Volume 108, Issue 2
June 1998, pages 95-215
pp 95-108 June 1998
In this paper we first discuss refinement of the Ramunujan asymptotic expansion for the classical hypergeometric functionsF(a,b;c;x), c ≤a + b, near the singularityx = 1. Further, we obtain monotonous properties of the quotient of two hypergeometric functions and inequalities for certain combinations of them. Finally, we also solve an open problem of finding conditions ona, b > 0 such that 2F(−a,b;a +b;r2) < (2−r2)F(a,b;a +b;r2) holds for all r∈(0,1).
pp 109-120 June 1998
The paper studies the degree of approximation of functions associated with Hardy Littlewood series in the generalized Hölder metric.
pp 121-131 June 1998
In this paper, we obtain some results on certain differential polynomials. We use the techniques of Hayman and Yang Lo. The results of Fred Gross on fix-points will be improved and generalized.
pp 133-136 June 1998
In this paper we prove that if a ringR satisfies the condition that for some integern > 1,an =a for everya inR, thenR a hopfian ring implies that the ringR [T] of polynomials is also hopfian. This generalizes a recent result of Varadarajan which states that ifR is a Boolean hopfian ring then the ringR[T] is also hopfian. We show furthermore that there are numerous ringsR satisfying the hypothesis of our theorem which are neither Boolean nor Noetherian.
pp 137-149 June 1998
In this paper we give a homotopy classification of symplectic isometric immersions following Gromov’sh-principle theorem.
pp 151-162 June 1998
This paper presents a translation of a theorem of Cartan into an equivariant setting. This work is largely based on the study of the homotopical algebra in the sense of Quillen of the category of simplicial objects over the category of rationalOg-vector spaces. The application is a solution to the equivariant commutative cochain problem. This solution is slightly better than the solution obtained earlier by Triantafillou in that the transformation groupG need not be finite.
pp 163-167 June 1998
In this paper, we use the game characterization of Kenderov and Moors  to construct an example of a non-fragmentable Banach space. More precisely, we will show that ifX is the tree-complete Banach algebra of Haydon and Zizler , (X/c0, weak) is not fragmentable by any metric. In particular, this shows thatX/c0 cannot be equivalently renormed to be rotund.
pp 169-177 June 1998
A class of evolution integrodifferential equation has been studied over the analytic semigroup of operators in a Banach space. Further the existence of weak and strong solutions in Banach space have been proved and extended to a maximum interval of existence.
pp 179-187 June 1998
In this paper we examine nonlinear parabolic problems with a discontinuous right hand side. Assuming the existence of an upper solution φ and a lower solution ψ such that ψ ≤ φ, we establish the existence of a maximum and a minimum solution in the order interval [ψ, φ]. Our approach does not consider the multivalued interpretation of the problem, but a weak one side “Lipschitz” condition on the discontinuous term. By employing a fixed point theorem for nondecreasing maps, we prove the existence of extremal solutions in [ψ, φ for the original single valued version of the problem.
pp 189-207 June 1998
The aim of this paper is to provide an alternate treatment of the homogenization of an optimal control problem in the framework of two-scale (multi-scale) convergence in the periodic case. The main advantage of this method is that we are able to show the convergence of cost functionals directly without going through the adjoint equation. We use a corrector result for the solution of the state equation to achieve this.
pp 209-215 June 1998
In the context of the linear theory of thermoelasticity without energy dissipation for homogeneous and isotropic materials, variational principles of Biot-and Hamilton-types and a reciprocal principle of Betti-Rayleigh-type are presented.