Showing papers in "Filomat in 2010"
TL;DR: Zhang et al. as mentioned in this paper obtained a new common fixed point theorem for four maps for generalized φ-weak contraction, which substantially generalizes comparable results in the literature, including the results in (Q. Zhang and Y. Song, fixed point theory for generalized (ψ, φ)-weak contraction).
Abstract: Contractive conditions introduced in (Q. Zhang and Y. Song, Fixed point theory for generalized φ-weak contraction, Appl. Math. Lett. 22(2009), 75-78) and (D. Đoric, Common fixed point for generalized (ψ, φ)-weak contractions, Applied Mathematics Letters, 22(2009), 1896-1900) are employed to obtain a new common fixed point theorem for four maps. Our result substantially generalizes comparable results in the literature. 2010 Mathematics Subject Classifications. 47H10. .
52 citations
TL;DR: Some new inequalities for the • Cebysev functional of two functions of self- adjoint linear operators in Hilbert spaces, under suitable assumptions for the involved functions and operators, are given in this paper.
Abstract: Some new inequalities for the • Cebysev functional of two functions of self- adjoint linear operators in Hilbert spaces, under suitable assumptions for the involved functions and operators, are given.
34 citations
TL;DR: In this paper, a harmonic mapping of the unit disc onto a C 1 domain is considered, and necessary and sufficient conditions in terms of boundary function that h is q.c.
Abstract: Suppose that h is a harmonic mapping of the unit disc onto a C 1; fi domain D. We give su‐cient and necessary conditions in terms of boundary function that h is q.c. We announce some new results and also outline application to
31 citations
TL;DR: In this article, the generalized Riesz B-difierence sequence spaces r q 1 (p;B);r q c (p,B); r q 0 (p),B) and r q p;B are defined.
Abstract: In this paper, we deflne the new generalized Riesz B-difierence sequence spaces r q 1 (p;B);r q c (p;B) , r q 0 (p;B) and r q (p;B) which consist of the sequences whose R q B-transforms are in the linear spaces l1 (p);c(p) , c0 (p) and l(p) , respectively, introduced by I.J.Maddox[8],[9]. We give some topological properties and compute the fii;fli and ∞iduals of these spaces. Also we determine the neccesary and su‐cient conditions on the matrix transformations from these spaces into l1 and c:
27 citations
TL;DR: In this paper, it was shown that for every a such that |a| < 1 (resp |a | = 1) the mapping ∫a = h + aĝ is an quasiconformal (a univalent) close-to-convex harmonic mapping.
Abstract: Let f = h + ĝ be a univalent sense preserving harmonic mapping of the unit disk U onto a convex domain Ω It is proved that: for every a such that |a| < 1 (resp |a| = 1) the mapping ∫a = h + aĝ is an |a| quasiconformal (a univalent) close-to-convex harmonic mapping This gives an answer to a question posed by Chuaqui and Hernandez (J Math Anal Appl (2007)) 2010 Mathematics Subject Classifications Primary 30C55, Secondary 31C05
20 citations
TL;DR: In this article, the concept of almost nonexpansive mappings is introduced and the existence of common fixed points for this new class of mappings are proved, and an invariant approximation result is obtained.
Abstract: The concept of a generalized almost nonexpansive mappings is introduced and the existence of common fixed points for this new class of mappings is proved. As an application, an invariant approximation result is obtained.
19 citations
TL;DR: In this paper, the Favard- Szasz-Mirakjan max-prod type operator is introduced and the question of the approximation order by this operator is raised.
Abstract: Starting from the study of the Shepard nonlinear operator of max-prod type in (6), (7), in the book (8), Open Problem 5.5.4, pp. 324-326, the Favard- Szasz-Mirakjan max-prod type operator is introduced and the question of the approximation order by this operator is raised. In the recent paper (1), by using a pretty complicated method to this open question an answer is given by obtaining an upper pointwise estimate of the approximation error of the form C!1(f; p x= p n) (with an unexplicit absolute constant C > 0) and the question of improving the order of approximation !1(f; p x= p n) is raised. The flrst aim of this note is to obtain the same order of approximation but by a simpler method, which in addition presents, at least, two advantages : it produces an explicit constant in front of !1(f; p x= p n) and it can easily be extended to other max-prod operators of Bernstein type. Also, we prove by a counterexample that in some sense, in general this type of order of approximation with respect to !1(f;¢) cannot be improved. However, for some subclasses of functions, including for example the bounded, nondecreasing concave functions, the essentially better order !1(f;1=n) is obtained. Finally, some shape preserving properties are obtained.
19 citations
TL;DR: By deflning a Lyapunov functional, the stability and boundedness of solutions to nonlinear third order difierential equations with constant delay were investigated in this paper.
Abstract: By deflning a Lyapunov functional, we investigate the stability and boundedness of solutions to nonlinear third order difierential equation with constant delay, r : x 000 (t) + g(x(t);x 0 (t))x 00 (t) + f(x(t i r);x 0 (t i r)) + h(x(t i r)) = p(t;x(t);x 0 (t);x(t i r);x 0 (t i r);x 00 (t)); when p(t;x(t);x 0 (t);x(t i r);x 0 (t i r);x 00 (t)) = 0 and 6 0; respectively. Our results achieve a stability result which exists in the relevant literature of ordinary nonlinear third order difierential equations without delay to the above functional difierential equation for the stability and boundedness of solutions. An example is introduced to illustrate the importance of the results obtained.
19 citations
TL;DR: In this article, the authors studied the Gilpin-Ayala competition with random perturbation and verified that the positive solution of the system does not explode in a finite time.
Abstract: In this paper we study the Gilpin-Ayala competition system with random perturbation which is more general and more realistic than the classical LotkaVolterra competition model. We verify that the positive solution of the system does not explode in a flnite time. Furthermore, it is stochastically ultimately bounded and continuous a.s. We also obtain certain results about asymptotic behavior of the stochastic Gilpin-Ayala competition model.
16 citations
TL;DR: In this paper, it was shown that the cosymplectic manifold does not admit warped product submanifolds in the form N⊥ ×fNθ and then some results for the existence of warped products of the type Nθ × fN⊵, where N⌉ and Nω are anti-invariant and proper slant sub-mansifolds, respectively.
Abstract: In this paper, we study warped product anti-slant submanifolds of cosymplectic manifolds. It is shown that the cosymplectic manifold do not admit non trivial warped product submanifolds in the form N⊥ ×fNθ and then we obtain some results for the existence of warped products of the type Nθ ×fN⊥, where N⊥ and Nθ are anti-invariant and proper slant submanifolds of a cosymplectic manifold M¯ , respectively.
16 citations
TL;DR: In this article, the maximum degree distance of n-vertex unicyclic graphs with given maximum degree was determined and the first seven maximum degree distances for n ≥ 6.
Abstract: The degree distance of a connected graph G with vertex set V(G) is defined as D'(G)= Σu∈V (G) dG (u)DG (u), where dG (u) denotes the degree of vertex u and DG (u) denotes the sum of distances between u and all vertices of G. We determine the maximum degree distance of n-vertex unicyclic graphs with given maximum degree, and the first seven maximum degree distances of n-vertex unicyclic graphs for n ≥ 6.
TL;DR: In this article, the relationship between the spectra of an upper triangulat Banach space operator and its operator satisfying Browder's or a-Weyl's theorem is studied.
Abstract: Let MC = µ A C 0 B ¶ 2 B(X ' X) be an upper triangulat Banach space operator. The relationship between the spectra of MC and M0, and their various distinguished parts, has been studied by a large number of authors in the recent past. This paper brings forth the important role played by SVEP, the single{valued extension property, in the study of some of these relations. Operators MC and M0 satisfying Browder’s, or a-Browder’s, theorem are characterized, and we prove necessary and su‐cient conditions for implications of the type \M0 satisfles a-Browder’s (or a-Weyl’s) theorem () MC satisfles a-Browder’s (resp., a-Weyl’s) theorem" to hold.
TL;DR: In this article, the warped product of the type M = NT × fN⊥ does not exist, where NT and N are invariant and anti-invariant submanifolds of an LP-cosymplectic manifold, respectively.
Abstract: In this paper, we study warped product CR-submanifolds of LP-cosymplectic manifolds. We have shown that the warped product of the type M = NT × fN⊥ does not exist, where NT and N⊥ are invariant and anti-invariant submanifolds of an LP-cosymplectic manifold M¯, respectively. Also, we have obtained a characterization result for a CR-submanifold to be locally a CR-warped product. 2010 Mathematics Subject Classifications. 53C15, 53C40, 53C42. .
TL;DR: In this article, it was shown that strong-weak exhaustiveness at a subset is equivalent to uniform convergence on compacta, and that strong exhaustiveness is the proper tool to investigate when the limit of a pointwise convergent sequence of functions fulfills the strong uniform continuity property.
Abstract: In this paper we continue, in the realm of metric spaces, the study of exhaustiveness and weak exhaustiveness at a point of a net of functions initiated by Gregoriades and Papanastassiou in 2008. We prove that exhaustiveness at every point of a net of pointwise convergent functions is equivalent to uniform convergence on compacta. We extend exhaustiveness-type properties to subsets. First, we introduce the notion of strong exhaustiveness at a subset B for sequences of functions and prove its equivalence with strong exhaustiveness at P0 (B) of the sequence of the direct image maps, where the hypersets are equipped with the Hausdorff metric. Furthermore, we show that the notion of strong-weak exhaustiveness at a subset is the proper tool to investigate when the limit of a pointwise convergent sequence of functions fulfills the strong uniform continuity property, a new pregnant form of uniform continuity discovered by Beer and Levi in 2009.
TL;DR: In this article, the authors introduce (I, γ)-generalized semi-closed sets in topological spaces and also introduce γS - TI-spaces and investigate some of their properties.
Abstract: In this paper we introduce (I , γ)-generalized semi-closed sets in topological spaces and also introduce γS - TI-spaces and investigate some of their properties. 2010 Mathematics Subject Classifications. 54B05, 54C08, 54D05. .
TL;DR: In this paper, the detour index of a connected graph is defined as the sum of detour distances between all unordered pairs of vertices, and the n-vertex unicyclic graphs whose vertices on its unique cycle all have degree at least three with the first, second and third smallest and largest detour indices respectively for n ≥ 7.
Abstract: The detour index of a connected graph is defined as the sum of detour distances between all unordered pairs of vertices. We determine the n-vertex unicyclic graphs whose vertices on its unique cycle all have degree at least three with the first, the second and the third smallest and largest detour indices respectively for n ≥ 7. 2010 Mathematics Subject Classifications. 05C12, 05C35, 05C90. .
TL;DR: In this article, a continuation of [5] and [6] is presented, using the 3rd and the 4th kind of covariant derivative of a submanifold XM of a generalized Riemannian space.
Abstract: The present work is a continuation of [5] and [6]. In [5] we have obtained derivational equations of a submanifold XM of a generalized Riemannian space GRN. Since the basic tensor in GRN is asymmetric and in this way the connection is also asymmetric, in a submanifold the connection is generally asymmetric too. By reason of this, we define 4 kinds of covariant derivative and obtain 4 kinds of derivational equations. In [6] we have obtained integrability conditions and Gauss-Codazzi equations using the 1st and the 2st kind of covariant derivative. The present work deals in the cited matter, using the 3rd and the 4th kind of covariant derivative. One obtains three new integrability conditions for derivational equations of tangents and three such conditions for normals of the submanifold, as the corresponding Gauss-Codazzi equations too.
TL;DR: In this paper, general formulas for the Tutte and Jones polynomials of families of knots and links given in Conway notation and corresponding plots of zeroes for the Jones polynomials are given.
Abstract: This article contains general formulas for the Tutte and Jones polynomials of families of knots and links given in Conway notation and the corresponding plots of zeroes for the Jones polynomials.
TL;DR: In this paper, it was shown that several theorems in the theory of HQC mappings cannot be strenghtened by weakening or omitting some of the conditions.
Abstract: We give examples that show that several of the theorems in the theory of HQC mappings cannot be strenghtened by weakening or omitting some of the conditions. In particular, we study Kellogg type problems and characterizations of HQC condition.
TL;DR: In this paper, the authors presented an investigation of difierential geometric structures arising on immersed manifolds in K-contact Riemannian manifolds admitting semi-symmetric non-metric connection.
Abstract: In this paper we present an investigation of difierential geometric structures arising on immersed manifolds in K-contact Riemannian manifolds admitting semi-symmetric non-metric connection. Some properties of semi-symmetric non-metric connection in K-Contact Riemannian manifolds are also obtained.
TL;DR: The partial fraction decomposition method is employed to establish two general algebraic identities, which contain consequently several binomial identities and their q{analogues as special cases as discussed by the authors. But this method is not suitable for algebraic data.
Abstract: The partial fraction decomposition method is employed to establish two general algebraic identities, which contain consequently several binomial identities and their q{analogues as special cases.
TL;DR: In this paper, several characterizations and further properties of I-submaximal ideal topological spaces are obtained, as well as several properties of ideal topology spaces are discussed.
Abstract: In [2], the notion of I-submaximal ideal topological spaces is introduced and studied. In this paper, several characterizations and further properties of I-submaximal ideal topological spaces are obtained.
TL;DR: In this article, the GA2 index is defined as ∑uv∈E(G) 2√ nu(e)nv(e), /nu(e)) + nv(e)+ nv (e), where nv is the number of vertices of G lying closer to v than u.
Abstract: Let G = (V, E) be a graph. For e = uv ∈ E(G), nu (e) is the number of vertices of G lying closer to u than to v and nv (e) is the number of vertices of G lying closer to v than u. The GA2 index of G is defined as ∑uv∈E(G) 2√ nu(e)nv(e) / nu(e) + nv(e). We explore here some mathematical properties and present explicit formulas for this new index under several graph operations. 2010 Mathematics Subject Classifications. 05C12, 05A15, 05A20, 05C05. .
TL;DR: This article introduced the class of almost essentially Ruston elements with respect to a homomorphism between two Banach algebras, a class intermediate between Ruston and Fredholm elements.
Abstract: We introduce the class of 'almost essentially Ruston elements' with respect to a homomorphism between two Banach algebras, a class intermediate between Ruston and Fredholm elements.
TL;DR: In this article, Molnar, Prok and Szirmai have constructed at least one hyperbolic space group for each truncated simplex in families F3, F4 and F6.
Abstract: There are investigated supergroups of some hyperbolic space groups with simplicial fundamental domain. If the vertices of these simplices are out of the absolute, we can truncate them by polar planes of the vertices and the new polyhedra are fundamental ones of the richer groups. In papers of E. Molnar, I. Prok and J. Szirmai the simplices, investigated here, are collected in families F3, F4 and F6. We have constructed at least one new hyperbolic space group for each truncated simplex in these families. 2010 Mathematics Subject Classifications. 51M20, 52C22, 20H15, 20F55. .
TL;DR: In this article, the authors give characterizations of various special types of bands of λ-semigroups and semilattices of matrices of the same type of matrix.
Abstract: Semigroups having a decomposition into a band of semigroups have been studied in many papers. In the present paper we give characterizations of various special types of bands of λ-semigroups and semilattices of matrices of λ- semigroups.
TL;DR: In this paper, a linear operator is deflated by means of the Hadamard product (or convolution) and two new subclasses of meromorphically multivalent functions are introduced.
Abstract: Making use of a linear operator, which is deflned here by means of the Hadamard product (or convolution), we introduce two novel subclasses ›a;c(p;A;B;‚) and › +(p;A;B;‚) of meromorphically multivalent functions. The main object of this paper is to investigate the various important properties and characteristics of those subclasses of meromorphically multivalent functions. We extend the familiar concept of neighborhoods of analytic functions to these subclasses of meromorphically multivalent functions. We also derive many results for the Hadamard products of functions belonging to the class › +(p;fi;fl;∞;‚).
TL;DR: In this paper, the authors presented new results supplementing their research with the characterization of classes of compact operators on those spaces, which are related to strong Cesµaro summability and boundedness.
Abstract: Many sequence spaces arise from difierent concepts of summability. Recent results obtained by Altay, Ba»sar and Malkowsky [2] are related to strong Cesµaro summability and boundedness. They determined fliduals of the new sequence spaces and characterized some classes of matrix transformations on them. Here, we will present new results supplementing their research with the characterization of classes of compact operators on those spaces.
TL;DR: In this paper, the authors derived some subordination and superordination results associated with the family of Jung-Kim-Srivastava integral operators deflned on the space of meromorphic functions.
Abstract: In this paper, we derive some subordination and superordination results associated with the family of Jung-Kim-Srivastava integral operators deflned on the space of meromorphic functions. Several sandwich-type results are also obtained.
TL;DR: The main object of as mentioned in this paper is to introduce and investigate some proper- ties and relations involving sequences of numbers Fn;m(r), for m = 2;3;4, and r is some real number.
Abstract: The main object of this paper is to introduce and investigate some proper- ties and relations involving sequences of numbers Fn;m(r), for m = 2;3;4, and r is some real number. These sequences are generalizations of the Jacobsthal and Jacobsthal Lucas numbers. Jn;m(x) = Jni1;m(x) + 2xJnim;m(x); (1) (n ‚ m; n;m 2N; J0;m(x) = 0; Jn;m(x) = 1; when n = 1;2;:::;m i 1); jn;m(x) = jni1;m(x) + 2xjnim;m(x); (2) (n ‚ m; n;m 2N; j0;m(x) = 2; jn;m(x) = 1; when n = 1;2;:::;m i 1); Fn;m(x) = Fni1;m(x) + 2xFnim;m(x) + 3; (3) (n ‚ m; n;m 2N; F0;m(x) = 0; Fn;m(x) = 1; when n = 1;2;:::;m i 1); fn;m(x) = fni1;m(x) + 2xfnim;m(x) + 5; (4) (n ‚ m; n;m 2N; f0;m(x) = 0; fn;m(x) = 1; when n = 1;2;:::;m i 1:) The polynomials Jn;2(x), jn;2(x), Fn;2(x) and fn;2(x) are considered in (3). For x = 1 and for a some real number r, by (3), we get the following sequences of numbers fCn;m(r)g: