AN ANALOGY OF HAHN–BANACH SEPARATION THEOREM FOR NEARLY TOPOLOGICAL LINEAR SPACES

In this paper, we introduce the notion of nearly topological linear spaces and use it to formulate an alternative definition of the Hahn–Banach separation theorem. We also give an example of a topological linear space to which the result is not valid. It is shown that \(\mathbb{R}\) with its ordinary topology is not a nearly topological linear space.

The Fisher Separation Theorem And Capital Budgeting Decisions Of Quoted Firms In Nigeria

This study explored the Fisher separation theorem and capital budgeting decisions of quoted firms on the Nigerian stock exchange. A sample of 60 questionnaires were filled and returned by staffs from particular sectors like manufacturing, health and agriculture. Descriptive statistics was employed to illustrate the data while the Spearman rank order correlation test was used to determine if a significant relationship exist among the variables. From the estimates, the Net Present Value and Modified Internal Rate of Return are regularly employed by firms in making capital budgeting decisions. Also, when firms employ capital budgeting tools, it creates wealth for both managers and shareholders, providing support for the Fisher’s separation theorem. Finally, a correlation coefficient of 0.827 reflect a positive and linear relationship between capital budgeting decision and Shareholders’ value creation. Thus, an increase in capital budgeting decisions result to an increase in value creation. This outcome is consistent with findings from other economies and previous studies. It thus recommends that firms in the Nigerian environment should ensure they play down on shareholders’ desire for dividends and instead redirect their funds to more investments by employing suitable capital budgeting decisions.

A converse of Sturm's separation theorem

We show that Sturm's classical separation theorem on the interlacing of the zeros of linearly independent solutions of real second order two-term ordinary differential equations necessarily fails in the presence of a turning point in the principal part of the equation. Related results are discussed.

On a Separation Theorem for Delta-Convex Functions

In the present paper we establish necessary and sufficient conditions under which two functions can be separated by a delta-convex function. This separation will be understood as a separation with respect to the partial order generated by the Lorentz cone. An application to a stability problem for delta-convexity is also given.