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, 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.

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.

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...

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.

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.

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...

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).

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

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.

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

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

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))

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.

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).

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...

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...

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...

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...

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 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...

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.

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

Using the concept of w-distance, we improve some well-known fixed point theorems.