International Journal of Mathematics and Mathematical Sciences

List of Papers (Total 206)

On the Hankel determinants of close-to-convex univalent functions

The rate of growth of Hankel determinant for close-to-convex functions is determined. The results in this paper are best possible.

Closed spectral measures in Fréchet spaces

Closed spectral measures, which are often used in the theory of operators, have the desirable property that their L1-space is complete. In this note criteria are given which assure the closedness of spectral measures acting in Fréchet spaces.

A note on generalized harmonic-Cesàro summability

This note shows that conjectures proposed by G. Das and P.C. Mohapatra [1] on inclusion relations between two generalized Harmonic-Cesàro methods of summability, are true.

Finite p′-nilpotent groups. I

In this paper we consider finite p′-nilpotent groups which is a generalization of finite p-nilpotent groups. This generalization leads us to consider the various special subgroups such as the Frattini subgroup, Fitting subgroup, and the hypercenter in this generalized setting. The paper also considers the conditions under which product of p′-nilpotent groups will be a p...

An energy concerving modification of numerical methods for the integration of equations of motion

In the integration of the equations of motion of a system of particles, conventional numerical methods generate an error in the total energy of the same order as the truncation error. A simple modification of these methods is described, which results in exact conservation of the energy.

An inequality of W. L. Wang and P. F. Wang

In this note we present a proof of the inequality Hn/H′n≤Gn/G′n where Hn and Gn (resp. H′n and G′n) denote the weighted harmonic and geometric means of x1,…,xn (resp. 1−x1,…,1−xn) with xi∈(0,1/2], i=1,…,n.

Measuring static complexity

The concept of “pattern” is introduced, formally defined, and used to analyze various measures of the complexity of finite binary sequences and other objects. The standard Kolmogoroff-Chaitin-Solomonoff complexity measure is considered, along with Bennett's ‘logical depth’, Koppel's ‘sophistication'’, and Chaitin's analysis of the complexity of geometric objects. The pattern...

Note on pointwise contractive projections

Let C(X) be the space of real-valued continuous functions on a Hausdorff completely regular topological space X. endowed with the compact-open topology. In this paper necessary and sufficient conditions are given for a subspace of C(X) to be the range of a pointwise contractive projection in C(X).

An oscillation criterion for inhomogeneous Stieltjes integro-differential equations

The aim of the paper is to give an oscillation theorem for inhomogeneous Stieltjes integro-differential equation of the form p(t)x′

Product involutions with 0 or 1-dimensional fixed point sets on orientable handlebodies

Let h be an involution with a 0 or 1-dimensional fixed point set on an orientable handlebody M. We show that obvious necessary conditions for fibering M as A×I so that h=τ×r with τ an involution of A and r reflection about the midpoint of I also turn out to be sufficient. We also show that such a “product” involution is determined by its fixed point set.

Decay of solutions of a nonlinear hyperbolic system in noncylindrical domain

In this paper we study the existence of solutions of the following nonlinear hyperbolic svstem|u″

Almost principal element lattices

In this paper, we investigate C-lattices for which every localization is a principal element lattice.

Existence theorems for a second order m-point boundary value problem at resonance

Let f:[0,1]×R2→R be function satisfying Caratheodory's conditions and e(t)∈L1[0,1]. Let η∈(0,1), ξi∈(0,1), ai≥0, i=1,2,…,m−2, with ∑i=1m−2ai=1, 0<ξ1<ξ2<…<ξm−2<1 be given. This paper is concerned with the problem of existence of a solution for the following boundary value problems x″(t)=f(t,x(t),x′(t))

Turán inequalities for symmetric orthogonal polynomials

A method is outlined to express a Turán determinant of solutions of a three term recurrence relation as a weighted sum of squares. This method is shown to imply the positivity of Turán determinants of symmetric Pollaczek polynomials, Lommel polynomials and q-Bessel functions.

Boundary value problems for the diffusion equation with piecewise continuous time delay

A study is made of partial differential equations with piecewise constant arguments. Boundary value problems for three types of equations are discussed delayed; alternately of advanced and retarded type; and most importantly, an equation of neutral type (that is, including the derivative at different values of time t).

n-Color partitions with weighted differences equal to minus two

In this paper we study those n-color partitions of Agarwal and Andrews, 1987, in which each pair of parts has weighted difference equal to −2 Results obtained in this paper for these partitions include several combinatorial identities, recurrence relations, generating functions, relationships with the divisor function and computer produced tables. By using these partitions an...

Some remarks concerning finitely Subadditive outer measures with applications

The present paper is intended as a first step toward the establishment of a general theory of finitely subadditive outer measures. First, a general method for constructing a finitely subadditive outer measure and an associated finitely additive measure on any space is presented. This is followed by a discussion of the theory of inner measures, their construction, and the...

Common fixed points of biased maps of type (A) and applications

A generalization of compatible maps of type (A) called “biased maps of type (A)” is introduced and used to prove fixed point theorems for certain contractions of four maps. Extensions of known results are thereby obtained, i.e., the results of Pathak, Prasad, Jungck et al. are improved. Some problems on convergence of self-maps and fixed points are also discussed. Further, we use...

Common fixed point theorems for semigroups on metric spaces

This paper consists of two main results. The first one shows that if S is a left reversible semigroup of selfmaps on a complete metric space (M,d) such that there is a gauge function φ for which d(f(x),f(y))≤φ(δ(Of (x,y))) for f∈S and x,y in M, where δ(Of (x,y)) denotes the diameter of the orbit of x,y under f, then S has a unique common fixed point ξ in M and, moreover, for any...

ℵ1-directed inverse systems of continuous images of arcs

The main purpose of this paper is to prove that if X={Xa,pab,A} is a usual ℵ1-directed inverse system of continuous images of arcs with monotone bonding mappings, then X=limX is a continuous image of an arc (Theorem 2.4). Some applications of this statement are also given.

A note on the comparison of topologies

A considerable problem of some bitopological covering properties is the bitopological unstability with respect to the presence of the pairwise Hausdorff separation axiom. For instance, if the space is RR-pairwise paracompact, its two topologies will collapse and revert to the unitopological case. We introduce a new bitopological separation axiom τS2σ which is appropriate for the...

Sufficient conditions for meromorphic starlikeness and close-to-convexity of order α

The object of the present paper is to derive a property of certain meromorphic functions in the punctured unit disk. Our main theorem contains certain sufficient conditions for starlikeness and close-to-convexity of order α of meromorphic functions.

On the Bohr transform of almost-periodic solutions for some differential equations in abstract spaces

We consider abstract differential equations of the form u′(t)=Au(t)