Duality in the optimal harvesting for a nonlinear age-spatial structured population dynamic model is studied in the framework of optimal control problem. In this paper the duality theory that displays the conjugacy of the primal problem is established and an application is given. Duality theory plays an important role in both optimization theory and methodology and the results may be applied to a realistic biological system on the point of optimal harvesting.

Related fixed point theorems on two or three metric spaces have been prove in different ways. However, so for the related fixed point theorem on fuzzy metric space have not been proved. Sharma, Deshpande and Thakur were the first who have establishe related fixed point theorem for four mappings on two complete fuzzy metric spaces. Their work was maiden in this line. In this paper we obtain a related fixed point theorem for six mappings on three complete fuzzy metric spaces. Of course this is a new result on this line.

We study Baer and quasi-Baer modules over some classes of rings. We also introduce a new class of modules called AI-modules, in which the kernel of every nonzero endomorphism is contained in a proper direct summand. The main results obtained here are: (1) A module is Baer iff it is an AI-module and has SSIP. (2) For a perfect ring R, the direct sum of Baer modules is Baer iff R is primary decomposable. (3) Every injective R-module is quasi-Baer iff R is a QI-ring.

The aim of this paper is to introduce and study the sequence spaces [w, , F, p, q], [w, , F, p, q] and [w, , F, p, q], which arise from the notions of generalized difference sequence space, lacunary convergence, invariant mean and a sequence of Moduli . We establish some inclusion relations between these spaces under some conditions.

In this paper we give a non-existence theorem for Hopf hypersurfaces M in complex two-plane Grassmannians whose normal Jacobi operator is parallel on the distribution F defined by , where [] = Span{}, = Span {, , } and , .

In the present paper, we are concerned with subordination problems related to -Robertson function. The radii of -spirallikeness and starlikeness of -Robert function are also determined.

In this paper, making use of transformation due to S. N. Singh [21], an at-tempt has been made to establish certain results involving basic bilateral hypergeometric series and continued fractions.

In this article we introduce the notion of b-locally open sets, sets, sets in bitopological spaces and obtain several characterizations and some properties of these sets.

The Chebyshev collocation method in [21] to solve stiff initial-value problems is generalized by using arbitrary degrees of interpolation polynomials and arbitrary collocation points. The convergence of this generalized Chebyshev collocation method is shown to be independent of the chosen collocation points. It is observed how the stability region does depend on collocation points. In particular, A-stability is shown by taking the mid points of nodes as collocation points.

We consider pseudo-symmetric and Ricci generalized pseudo-symmetric N() contact metric manifolds. We also consider N()-contact metric manifolds satisfying the condition = 0 where R and S denote the curvature tensor and the Ricci tensor respectively. Finally we give some examples.