Showing papers in "International Journal of Mathematics and Mathematical Sciences in 1993"
TL;DR: In this paper, sufficient conditions are obtained for the global asymptotic stability of the positive equilibrium of a regulated logistic growth with a delay in the state feedback of the control modelled by.
Abstract: Sufficient conditions are obtained for the global asymptotic stability of the positive equilibrium of a regulated logistic growth with a delay in the state feedback of the control modelled by
122 citations
TL;DR: In this article, the relatioship between the asymptotic equivalence of two-sequences ( lim n x n / y n = 1 ) and three variatious of this equivalence for a sequence-to-sequence transformation was studied.
Abstract: This paper is a study of the relatioship. between the asymptotic equivalence of two
sequences ( lim n x n / y n = 1 ) and three variatious of this equivalence for a sequence-to-sequence
transformation A , the three variations are give by the ratios R m A x / R m A y . S m A x / S m A y , And μ m A x / μ m A y , where R m A z : = ∑ n ≥ m | ( A z ) n | , S m A z : = ∑ n ≤ m | ( A z ) n | , and μ m A z : = sup n ≥ m | ( A z ) n | .
85 citations
TL;DR: In this paper, the existence of ( ϵ )-almost contact metric structures and examples of Sasakian manifolds was shown and a classification theorem for real hypersurfaces of indefinite complex space-forms with parallel structure vector field was given.
Abstract: We show the existence of ( ϵ )-almost contact metric structures and give examples of ( ϵ )-Sasakian manifolds. Then we get a classification theorem for real hypersurfaces of indefinite complex space-forms with parallel structure vector field. We prove that ( ϵ )-Sasakian real hypersurfaces of a semi-Euclidean space are either open sets of the pseudosphere S2S2n
79 citations
TL;DR: In this article, a collection of fixed point theorems is generalized by replacing hypothesized commutativity or weak commutivity of functions involved by compatibility, and a set of fixed-point functions are replaced with fixed point functions by compatibility.
Abstract: A collection of fixed point theorems is generalized by replacing hypothesized commutativity or weak commutativity of functions involved by compatibility.
64 citations
TL;DR: In this paper, a new class TP(α) of meromorphic functions with positive coefficients in D =z:0l|z|l1 was introduced, and the aim of the present paper is to prove some properties for the class Tp(α).
Abstract: In this paper, we introduce a new class TP(α) of meromorphic functions with positive coefficients in D={z:0l|z|l1}. The aim of the present paper is to prove some properties for the class Tp(α).
37 citations
TL;DR: In this paper, the spectral analysis of differential forms on the disk was extended to the Riemann sphere S 2, and a concrete orthogonal base in the Hilbert space L ν, 2 (S 2 ) was determined.
Abstract: We extend the spectral analysis of differential forms on the disk (viewed as the
non-Euclidean plane) in recent work by J. Peetre L. Peng G. Zhang to the dual situation of
the Riemann sphere S 2 . In particular, we determine a concrete orthogonal base in the relevant
Hilbert space L ν , 2 ( S 2 ) , where − ν 2 -is the degree of the form, a section of a certain holomorphic
line bundle over the sphere S 2 . It turns out that the eigenvalue problem of the corresponding
invariant Laplacean is equivalent to an infinite system of one dimensional Schrodinger operators.
They correspond to the Morse potential in the case of the disk. In the course of the discussion
many special functions (hypergeometric functions, orthogonal polynomials etc.) come up. We
give also an application to Ha-plitz theory.
29 citations
TL;DR: In this paper, the concept of compatible mappings of type (A) on a metric space was introduced, which is equivalent to the notion of compatible mapping under some conditions, and gave a common fixed point theorem of Meir and Keeler type.
Abstract: In this paper, we introduce the concept of compatible mappings of type (A) on a metric space, which is equivalent to the concept of compatible mappings under some conditions, and give a common fixed point theorem of Meir and Keeler type. Our result extends, generalized and improves some results of Meir-Keeler, Park-Bae, Park-Rhoades, Pant and Rao-Rao, etc.
22 citations
TL;DR: In this article, it was shown that T has a unique fixed point in K and the condition T(∂K)⫅K. This result generalizes the corresponding theorem of Assad [2] and improves the Theorem of Rhoades [1].
Abstract: Let X be a Banach space, K a non-empty closed subset of X and T:K→X a mapping satisfying the contractive definition (1.1) below and the condition T(∂K)⫅K. Then T has a unique fixed point in K. This result improves Theorem of Rhoades [1] and generalizes the corresponding theorem of Assad [2].
21 citations
TL;DR: In this paper, the first order and second order piecewise polynomial finite approximation schemes for the computation of invariant measures of a class of nonsingular measurable transformations on the unit interval of the real axis were constructed.
Abstract: We construct in this paper the first order and second order piecewise polynomial finite approximation schemes for the computation of invariant measures of a class of nonsingular measurable transformations on the unit interval of the real axis. These schemes are based on the Galerkin's projection method for L1-spaces and are proved to be convergent for the class of Frobenius-Perron operators.
19 citations
TL;DR: In this article, the authors discuss congruences involving the function c ϕ m ¯ ( n ), which denotes the number of generalized Frobenius partitions of n with m colors whose order is cyclic under cyclic permutation of the m colors.
Abstract: The goal of this paper is to discuss congruences involving the function c ϕ m ¯ ( n ) ,
which denotes the number of generalized Frobenius partitions of n with m colors whose order is
m under cyclic permutation of the m colors.
18 citations
TL;DR: Several important lnetric space fixed point theorems are proved for a lnrge class of non-metric spaces in this paper, which is surprising since the distance function used need not be symmetric and need not have a constant number of vertices.
Abstract: Several important lnetric space fixed point theorems are proved for a lnrge class of non-metric spaces. In some cases the metric space proofs need only minor changes. This is surprising since the distance function used need not be symmetric and need not sa.tisfy the
TL;DR: In this article, two topologies on the set of all continuous real-valued functions on a Tychonoff space which lie between the topologies of compact convergence and uniform convergence are studied.
Abstract: This paper studies two topologies on the set of all continuous real-valued functions
on a Tychonoff space which lie between the topologies of compact convergence and uniform
convergence.
TL;DR: In this paper, the concept of relatively nonexpansive maps is introduced and fixed point and coincidence results for families of four self-maps of metric spaces are obtained, and two theorems of Dotson are generalized.
Abstract: The concept of relatively nonexpansive maps is introduced. Fixed point and coincidence results for families of four self maps of metric spaces are obtained. Non-continuous compatible and relatively nonexpansive maps on star-shaped compact subsets of normed linear spaces are highlighted, and two theorems of Dotson are generalized.
TL;DR: In this paper, the authors derived new classes of infinite products taken over the primes of Riemann zeta functions, for example, ∏ p ( 1 1 − p − n ) ( 1 −p − m ) − 1 / β, which is an infinite produce over the set of rational numbers α / β geater than zero with a relatively prime to β ζ ( n ) ∏ α, β ε ( α m + β n ) 1/ β.
Abstract: We derive new classes of infinite products taken over the primes, for example
expressing
∏ p ( 1 1 − p − n ) ( 1 − p − m ) − 1
as an infinite produce of Riemann zeta functions, this product being taken over the set of rational
numbers α / β geater than zero with a relatively prime to β ζ ( n ) ∏ α , β ζ ( α m + β n ) 1 / β .
TL;DR: In this article, the authors consider a mapping S of the form S = α 0 I + α 1 T + α 2 T 2 + α K T K, where α i ≥ 0. 0$ and show that in a uniformly convex Banach space, the Picard iterates of S converges to a fixed point of T when T is nonexpansive or generalized nonexpanive or even quasinonexpansive.
Abstract: In this paper we consider a mapping S of the form
S = α 0 I + α 1 T + α 2 T 2 + … + α K T K ,
where α i ≥ 0 . 0$" xmlns:mml="http://www.w3.org/1998/Math/MathML"> α 1 > 0 with ∑ i = 0 k α i = 1 , and show that in a uniformly convex Banach space the Picard iterates
of S converge to a fixed point of T when T is nonexpansive or generalized nonexpansive or even quasinonexpansive.
TL;DR: In this article, some results on fixed points of involution maps in 2-Banach spaces have been obtained, which are extensions of those proved earlier by Goebel-Zlotkiewicz, Sharma-Sharma, Assad-Sessa and Iśeki.
Abstract: Some results on fixed points of involution maps in 2-Banach spaces have been obtained. These are extensions of those proved earlier by Goebel-Zlotkiewicz, Sharma-Sharma, Assad-Sessa and Iśeki.
TL;DR: In this article, it was shown that every ring with a finite maximal subring is a finite ring and it is conjectured that every PI-ring with a maximal sub-ring is finite.
Abstract: It is conjectured that every ring with a finite maximal subring is finite. We prove this conjecture for PI-rings.
TL;DR: In this article, the existence of a weak solution for the initial-boundary value problem is established for the system ff-iut-div(O(u)7u)+r(u,a,u)TuTv=a(u))Tvl2,div(a,U)Vv)=O.
Abstract: Existence of a weak solution is established for the initial-boundary value problem for the system ff-iut-div(O(u)7u)+r(u)a(u)TuTv=a(u))Tvl2,div(a(u)Vv)=O. The question of uniqueness is also considered in some special cases.
TL;DR: In this paper, the authors show that T∘∘ is equivalent to the topology induced on H(X) by the Pervin quasi-uniformity on X.
Abstract: Let (X,T) and (Y,T*) be topological spaces and let F⊂YX. For each U∈T, V∈T*, let (U,V)={f∈F:f(U)⊂V}. Define the set S∘∘={(U,V):U∈T and V∈T*}. Then S∘∘ is a subbasis for a topology, T∘∘ on F, which is called the open-open topology. We compare T∘∘ with other topologies and discuss its properties. We also show that T∘∘, on H(X), the collection of all self-homeomorphisms on X, is equivalent to the topology induced on H(X) by the Pervin quasi-uniformity on X.
TL;DR: In this article, the authors investigated the heating of the solar corona by the resonant absorption of Alfven waves in a viscous and isothermal atmosphere permeated by a horizontal magnetic field.
Abstract: In this paper, we will investigate the heating of the solar corona by the resonant absorption of Alfven waves in a viscous and isothermal atmosphere permeated by a horizontal magnetic field. It is shown that if the viscosity dominates the motion in a high (low)- β plasma, it creates an absorbing and reflecting layer and the heating process is acoustic (magnetoacoustic). When the magnetic field dominates the oscillatory process it creates a non-absorbing reflecting layer. Consequently, the heating process is magnetohydrodynamic. An equation for resonance is derived. It shows that resonances may occur for many values of the frequency and of the magnetic field if the wavelength is matched with the strength of the magnetic field. At the resonance frequencies, magnetic and kinetic energies will increase to very large values which may account for the heating process. When the motion is dominated by the combined effects of the viscosity and the magnetic field, the nature of the reflecting layer and the magnitude of the reflection coefficient depend on the relative strengths of the magnetic field and the viscosity.
TL;DR: Some existence theorems for the general implicit complementarity problem in an infinite dimensional space are considered in this paper, where the authors consider the problem in the context of infinite-dimensional spaces.
Abstract: Some existence theorems for the general implicit complementarity problem in an infinite dimensional space are considered.
TL;DR: In this article, it was shown that a digraph D is an antipodal digraph if and only if D is the antipodial digraph of its complement, where the arc (u, v) is included in A(D) if d(u,v) is the diameter of D.
Abstract: The antipodal graph of a graph G, denoted by A(G), has the same vertex set as G with an edge joining vertices u and v if d(u,v) is equal to the diameter of G. (If G is disconnected, then diam G=∞.) This definition is extended to a digraph D where the arc (u,v) is included in A(D) if d(u,v) is the diameter of D. It is shown that a digraph D is an antipodal digraph if and only if D is the antipodal digraph of its complement. This generalizes a known characterization for antipodal graphs and provides an improved proof. Examples and properties of antipodal digraphs are given. A digraph D is self-antipodal if A(D) is isomorphic to D. Several characteristics of a self-antipodal digraph D are given including sharp upper and lower bounds on the size of D. Similar results are given for self-antipodal graphs.
TL;DR: In this paper, the authors investigated the infinitary analogues of such familiar number theoretic functions as the divisor sum function, Euler's phi function and the Mbbius function.
Abstract: The infinitary divisors of a natural number n are the products of its divisors of the form pu2, where pV is a prime-power component of n and ya2 (where ya 0 or 1) is the binary representation of y. In this paper, we investigate the infinitary analogues of such familiar number theoretic functions as the divisor sum function, Euler's phi function and the Mbbius function.
TL;DR: In this article, an array of rowwise independent random elements in a sep- arable Banach space of type r, 1 r < r r < 2, complete convergence of n )/p X. to 0 k=l
Abstract: Let {X,} be an array of rowwise independent random elements in a sep- arable Banach space of type r, 1 _< r _< 2. Complete convergence of n )/p X. to 0 k=l
TL;DR: In this paper, zero-one measure characterizations of lattice properties such as normality are extended to more general measures and necessary and sufficient conditions for the measure and outer measures to be equal on the lattice or its complement are provided.
Abstract: Zero-one measure characterizations of lattice properties such as normality are
extended to more general measures. For a given measure, we consider two associated outer
measures and attempt to obtain the outer-measurable sets. We also seek necessary and sufficient
conditions for the measure and outer measures to be equal on the lattice or its complement.
TL;DR: In this article, the geometry of an arbitrary multiply connected bounded region in R 3 together with the mixed boundary conditions, from the complete knowledge of the eigenvalues {,}= for the negative Laplacian, using the asymptotic expansion of the spectral function O(t)= ezp(- tA) as t-,O.
Abstract: The basic problem in this paper is that of detemnining the geometry of an arbitrary multiply connected bounded region in R 3 together with the mixed boundary conditions, from the complete knowledge of the eigenvalues {,}= for the negative Laplacian, using the asymptotic expansion of the spectral function O(t)= ezp(- tA) as t-,O.
TL;DR: In this paper, the authors introduce a new formulation of the theory of continuous spectrum eigenfunction expansions for self-adjoint operators and analyze the question of when operators may be approximated in an operator norm by finite sums of multiples of eigenprojections of multiplicity one.
Abstract: In this paper, we introduce a new formulation of the theory of continuous spectrum eigenfunction expansions for self-adjoint operators and analyze the question of when operators may be approximated in an operator norm by finite sums of multiples of eigenprojections of multiplicity one. The theory is designed for application to ordinary and partial differential equations; relationships between the abstract theory and differential equations are worked out in the paper. One motivation for the study is the question of whether these expansions are susceptible to computation on a computer, as is known to be the case for many examples in the discrete spectrum case. The point of the paper is that continuous and discrete spectrum eigenfunction expansions are treated by the same formalism; both are limits in an operator norm
TL;DR: Somenewcoincidence point and fixed pointtheorems formultivaluedmappings incomplete metric space are proved in this paper, and the results presented in this paper enrich and extend the corresponding results
Abstract: Somenewcoincidence pointandfixed pointtheorems formultivaluedmappings incomplete metric space are proved. The results presented in this paper enrich and extend the corresponding results
TL;DR: In this article, the general solution of a conditional Cauchy functional equation of several variables is obtained and its applications to the characterizations of multivariate stable distributions are studied, and its application to the analysis of stable distributions is discussed.
Abstract: The general solution of a conditional Cauchy functional equation of several variables is obtained and its applications to the characterizations of multivariate stable distributions are studied.
TL;DR: In this paper, the weak-star convergence of orthogonal polynomials w.r.t, varying measures has been studied in the unit circle in the complex plane.
Abstract: We point out the relation between the orthogonal polynomials with respect to
(w.r.t.) varying measures and the so-called orthogonal rationals on the unit circle in the complex
plane. This observation enables us to combine different techniques in the study of these
polynomials and rationals. As an example, we present a simple and short proof for a known result
on the weak-star convergence of orthogonal polynomials w.r.t, varying measures. Some related
problems are also considered.