Showing papers in "Kyungpook Mathematical Journal in 2014"
TL;DR: In this article, the adaptive backstep-ping control design based on recursive feedback control was investigated for WINDMI (J. C. Sprott, 2003) and Coullet (P. Coullet et al, 1979) chaotic systems.
Abstract: In this paper, global chaos synchronization is investigated for WINDMI (J. C. Sprott, 2003) and Coullet (P. Coullet et al, 1979) chaotic systems using adaptive backstep- ping control design based on recursive feedback control. Our theorems on synchronization for WINDMI and Coullet chaotic systems are established using Lyapunov stability the- ory. The adaptive backstepping control links the choice of Lyapunov function with the design of a controller and guarantees global stability performance of strict-feedback chaotic systems. The adaptive backstepping control maintains the parameter vector at a predeter- mined desired value. The adaptive backstepping control method is efiective and convenient to synchronize and estimate the parameters of the chaotic systems. Mainly, this technique gives the ∞exibility to construct a control law and estimate the parameter values. Numeri- cal simulations are also given to illustrate and validate the synchronization results derived in this paper.
113 citations
TL;DR: In this article, the authors established some new nonlinear integral inequalities of Gronwall-Bellman type, which generalize some famous inequalities which can be used in applications as handy tools to study the qualitative as well as quantitative properties of solutions of some nonlinear ordinary differential and integral equations.
Abstract: Abstract. In this paper, we establish some new nonlinear integral inequalities of Gronwall-Bellman type. These inequalities generalize some famous inequalities which can be used in applications as handy tools to study the qualitative as well as quantitative properties of solutions of some nonlinear ordinary differential and integral equations. More accurately we extend certain results which have been proved in A. Abdeldaim and M. Yakout [1] and H. El-Owaidy, A. A. Ragab, A. Abdeldaim [7] too.
34 citations
TL;DR: In this article, the notions of interior and closure are generalized using these sets, and a detail study is carried out on properties of semi-open, semiclosed soft sets, semi interior and semi closure of a soft set in a soft topological space.
Abstract: This paper introduces semiopen and semiclosed soft sets in soft topological spaces. The notions of interior and closure are generalized using these sets. A detail study is carried out on properties of semiopen, semiclosed soft sets, semi interior and semi closure of a soft set in a soft topological space. Various forms of soft functions, like semicontinuous, irresolute, semiopen soft functions are introduced and characterized. Further soft semicompactness,soft semiconnectedness and soft semiseparation axioms are introduced and studied.
29 citations
TL;DR: In this article, the authors introduce S-metric spaces and give their properties, and present a common xed point theorem for multivalued maps on complete S-matric spaces.
Abstract: In this paper, we introduce S-metric spaces and give their some properties. Also we present a common xed point theorem for multivalued maps on complete S-metric spaces. The single valued case and an illustrative example are given.
18 citations
TL;DR: In this paper, it was shown that separation axiom T2 is equivalent to T2, T0 is equivalence to semi T0, and semi T 1 is equivalency to semi TD.
Abstract: We show that in quasi-topological spaces, separation axiom T2 is equivalent to T2; T0 is equivalent to semi T0; and semi T 1 is equivalent to semi TD: Also, we give characterizations for T1; semi T1 and semi T 1 generalized topological spaces.
18 citations
TL;DR: In this paper, a structural characterization of super line symmetric n-sigraphs of index r is presented. But the characterization is restricted to the case where the underlying graph of the super line graph is an ordered pair.
Abstract: An n-tuple (a1,a2, � � � ,an) is symmetric, if ak = an−k+1,1 ≤ k ≤ n. Let Hn = {(a1,a2, � � � ,an) : ak ∈ {+, −},ak = an−k+1,1 ≤ k ≤ n} be the set of all symmetric n-tuples. Asymmetric n-sigraph (symmetric n-marked graph) is an ordered pair Sn = (G,�) (Sn = (G,µ)), where G = (V,E) is a graph called the underlying graph of Sn and � : E → Hn (µ : V → Hn) is a function. In Bagga et al. (1995) introduced the concept of the super line graph of index r of a graph G, denoted by Lr(G). The vertices of Lr(G) are the r- subsets of E(G) and two vertices P and Q are adjacent if there exist p ∈ P and q ∈ Q such that p and q are adjacent edges in G. Analogously, one can define the super line symmetric n-sigraph of index r of a symmetric n-sigraph Sn = (G,�) as a symmetric n- sigraph Lr(Sn) = (Lr(G),� ' ), where Lr(G) is the underlying graph of Lr(Sn), where for any edge PQ in Lr(Sn), � ' (PQ) = �(P)�(Q). It is shown that for any symmetric n- sigraph Sn, its Lr(Sn) is i-balanced and we offer a structural characterization of super line symmetric n-sigraphs of index r. Further, we characterize symmetric n-sigraphs Sn for which Sn ∼ L2(Sn), L2(Sn) ∼ L(Sn) and L2(Sn) ∼ Sn where ∼ denotes switching equivalence and L2(Sn), L(Sn) and Sn are denotes the super line symmetric n-sigraph of index 2, line symmetric n-sigraph and complementary symmetric n-sigraph of Sn respectively. Also, we characterize symmetric n-sigraphs Sn for which Sn ∼ L2(Sn) and L2(Sn) ∼ L(Sn).
17 citations
TL;DR: In this paper, the authors introduce the concept of strongly extending modules which are particular subclass of the class of extending modules, and study some basic properties of this new class of modules, such as strongly summand intersection property and weakly co-Hopflan property.
Abstract: The purpose of this paper is to introduce the concept of strongly extending modules which are particular subclass of the class of extending modules, and study some basic properties of this new class of modules. A module M is called strongly extending if each submodule of M is essential in a fully invariant direct summand of M. In this paper we examine the behavior of the class of strongly extending modules with respect to the preservation of this property in direct summands and direct sums and give some proper- ties of these modules, for instance, strongly summand intersection property and weakly co-Hopflan property. Also such modules are characterized over commutative Dedekind domains.
14 citations
TL;DR: In this article, different types of multiplier I-convergent double sequence spaces are introduced and their algebraic and topological properties like solidity, symmetricity, completeness etc.
Abstract: In this article we introduce different types of multiplier I-convergent double sequence spaces. We study their different algebraic and topological properties like solidity, symmetricity, completeness etc. The decomposition theorem is established and some inclusion results are proved.
14 citations
TL;DR: Different properties of the statistically convergent and statistically null sequence classes of fuzzy real numbers with fuzzy metric, like complete- ness, solidness, sequence algebra, symmetricity and convergence free are studied.
Abstract: In this article we study different properties of the statistically convergent and statistically null sequence classes of fuzzy real numbers with fuzzy metric, like complete- ness, solidness, sequence algebra, symmetricity and convergence free.
8 citations
8 citations
TL;DR: In this paper, the authors characterized intra-regular involution po-semigroups and proved that the ideal of S is prime if and only if S is commutative.
Abstract: The concept of prime and weakly prime ideal in semigroups has been intro- duced by G. Szasz (4). In this paper, we dene the involution in po--semigroups, then we extend some results on prime, semiprime and weakly prime ideals to the involution po--semigroup S. Also, we characterize intra-regular involution po--semigroups. We establish that in the involution po--semigroup S such that the involution preserves the order, an ideal of S is prime if and only if it is both weakly prime and semiprime and if S is commutative, then the prime and weakly prime ideals of S coincide. Finally, we prove that if S is a po--semigroup with order preserving involution, then the ideals of S are prime if and only if S is intra-regular.
TL;DR: In this article, a new Ostrowski-type inequality involving functions of two inde- pendent variables, as well as some related results, are presented. But they do not consider the relation between functions of the two variables.
Abstract: We provide a new Ostrowski-type inequality involving functions of two inde- pendent variables, as well as some related results.
TL;DR: The re∞exive index for a family of subsets of a given set was introduced in this paper, and it is shown that the index of a flnite or countably inflnite set is always flninite.
Abstract: As a further study on re∞exive families of subsets, we introduce the re∞exive index for a family of subsets of a given set and show that the index of a flnite family of subsets of a flnite or countably inflnite set is always flnite. The re∞exive indices of some special families are also considered. Given a set X, let Sub(X) denote the set of all subsets of X and End(X) denote the set of all endomappings f : X i! X. For any A µ Sub(X) and F µ End(X) deflne Alg(A) = ff 2 End(X) : f(A) µ A for all A 2 Ag; Lat(F) = fA 2 Sub(X) : f(A) µ A for all f 2 Fg: A family A µ Sub(X) is called re∞exive if A = Lat(Alg(A)), or equivalently, A = Lat(F) for some F µ End(X). As was shown in (9), A µ Sub(X) is re∞exive ifi it is closed under arbitrary unions and intersections and contains the empty set and X. The re∞exive families F µ End(X) were also introduced and characterized as those subsemigroups L of (End(X);-) such that L is a lower set and contains all existing suprema of subsets of L with respect to a naturally deflned partial order on End(X). The similar work in functional analysis is on the re∞exive invariant subspace lattices and re∞exive operator algebras (1-6). For any A µ Sub(X), let ^ A = Lat(Alg(A)). Then ^ A is the smallest family of subsets containing A which is closed under arbitrary unions and intersections containing empty set ; and X, and ^
TL;DR: In this paper, the authors introduce two new types of irresolute functions, completely D-irresolute and weakly D-IRresolute, and obtain their char- acterizations and their basic properties.
Abstract: In this paper, we introduce two new types of irresolute functions namely completely D-irresolute functions and weakly D-irresolute functions.We obtain their char- acterizations and their basic properties.
TL;DR: In this paper, a new generalization of q-Genocchi polynomials and numbers of higher order was introduced, and a new q-Hurwitz-Zeta type function was defined.
Abstract: In the present paper, we introduce the new generalization of q-Genocchi polynomials and numbers of higher order. Also, we give some interesting identi- ties. Finally, by applying q-Mellin transformation to the generating function for q-Genocchi polynomials of higher order put we define novel q-Hurwitz-Zeta type function which is an interpolation for this polynomials at negative integers.
TL;DR: In this article, the concepts of pure ideals, weakly pure ideals and purely prime ideals in ordered semigroups are introduced, and the set of all pure prime ideals is topologized.
Abstract: In this paper the concepts of pure ideals, weakly pure ideals and purely prime ideals in ordered semigroups are introduced. We obtain some characterizations of pure ideals and prove that the set of all pure prime ideals is topologized. 1. Introduction and Preliminaries In (1), Ahsan and Takahashi introduced the notions of pure ideals and purely prime ideals in a semigroup without order. Recently, Bashir and Shabir (3) dened the concepts of pure ideals, weakly pure ideals and purely prime ideals in a ternary semigroup. The authors gave some characterizations of pure ideals and showed that the set of all purely prime ideals of a ternary semigroup is topologized. In this paper, we do in the line of Bashir and Shabir. We introduce the concepts of pure ideals, weakly pure ideals and purely prime ideals on an ordered semigroup. We characterize pure ideals and prove that the set of all purely prime ideals of an ordered semigroup is topologized. Note that the results on semigroups without order become then special cases. For the rest of this section, we recall some denitions and results used through- out the paper. A semigroup S with an order relation ≤ is called an ordered semigroup ((2), (5)) if for x;y;z ∈ S, x ≤ y implies zx ≤ zy and xz ≤ yz. An element 0 of S is called a zero element of S if 0x = x0 = 0 for all x ∈ S and 0 ≤ x for all x ∈ S. A nonempty subset A of S is called a subsemigroup of S if xy ∈ A for all x;y ∈ A. Note that every subsemigroup of S is an ordered semigroup under the order relation on S. For nonempty subsets A and B of S, let AB = {xy | x ∈ A;y ∈ B}. For x ∈ S, let Ax = A{x} and xA = {x}A. A nonempty subset A of S is a subsemigroup of S if and only if AA ⊆ A.
TL;DR: In this article, it was shown that there is no pseudo null (1, 3)-Bertrand curve with curvature functions other than itself in Minkowski space-time E 4.
Abstract: In this paper, we prove that there are no pseudo null Bertrand curve with curvature functions k1(s) = 1; k2(s) 0 and k3(s) other than itself in Minkowski space- time E 4 and by using the similar idea of Matsuda and Yorozu (13), we define a new kind of Bertrand curve and called it pseudo null (1; 3)-Bertrand curve. Also we give some characterizations and an example of pseudo null (1; 3)-Bertrand curves in Minkowski space- time.
TL;DR: In this paper, the authors derived some results for certain new class of analytic functions defined by using Ruscheweyh derivative with varying arguments, which they used to derive the results for a class of analytical functions.
Abstract: In this paper we derive some results for certain new class of analytic functions defined by using Ruscheweyh derivative with varying arguments.
TL;DR: In this paper, it was shown that a ring whose simple singular modules are PS-injective is a semiprimitive ring with identity and all modules are unitary.
Abstract: . Let R be a ring. A right R -module M is PS -injective if every R -homomorphism f : aR ! M for every principally small right ideal aR can be extendedto R ! M . We investigate, in this paper, rings whose simple singular modules are PS -injective. New characterizations of semiprimitive rings and semisimple Artinian rings aregiven. 1. IntroductionThroughout this paper, R is an associative ring with identity and all modulesare unitary. The Jacobson radical of R is denoted by J ( R ) and the right singularideal is denoted by Z ( R R ). For a ∈ R , l ( a )(resp. r ( a )) denote the left (resp. right)annihilator of a in R . For the usual notations we refer the reader to [3], [7] and [10].A right ideal I of R is called small if for every proper right ideal K of R , K + I = R . A right R -module M is right PS -injective if every R -homomorphism f : aR → M for every principally small right ideal aR can be extended to R → M (see [13]). The ring R is said to be right PS -injective if R R
TL;DR: In this article, the ∗-Nagata ring of AP∗MDs was studied, and it was shown that D is an AP ∗MD and D[X] ⊆ D [X] is a root extension.
Abstract: Let D be an integral domain with quotient field K, D denote the integral closure of D in K and ∗ be a star-operation on D. In this paper, we study the ∗-Nagata ring of AP∗MDs. More precisely, we show that D is an AP∗MD and D[X] ⊆ D[X] is a root extension if and only if the ∗-Nagata ring D[X]N∗ is an AB-domain, if and only if D[X]N∗ is an AP-domain. We also prove that D is a P∗MD if and only if D is an integrally closed AP∗MD, if and only if D is a root closed AP∗MD.
TL;DR: In this article, the authors considered Fekete-Szeg problem with complex parameter and also found upper bound of the second Hankel determinant for functions belonging to a new class using Toeplitz determinants.
Abstract: In the present investigation we consider Fekete-Szeg problem with complex parameter and also find upper bound of the second Hankel determinant for functions belonging to a new class using Toeplitz determinants.
TL;DR: Some inclusion relations are obtained involving these sequence spaces of fuzzy real numbers with fuzzy metric of solidness, sym- metricity, convergence-free etc.
Abstract: The sequence spaces c F (M ), c F (M ) and l F (M ) of fuzzy real numbers with fuzzy metric are introduced. Some properties of these sequence spaces like solidness, sym- metricity, convergence-free etc. are studied. We obtain some inclusion relations involving these sequence spaces.
TL;DR: In this paper, the authors introduce difference paranormed sequence spaces, which are de-fineed by a Musielak-Orlicz function over n-normed spaces.
Abstract: In the present paper we introduce difference paranormed sequence spaces c0(M; ∆ n;p;u;jj ; ;jj ), c(M; ∆ n;p;u;jj ; ;jj ) and l1(M; ∆ n;p;u;jj ; ;jj ) de- fined by a Musielak-Orlicz function M = (Mk) over n-normed spaces. We also study some topological properties and some inclusion relations between these spaces.
TL;DR: In this paper, strong convergence of Halpern's iteration for a countable family of strongly relatively nonexpansive mappings in the framework of uniformly convex and uniformly smooth Banach spaces is investigated.
Abstract: We investigate strong convergence of Halpern’s iteration for a countable family of strongly relatively nonexpansive mappings in the framework of uniformly convex and uniformly smooth Banach spaces. Our results extend those announced by many authors.
TL;DR: In this paper, three more right Jacobson-type radicals, J r g, were introduced for near-rings which generalize the Jacobson radical of rings, 2 f0;1;2g.
Abstract: In this paper three more right Jacobson-type radicals, J r g , are introduced for near-rings which generalize the Jacobson radical of rings, 2 f0;1;2g. It is proved that J r g is a special radical in the class of all near-rings. Unlike the known right Jacobson semisimple near-rings, a J r g -semisimple near-ring R with DCC on right ideals is a direct sum of minimal right ideals which are right R-groups of type-g , 2 f0;1;2g. Moreover, a nite right g2-primitive near-ring R with eRe a non-ring is a near-ring of matrices over a near-eld (which is isomorphic to eRe), where e is a right g2-primitive idempotent in R.
TL;DR: This paper gives a necessary condition for a virtual knot invariant to be of finite type by using t(a1, · · · , am)–sequences of virtual knots and shows that the higher derivatives f (n) K (a) of the f–polynomial fK(A) of a virtual knots K at any point a are not of finiteType unless n ≤ 1 and a = 1.
Abstract: In [9], Kauffman introduced virtual knot theory and generalized many classical knot invariants to virtual ones. For example, he extended the Jones polynomials VK(t) of classical links to the f–polynomials fK(A) of virtual links by using bracket polynomials. In [4], M. Goussarov, M. Polyak and O. Viro introduced finite type invariants of virtual knots. In this paper, we give a necessary condition for a virtual knot invariant to be of finite type by using t(a1, · · · , am)–sequences of virtual knots. Then we show that the higher derivatives f (n) K (a) of the f–polynomial fK(A) of a virtual knot K at any point a are not of finite type unless n ≤ 1 and a = 1.
TL;DR: In this article, two uniqueness theorem on meromorphic functions sharing one value was proved and a relaxation of the nature of sharing value from CM to IM was also discussed, which generalizes a recent result of R. S. Dyavanal 2.
Abstract: In this paper, we prove two uniqueness theorem on meromorphic functions sharing one value which generalize a recent result of R. S. Dyavanal 2, and on the other hand, we relax the nature of sharing value from CM to IM.
TL;DR: In this paper, almost pseudo conharmonically symmetric manifolds have been studied under certain curvature conditions, and three examples of such manifolds are given in terms of geometric properties.
Abstract: The object of the present paper is to study almost pseudo conharmonically symmetric manifolds. Some geometric properties of almost pseudo conharmonically sym- metric manifolds have been studied under certain curvature conditions. Finally, we give three examples of almost pseudo conharmonically symmetric manifolds.