a package for teaching the graphical solution of two-dimensional and three-dimensional linear programming problems is developed, where the computer algebra system in MATHEMATICA and its graphical capabilities can be used in optimization.
Abstract: We show how the computer algebra system in MATHEMATICA and its graphical capabilities can be used in optimization. A package for teaching the graphical solution of two-dimensional and three-dimensional linear programming problem is developed.