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Sylvester inertia law in commutative Leibniz algebras with logarithms

Przeworska-Rolewicz D.

Demonstratio Mathematica

2007

Vol. 40, nr 3

659-669

In algebras with logarithms induced by a given right invertible operator D one can define quadratic forms by means of power mappings induced by logarithmic mapping. Main results of this paper will be concerned with the case when an algebra X under consideration is commutative and has a unit and the operator D satisfies the Leibniz condition, i.e. D(xy) = xDy+yDx for x, y is an element of dom D. If X is an locally m-convex algebra then these forms have the similar properties as quadratic forms in the Euclidian spaces En, including the Sylvester inertia law.

The integral inequalities for alpha-star-convex functions

Kanas S., Kowalczyk J.

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

2001

z. 25 [190]

71-80

Let alphis an element of [0,1]. A function f :I -> R (0 is an element of I) is said to be alpha-star-convex on [...]. In this note we will present new geometric interpretation of alpha-star-convex functions and some Hadamards' like integral inequalities for such functions.

The constant limits of sequences of defective random elements

Startek M.

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

2000

z. 24 [181]

117-123

Let X, X1, X2,... be random elements. It is known, that if the sequence {Xn, n > 1} converges vaguely in probability to the random element X, then this sequence converges also vaguely to X, but not converse. In this paper it is proved, that if the limit random element X is constant, then the converse is true, i.e. if the sequence converges vaguely, then it also converges vaguely in probability. A similar dependence we have for convergences vaguely essentionaly and vaguely almost surely.

A new generalization of browder fixed point theorem with applications

Wu X., Xu Y.

Journal of Applied Analysis

1998

Vol. 4, nr 2

205-214

In the present paper, a new generalization of Browder fixed point theorem is obtained. As its applications, we obtain some generalized versions of Browder's theorems for quasivariational inequality and Ky Fan's minimax inequality and minimax principle.