scispace - formally typeset
Search or ask a question

Showing papers in "Filomat in 2012"


Journal ArticleDOI
01 Jan 2012-Filomat
TL;DR: The notion of strong intuitionistic fuzzy graphs is introduced and some of their properties are investigated and some propositions of self complementary and self weak complementary strong intuitionists fuzzy graphs are discussed.
Abstract: We introduce the notion of strong intuitionistic fuzzy graphs and investigate some of their properties. We discuss some propositions of self complementary and self weak complementary strong intuitionistic fuzzy graphs. We introduce the concept of intuitionistic fuzzy line graphs.

200 citations


Journal ArticleDOI
01 Jan 2012-Filomat
TL;DR: In this paper, the authors define a new version of Zagreb indices as M*1 (G) = vE(G) [G(u)+ Gs()
Abstract: The Zagreb indices have been introduced by Gutman and Trinajstic as M1(G) = V(G)(dG)())2 and M2(G) = vE(G) dG(u)dG(), where dG(u) denotes the degree of vertex u. We now define a new version of Zagreb indices as M*1 (G) = vE(G) [G(u)+ G()] and M*2(G)= vE(G) G(u)G(), where G(u) is the largest distance between u and any other vertex  of G. The goal of this paper is to further the study of these new topological index.

101 citations


Journal ArticleDOI
01 Jan 2012-Filomat
TL;DR: The atom-bond connectivity index (ABC) as mentioned in this paper is a vertex-degree based graph invariant index, put forward in the 1990s, having applications in chemistry and has been applied in many applications.
Abstract: The atom-bond connectivity index (ABC) is a vertex-degree based graph invariant, put forward in the 1990s, having applications in chemistry. Let G = (V,E) be a graph, di the degree of its vertex i, and ij the edge connecting the vertices i and j. Then ABC = ∑ijE √(di+dj−2)/(didj). Upper bounds and Nordhaus-Gaddum type results for ABC are established.

61 citations


Journal ArticleDOI
01 Jan 2012-Filomat
TL;DR: In this paper, the power graph P(G) of a group G is defined as the graph whose vertex set is the group of vertices of two elements and two elements are adjacent if one is a power of the other.
Abstract: The power graph P(G) of a group G is the graph whose vertex set is the group elements and two elements are adjacent if one is a power of the other. In this paper, we consider some graph theoretical properties of a power graph P(G) that can be related to its group theoretical properties. As consequences of our results, simple proofs for some earlier results are presented.

58 citations


Journal ArticleDOI
01 Jan 2012-Filomat
TL;DR: In this article, a coupled integrable dispersionless system (CIDS) is studied and symmetry reductions and exact solutions with the aid of simplest equation method are obtained, and conservation laws of the CIDS are also derived using the multiplier (and homotopy) approach.
Abstract: In this paper we study the coupled integrable dispersionless system (CIDS), which arises in the analysis of several problems in applied mathematics and physics. Lie symmetry analysis is performed on CIDS and symmetry reductions and exact solutions with the aid of simplest equation method are obtained. In addition, the conservation laws of the CIDS are also derived using the multiplier (and homotopy) approach.

49 citations


Journal ArticleDOI
01 Jan 2012-Filomat
TL;DR: Several summation formulae for finite and infinite series involving the classical harmonic numbers are presented in this paper, where the summation is based on the sum of the number of harmonic numbers in the series.
Abstract: Several summation formulae for finite and infinite series involving the classical harmonic numbers are presented.

46 citations


Journal ArticleDOI
01 Jan 2012-Filomat
TL;DR: In this paper, the atom-bond connectivity (ABC) index of a graph G is the sum of √ d(u)+d(v)−2d(u)d(V) over all edges uv of G, where uv is the degree of vertexuinG.
Abstract: The atom-bond connectivity (ABC) index of a graph G is the sum of √ d(u)+d(v)−2 d(u)d(v) over all edges uv ofG, whered(u) is the degree of vertexuinG. We characterize the extremal trees withfixed degree sequence that maximize and minimize the ABC index, respectively. We also provide algorithms to construct such trees.

45 citations


Journal ArticleDOI
01 Jan 2012-Filomat
TL;DR: For functions f(z) = z + a2z 2 + · · · with fixed second coeffcient a2, sharp radius of starlikeness of order β for several subclasses of functions are obtained as discussed by the authors.
Abstract: Several radii problems are considered for functions f(z) = z + a2z 2 + · · · with fixed second coeffcient a2. For 0 ≤ β < 1, sharp radius of starlikeness of order β for several subclasses of functions are obtained. Theseincludetheclassofparabolicstarlikefunctions, theclassofJanowskistarlikefunctions, and the class of strongly starlike functions. Sharp radius of convexity of order β for uniformly convex functions, and sharp radius of strong-starlikeness of order γ for starlike functions associated with the lemniscate of Bernoulli are also obtained as special cases.

44 citations


Journal ArticleDOI
01 Jan 2012-Filomat
TL;DR: Some boundedness properties in fuzzy metric spaces are introduced and studied, related to the classical covering properties of Menger, Hurewicz and Rothberger.
Abstract: We introduce and study some boundedness properties in fuzzy metric spaces. These properties are related to the classical covering properties of Menger, Hurewicz and Rothberger.

43 citations


Journal ArticleDOI
01 Jan 2012-Filomat
TL;DR: In this article, the authors prove a common fixed point theorem for two self-mappings satisfying certain conditions over the class of partial metric spaces, and extend some well-known fixed point theorems in the literature on this topic.
Abstract: In this paper, we prove a common fixed point theorem for two self-mappings satisfying certain conditions over the class of partial metric spaces. In particular, the main theorem of this manuscript extends some well-known fixed point theorems in the literature on this topic.

41 citations


Journal ArticleDOI
01 Jan 2012-Filomat
TL;DR: In this article, the first and second Zagreb indices of cacti with k pendant vertices were investigated and sharp bounds for M1-, M2-values of n-vertex cactis with k-pendant nodes were obtained.
Abstract: Fora(molecular)graph, thefirstZagrebindexM1 isequaltothesumofsquaresofitsvertexdegrees, and the second Zagreb index M2 is equal to the sum of products of degrees of pairs of adjacent vertices. A connected graph G is a cactus if any two of its cycles have at most one common vertex. In this paper, we investigate the first and the second Zagreb indices of cacti with k pendant vertices. We determine sharp bounds for M1-, M2-values of n-vertex cacti with k pendant vertices. As a consequence, we determine the n-vertex cacti with maximal Zagreb indices and we also determine the cactus with a perfect matching having maximal Zagreb indices.

Journal ArticleDOI
01 Jan 2012-Filomat
TL;DR: In this article, the existence and uniqueness of fixed points of a class of cyclic operators defined on a closed subset of a Banach space is discussed and fixed point theorems for some contractions from this class are introduced and illustrative examples are given.
Abstract: In this manuscript, the existence and uniqueness of fixed points of a class of cyclic operators defined on a closed subset of a Banach space is discussed. Fixed point theorems for some contractions from this class are introduced and illustrative examples are given.

Journal ArticleDOI
01 Jan 2012-Filomat
TL;DR: In this article, the Szeged, vertex PI and the first and second Zagreb indices of the corona product of graphs are computed and shown to be the same as in this paper.
Abstract: The corona product GoH of two graphs G and H is defined as the graph obtained by taking one copy of G and |V(G)| copies of H and joining the i-th vertex of G to every vertex in the i−th copy of H. In this paper, the Szeged, vertex PI and the first and second Zagreb indices of corona product of graphs are computed.

Journal ArticleDOI
Xiangling Zhu1
01 Jan 2012-Filomat
TL;DR: In this paper, new criteria for the boundedness and compactness of generalized weighted composition operators from Bloch spaces into Bers-type spaces are given, where the compactness criterion is based on the weighted composition operator's compactness.
Abstract: New criteria for the boundedness and the compactness of the generalized weighted composition operators from Bloch spaces into Bers-type spaces are given in this paper.

Journal ArticleDOI
01 Jan 2012-Filomat
TL;DR: In this paper, the notion of ∆ n -ideal convergence was introduced, and the concept of ideal Cauchy sequences in random 2-normed spaces was studied.
Abstract: An ideal I is a family of subsets of positive integers N which is closed under taking finite unions andsubsetsofitselements. In(17),Kostyrkoet. alintroducedtheconceptofidealconvergenceasasequence (xk) of real numbers is said to be I-convergent to a real number l, if for each e > 0 the set fk 2 N : jxk lj eg belongs to I. In (28), Mursaleen and Alotaibi introduced the concept of I-convergence of sequences in random 2-normed spaces. In this paper, we define and study the notion of ∆ n -ideal convergence and ∆ n -ideal Cauchy sequences in random 2-normed spaces, and prove some interesting theorems.

Journal ArticleDOI
01 Jan 2012-Filomat
TL;DR: In this article, the first and second Zagreb coindices of a nontrivial graph G are defined, respectively, as M1(G) = ∑ uv
Abstract: For a nontrivial graph G, its first and second Zagreb coindices are defined, respectively, as M1(G) = ∑ uv

Journal ArticleDOI
01 Jan 2012-Filomat
TL;DR: In this article, the main purpose of the paper is to display the main structural properties of the hypercyclic and chaotic integrated C-cosine functions and provide several examples which justify their abstract theoretical approach.
Abstract: The main purpose of the paper is to display the main structural properties of hypercyclic and chaotic integrated C-cosine functions. The notions of hypercyclicity, mixing and chaoticity of an α-times integrated C-cosine function (α≥0) are defined by using distributional techniques. We provide several examples which justify our abstract theoretical approach.[Projekat Ministarstva nauke Republike Srbije, br. 144016]

Journal ArticleDOI
01 Jan 2012-Filomat
TL;DR: Algorithms for computing the greatest solutions to weakly linear systems in the state reduction of fuzzy automata, the study of simulation, bisimulation and equivalence of fuzzy Automata, and in the social network analysis are presented.
Abstract: Weakly linear systems of fuzzy relation inequalities and equations have recently emerged from research in the theory of fuzzy automata. From the general aspect of the theory of fuzzy relation equations and inequalities homogeneous and heterogeneousweakly linear systems have been discussedin two recent papers. Here we give a brief overview of the main results from these two papers, as well as from a series of papers on applications of weakly linear systems in the state reduction of fuzzy automata, the study of simulation, bisimulation and equivalence of fuzzy automata, and in the social network analysis. Especially, we present algorithms for computing the greatest solutions to weakly linear systems.

Journal ArticleDOI
01 Jan 2012-Filomat
TL;DR: In this article, it was shown that if (1,V, λ) is a Ricci soliton where V is collinear with the characteristic vector field ξ, then V is a constant multiple of ξ and the manifold is of constant scalar curvature provided α, β =constant.
Abstract: The object of the present paper is to study 3-dimensional trans-Sasakian manifolds admitting Ricci solitons and gradient Ricci solitons. We prove that if (1,V, λ) is a Ricci soliton where V is collinear with the characteristic vector field ξ, then V is a constant multiple of ξ and the manifold is of constant scalar curvature provided α, β =constant. Next we prove that in a 3-dimensional trans-Sasakian manifold with constant scalar curvature if 1 is a gradient Ricci soliton, then the manifold is either a β-Kenmotsu manifold or an Einstein manifold. As a consequence of this result we obtain several corollaries.

Journal ArticleDOI
01 Jan 2012-Filomat
TL;DR: In this article, Bae and Suzuki type generalizations of Caristi's fixed point theorem on partial metric space were given, and they were shown to be equivalent to the Bae-Suzuki type generalization.
Abstract: In the persent paper, we give Bae and Suzuki type generalizations of Caristi’s fixed point theorem on partial metric space.

Journal ArticleDOI
01 Nov 2012-Filomat
TL;DR: In this paper, the concepts of statistically convergent and statistically Cauchy double sequences in the framework of fuzzy normed spaces were studied and the relationship between them was discussed. And the statistical limit point and statistical cluster point for double sequences were introduced.
Abstract: In this paper, we study the concepts of statistically convergent and statistically Cauchy double sequences in the framework of fuzzy normed spaces which provide better tool to study a more general class of sequences. We also introduce here statistical limit point and statistical cluster point for double sequences in this framework and discuss the relationship between them.

Journal ArticleDOI
01 Jan 2012-Filomat
TL;DR: This work gives two examples on the geometric series of fuzzy numbers and by using the four different cases of u n of n th power of a fuzzy number u, it interest in the convergence of a power series of fuzzies with fuzzy coefficients.
Abstract: Following Talo and Basar (Determination of the duals of classical sets of sequences of fuzzy numbers and related matrix transformations, Comput. Math. Appl. 58 (2009) 717-733), we essentially deal with the power series of fuzzy numbers. We give two examples on the geometric series of fuzzy numbers and by using the four different cases of u n of n th power of a fuzzy number u, we interest in the convergence of a power series of fuzzy numbers. Finally, we introduce the concept of a power series of fuzzy numbers with fuzzy coefficients.

Journal ArticleDOI
01 Jan 2012-Filomat
TL;DR: In this article, the authors investigate fundamental properties of I-exhaustiveness and I-convergence of real-valued function sequences, and establish new versions of Ascoli and Helly theorems, giving also applications to measure theory.
Abstract: We investigate fundamental properties of I-exhaustiveness and I-convergence of real-valued function sequences, giving some characterizations. Furthermore, we establish new versions of Ascoli and Helly theorems, giving also applications to measure theory. Finally, we pose an open problem.

Journal ArticleDOI
01 Jan 2012-Filomat
TL;DR: In this article, a new homotopy thinning suitable for the study of Khalimsky topological spaces was developed, which can support the discrete geometric transformation and a homotopic thinning was developed suitable for studying the topological space.
Abstract: Aiming at the study of the compression of Khalimsky topological spaces which is an interesting field in digital geometry and computer science, the present paper develops a new homotopy thinning suitable for the work. Since Khalimsky continuity of maps between Khalimsky topological spaces has some limitations of performing a discrete geometric transformation, the paper uses another continuity (see Definition 3.4) that can support the discrete geometric transformation and a homotopic thinning suitable for studying Khalimsky topological spaces. By using this homotopy, we can develop a new homotopic thinning for compressing the spaces and can write an algorithm for compressing 2D Khalimsky topological spaces.

Journal ArticleDOI
30 Sep 2012-Filomat
TL;DR: A direct method for removing uniform linear motion blur from images based on a straightforward construction of the Moore-Penrose inverse of the blurring matrix for a given mathematical model is presented.
Abstract: We present a direct method for removing uniform linear motion blur from images. The method is based on a straightforward construction of the Moore-Penrose inverse of the blurring matrix for a given mathematical model. The computational load of the method is decreased significantly with respect to other competitive methods, while the resolution of the restored images remains at a very high level. The method is implemented in the programming package MATLAB and respective numerical examples are presented.

Journal ArticleDOI
01 Jan 2012-Filomat
TL;DR: In this paper, the conditions of the theorem are not stringent in the sense that a simple moving average sequence serves as an example, and the conditions are not assumed to be independent.
Abstract: Inthisnote,weproveacentrallimittheoremforthesumofarandomnumberNn ofm-dependent randomvariables. ThesequenceNn andthetermsinthesumarenotassumedtobeindependent. Moreover, the conditions of the theorem are not stringent in the sense that a simple moving average sequence serves as an example.

Journal ArticleDOI
01 Jan 2012-Filomat
TL;DR: In this article, the authors define and study both slant light-like submanifolds and screen slant-light-like subsets of an indefinite Sasakian manifold.
Abstract: In this paper, we define and study both slant lightlike submanifolds and screen slant lightlike submanifolds of an indefinite Sasakian manifold. We provide non-trivial examples and obtain necessary and sufficient conditions for the existence of a slant lightlike submanifold.

Journal ArticleDOI
01 Jan 2012-Filomat
TL;DR: The theoretical results of this paper can be extended to other methods of gradient-type based and results of numerical experiments are consistent with the theoretical findings.
Abstract: A hierarchical gradient based iterative algorithm of (L. Xie et al., Computers and Mathematics with Applications 58 (2009) 1441-1448) has been presented for finding the numerical solution for general linear matrix equations, and the convergent factor has been discussed by numerical experiments. However, they pointed out that how to choose a best convergence factor is still a project to be studied. In this paper, we discussed the optimal convergent factor for the gradient based iterative algorithm and obtained the optimal convergent factor. Moreover, the theoretical results of this paper can be extended to other methods of gradient-type based. Results of numerical experiments are consistent with the theoretical findings.

Journal ArticleDOI
01 Jan 2012-Filomat
TL;DR: In this article, an extension of the notion of well-posedness by perturbations, introduced by Zolezzi for a minimization problem, to a class of variational-hemivariational inequalities with perturbation in Banach spaces, including as a special case the class of mixed variational in-equalities, is considered.
Abstract: In this paper, we consider an extension of the notion of well-posedness by perturbations, introduced by Zolezzi for a minimization problem, to a class of variational-hemivariational inequalities with perturbations in Banach spaces, which includes as a special case the class of mixed variational in- equalities. Under very mild conditions, we establish some metric characterizations for the well-posed variational-hemivariational inequality, and show that the well-posedness by perturbations of a variational- hemivariational inequality is closely related to the well-posedness by perturbations of the corresponding inclusion problem. Furthermore, in the setting of finite-dimensional spaces we also derive some condi- tions under which the variational-hemivariational inequality is strongly generalized well-posed-like by perturbations.

Journal ArticleDOI
01 Jan 2012-Filomat
TL;DR: In this paper, a generalization of the classical complex conjugate graduate iterative algorithm was proposed to find the existence conditions of solution to the coupled quaternion matrix equations.
Abstract: This note studies the iterative solution to the coupled quaternion matrix equations ( ∑ p=1 T1i(Xi), ∑ p i=1 T2i(Xi); · · · ; ∑ p i=1 Tpi(Xi)) = (M1;M2; · · · ;Mp), where Tsi;s = 1;2; · · · ;p; is a linear operator from Q mi×ni onto Q ps×qs, Ms ∈ Q ps×qs;s = 1;2; · · · ;p: i = 1;2; · · · ;p. by making use of a generalization of the classical complex conjugate graduate iterative algorithm. Based on the proposed iterative algorithm, the existence conditions of solution to the above coupled quaternion matrix equations can be determined. When the considered coupled quaternion matrix equations is consistent, it is proven by using a real inner product in quaternion space as a tool that a solution can be obtained within finite iterative steps for any initial quaternion matrices (X1(0); · · · ;Xp(0)) in the absence of round-off errors and the least Frobenius norm solution can be derived by choosing a special kind of initial quaternion matrices. Furthermore, the optimal approximation solution to a given quaternion matrix can be derived. Finally, a numerical example is given to show the efficiency of the presented iterative method.