Showing papers in "Filomat in 2013"
TL;DR: In this article, an interesting subclass NΣh,p (λ, μ) of analytic and bi-univalent functions in the open unit disk U is introduced and investigated, and the first two Taylor-Maclaurin coefficients |a2| and |a3| are obtained.
Abstract: In this paper, we introduce and investigate an interesting subclass NΣh,p (λ, μ) of analytic and bi-univalent functions in the open unit disk U. For functions belonging to the class NΣh,p (λ, μ), we obtain estimates on the first two Taylor-Maclaurin coefficients |a2| and |a3|. The results presented in this paper would generalize and improve some recent works of Caǧlar et al. [3], Xu et al. [10], and other authors.
164 citations
TL;DR: In this article, the fixed point results for closed multi-valued F-contractions were presented for complete metric spaces or complete ordered metric spaces, and two applications for the solution of certain functional and integral equations were given to illustrate the usability of the obtained results.
Abstract: Wardowski (Fixed Point Theory Appl., 2012:94) introduced a new concept of contraction and proved a fixed point theorem which generalizes Banach contraction principle. Following this direction of research, we will present some fixed point results for closed multi-valued F-contractions or multi-valued mappings which satisfy an F-contractive condition of Hardy-Rogers-type, in the setting of complete metric spaces or complete ordered metric spaces. An example and two applications, for the solution of certain functional and integral equations, are given to illustrate the usability of the obtained results.
151 citations
TL;DR: In this article, the Hermite-Hadamard type inequalities of m- and (; m)-logarithmically convex functions were established for the first time.
Abstract: In the paper, the authors introduce concepts of m- and (; m)-logarithmically convex functions and establish some Hermite-Hadamard type inequalities of these classes of functions.
114 citations
TL;DR: In this article, two new subclasses N Σ (; ) and N ǫ ( ; ) of bi-univalent functions defined in the open unit disk U = {z : |z| < 1}.
Abstract: In the present investigation, we consider two new subclasses N Σ (; ) and N Σ ( ; ) of bi- univalent functions defined in the open unit disk U = {z : |z| < 1}: Besides, we find upper bounds for the second and third coefficients for functions in these new subclasses.
98 citations
TL;DR: In this paper, the authors considered a certain King type operators which includes general families of Sz´ asz-Mirakjan, Baskakov, Post-Widder and Stancu operators.
Abstract: In this paper, we consider a certain King type operators which includes general families of Sz´ asz-Mirakjan, Baskakov, Post-Widder and Stancu operators. By introducing two parameter family of Lipschitz type space, which provides global approximationfortheabovementionedoperators,weobtaintherateofconvergence of this class. Furthermore, we give local approximation results by using the first and the second modulus of continuity.
91 citations
TL;DR: It is shown that any fuzzy relation may be considered as a soft binary relation and the notion of soft homomorphisms is presented and isomorphism theorems for soft semigroups are established based on soft congruence relations.
Abstract: Binary relations, in particular, equivalence relations play an important role in both mathematics and information sciences. The concept of soft sets was initiated by Molodtsov as a general mathematical frameworkfordealingwithuncertainty. Thepresentpaperestablishesapossibleconnectionbetweenbinary relations and soft sets. The concept of soft binary relations is introduced and some related properties are investigated. It is shown that any fuzzy relation may be considered as a soft binary relation. Moreover, we discuss the application of soft binary relations in semigroup theory. We consider soft congruence relations over semigroups and show that all soft congruence relations over a semigroup with a fixed parameter set form a lattice. Finally, the notion of soft homomorphisms is presented and isomorphism theorems for soft semigroups are established based on soft congruence relations.
68 citations
TL;DR: In this article, the authors present the state of the art of the search for minimal-ABC trees, and provide a complete bibliography on ABC index, and some structural features of such trees have been determined.
Abstract: The atom-bond connectivity (ABC) index of a graph G is defined as the sum over all pairs of adjacent vertices u;v, of the terms √ (d(u) + d(v) 2)=(d(u)d(v)), where d(v) denotes the degree of the vertex v of the graph G. Whereas the finding of the graphs with the greatest ABC-value is an easy task, the characterization of the graphs with smallest ABC-value, in spite of numerous attempts, is still an open problem. What only is known is that the connected graph with minimal ABC index must be a tree, and some structural features of such trees have been determined. Several conjectures on the structure of the minimal-ABC trees, were disproved by counterexamples. In this review we present the state of art of the search for minimal-ABC trees, and provide a complete bibliography on ABC index.
56 citations
TL;DR: In this paper, it was shown that the set of slowly oscillating continuous functions is equal to the subset of uniformly continuous functions on a slowly oscillated compact subset of a topological vector space valued cone metric space.
Abstract: In this paper, we investigate slowly oscillating continuity in cone metric spaces. It turns out that the set of slowly oscillating continuous functions is equal to the set of uniformly continuous functions on a slowly oscillating compact subset of a topological vector space valued cone metric space.
49 citations
TL;DR: The harmonic index H(G) of a graph G is defined as the sum of the weights 2 d(u)+d(v) of all edges uv of G, where uv denotes the degree of a vertex u in G.
Abstract: The harmonic index H(G) of a graph G is defined as the sum of the weights 2 d(u)+d(v) of all edges uv of G, where d(u) denotes the degree of a vertex u in G We give a best possible lower bound for the harmonic index of a graph (a triangle-free graph, respectively) with minimum degree at least two and characterize the extremal graphs
47 citations
TL;DR: In this paper, some new inequalities of the Hermite-Hadamard type for h-convex functions via Riemann-Liouville fractional integral are given.
Abstract: In this paper, some new inequalities of the Hermite-Hadamard type for h-convex functions via Riemann-Liouville fractional integral are given.
40 citations
TL;DR: In this paper, a q-analogue of the Bernstein-Kantorovich operators is introduced and the approximation properties of the q-Bernstein-Kanagalakis operator are investigated.
Abstract: In the present paper we introduce a q-analogue of the Bernstein-Kantorovich operators and investigate their approximation properties. We study local and global approximation properties and Voronovskaja type theorem for the q-Bernstein-Kantorovich operators in case 0 < q < 1.
TL;DR: In this article, the authors introduce and examine a class of sequences of fuzzy numbers and study some properties like completeness, solidity, symmetricity, and inclusion relations related to this class.
Abstract: The idea of difference sequences of real (or complex) numbers was generalized by Et and Colak (9). In this paper, using the difference operator ∆ m and an Orlicz function, we introduce and examine a class of sequences of fuzzy numbers. We study some of their properties like completeness, solidity, symmetricity etc. We also give some inclusion relations related to this class.
TL;DR: The Laplace transform in Komatsu ultradistributions is considered in this paper, where conditions are given under which an analytic function is a Laplace transformation of an ultradimensional distribution.
Abstract: The Laplace transform in Komatsu ultradistributions is considered Also, conditions are given under which an analytic function is a Laplace transformation of an ultradistribution
TL;DR: A new family of polynomials is introduced which generates reversible codes over a finitefield with sixteenelements(F16 orGF(16)).
Abstract: In this paper, we introduce a new family of polynomials which generates reversible codes over a finitefieldwithsixteenelements(F16 orGF(16)). Wenamethepolynomialsinthisfamilyasliftedpolynomials. Some advantages of lifted polynomials are that they are easy to construct, there are plenty of examples of them and it is easy to determine the dimension of codes generated by them. Furthermore we introduce 4-lifted polynomials which provide a rich source for DNA codes. Also we construct codes over F4 that have the best possible parameters from lifted polynomials. In addition we obtain some reversible codes over F4.
TL;DR: In this paper, the gamma function and the digamma function at their singularities are shown to be independent functions, and alternative proofs for limitformulas of ratio-of-ratios are presented.
Abstract: Inthenote, theauthorpresentsalternativeproofsforlimitformulasofratiosbetweenderivatives of the gamma function and the digamma function at their singularities.
[...]
TL;DR: In this article, the concept of I-Baire spaces is introduced and characterizations and properties of these spaces are given, and it is shown that (X; ) is Baire if and only if (X;; I) is I-baire for any ideal I on X.
Abstract: In this paper, the concept of I-Baire spaces is introduced, and characterizations and properties of these spaces are given. It is shown that (X; ) is Baire if and only if (X;; I) is I-Baire for any ideal I on X.
TL;DR: In this article, the extremal structures of trees with various constraints that maximize or minimize the Wiener index have been extensively investigated, and some general statements regarding functions of distances of a tree, from which some of the extreme structures with respect to the Harary index and a generalized version of it are characterized.
Abstract: Introducedin1947, theWienerindexW(T) = ∑ {u,v}⊆V(T) d(u,v)isoneofthemostthoroughlystud- ied chemical indices. The extremal structures (in particular, trees with various constraints) that maximize or minimize the Wiener index have been extensively investigated. The Harary index H(T) = ∑ {u,v}⊆V(T) 1 d(u,v) , introduced in 1993, can be considered as the "reciprocal analogue" of the Wiener index. From recent stud- ies, it is known that the extremal structures of the Harary index and the Wiener index coincide in many instances, i.e., the graphs that maximize the Wiener index minimize the Harary index and vice versa. In this note we provide some general statements regarding functions of distances of a tree, from which some of the extremal structures with respect to the Harary index (and a generalized version of it) are characterized. Among the results a recent conjecture of IliYu and Feng is proven. A case when the extremal structures of these two indices differ is also provided. Finally, we derive some previously known extremal results as immediate corollaries.
TL;DR: In this article, the existence of fixed points of certain self-maps in the context of partial metric spaces has been proved and the fixed point theorems presented here can be considered as a continuation, in part, of the works of L.B.
Abstract: In this paper we prove the existence of fixed points of certain self-maps in the context of partial metric spaces. In fact, the fixed point theorems presented here can be considered as a continuation, in part, of the works of L.B. ´ Cirion the existence of fixed points but not uniqueness in the realm of metric spaces. Our results generalize, enrich and improve earlier results on the topic in the literature.
TL;DR: In this paper, the authors introduced the Bernstein-Chlodowsky-Gadjiev polynomials and showed that these operators are more efficient in weighted approximating to function having polynomial growth since they contain a factor bn tending to infinity.
Abstract: In the present paper, we introduce Bernstein-Chlodowsky-Gadjiev operators taking into con- sideration the polynomials introduced by Gadjiev and Ghorbanalizadeh (2). The interval of convergence of the operators is a moved interval as polynomials given in (2) but grows as n → ∞ as in the classical Bernstein-Chlodowsky polynomials. Also their knots are shifted and depend on x. We firstly study weighted approximation properties of these operators and show that these operators are more efficient in weighted approximating to function having polynomial growth since these operators contain a factor bn tending to infinity. Secondly we calculate derivative of new Bernstein-Chlodowsky- Gadjiev operators and give a weighted approximation theorem in Lipchitz space for the derivatives of these operators.
TL;DR: In this article, the existence and uniqueness of fixed points for new classes of mappings defined on a complete metric space is discussed, and the results generalize some recent theorems in the literature.
Abstract: The purpose of this paper is to discuss the existence and uniqueness of fixed points for new classes of mappings defined on a complete metric space. The obtained results generalize some recent theorems in the literature. Several applications and interesting consequences of our theorems are also given.
TL;DR: In this article, the authors extend the notion of anti-invariant and Langrangian Riemannian submersion to the case when the total manifold is nearly Kaehler.
Abstract: We extend the notion of anti-invariant and Langrangian Riemannian submersion to the case when the total manifold is nearly Kaehler. We obtain the integrability conditions for the horizontal distri- bution while it is noted that the vertical distribution is always integrable. We also investigate the geometry of the foliations of the two distributions and obtain the necessary and sufficient condition for a Langrangian submersion to be totally geodesic. The decomposition theorems for the total manifold of the submersion are obtained.
TL;DR: In this article, Filipovic et al. proved fixed and periodic point theorems for T-contraction of two maps on cone metric spaces with solid cones, and extended and generalized well-known comparable results in the literature.
Abstract: Recently, Filipovic et al. [M. Filipovic, L. Paunovic, S. Radenovic, M. Rajovic, Remarks on 'Cone metric spaces and fixed point theorems of T-Kannan and T-Chatterjea contractive mappings', Math. Comput. Modelling. 54 (2011) 1467-1472] proved several fixed and periodic point theorems for solid cones on cone metric spaces. In this paper several fixed and periodic point theorems for T-contraction of two maps on cone metric spaces with solid cone are proved. The results of this paper extend and generalize well-known comparable results in the literature.
TL;DR: In this article, the authors elementarily sharpen and generalize Shafer-Fink's double inequality for the arc sine function, and show that the double inequality can be generalized to the case of arc sines.
Abstract: In the paper, the authors elementarily sharpen and generalize Shafer-Fink's double inequality for the arc sine function.
TL;DR: Aouchiche et al. as mentioned in this paper established maximal trees and graphs for the difference of average distance and proximity, proving that the corresponding conjecture posed in M. Aouchiche, P. Hansen, and Networks 58 (2) (2011) 95102 hold for trees.
Abstract: We establish maximal trees and graphs for the difference of average distance and proximity proving thus the corresponding conjecture posed in M. Aouchiche, P. Hansen, Proximity and remoteness in graphs: results and conjectures, Networks 58 (2) (2011) 95102. We also establish maximal trees for the difference of average eccentricity and remoteness and minimal trees for the difference of remoteness and radius proving thus that the corresponding conjectures posed in M. Aouchiche, P. Hansen, Proximity and remoteness in graphs: results and conjectures, Networks 58 (2) (2011) 95102 hold for trees.
TL;DR: The q-Sumudu transform is the theoritical dual of the Laplace transform as discussed by the authors, and it has many applications in sciences and engineering for its special fundamental properties.
Abstract: Although Sumudu transform is the theoritical dual of the Laplace transform, it has many applications in sciences and engineering for its special fundamental properties. In a previous paper (3), we studied q-analogues of the Sumudu transform and derived some fundamental properties. This paper follows the previous paper and aims to provide some applications of the q-Sumudu transform. The authors give q-Sumudu transforms of some q-polynomials and q-functions. Also, we evaluated the q-Sumudu transform of basic analogue of Fox's H-function.
TL;DR: In this paper, the class of analytic functions in the unit disk D with the normalization f(0) = f'(0) − 1 = 0, where f is the number of points in the disk.
Abstract: Let A denote be the class of analytic functions in the unit disk D with the normalization f(0) = f ' (0) − 1 = 0. For z/f(z) , 0 in D, consider Uf(z) = ( z f(z) )2 f ' (z) and B(z) = f(z) z .
TL;DR: In this article, it was shown that any ideal ward continuous function is uniformly continuous either on an interval or on an ideal ward compact subset of R. A characterization of uniform continuity is also given via ideal quasi-Cauchy sequences.
Abstract: In this paper, we prove that any ideal ward continuous function is uniformly continuous either on an interval or on an ideal ward compact subset of R. A characterization of uniform continuity is also given via ideal quasi-Cauchy sequences.
TL;DR: In this article, the authors considered the Cauchy problem for incompressible hydrodynamic flow of nematic liquid crystals in three dimensions and proved the global existence and uniqueness of the strong solutions with nonnegative ρ0 and small initial data.
Abstract: We consider the Cauchy problem for incompressible hydrodynamic flow of nematic liquid crystals in three dimensions. We prove the global existence and uniqueness of the strong solutions with nonnegative ρ0 and small initial data.
TL;DR: In this paper, the authors established new integral inequalities of Hermite-Hadamard type for functions whose n-th derivatives are of (α, m)-convexity and deduced some known results.
Abstract: In the paper, the authors establish some new integral inequalities of Hermite-Hadamard type for functions whose n-th derivatives are of (α, m)-convexity and, from these, deduce some known results.
TL;DR: In this paper, the characteristics of quarter-symmetric metric connections are studied and some invariants with respect to the projective transformation are obtained, where the invariants depend on the dimension of the connection.
Abstract: This paper studies the characteristics of quarter-symmetric metric connections. Some invariants with respect to the projective transformation are obtained.