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Non-Leibniz algebras with logarithms do not have the trigonometric identity

D. Przeworska-Rolewicz (2000)

Banach Center Publications

Let X be a Leibniz algebra with unit e, i.e. an algebra with a right invertible linear operator D satisfying the Leibniz condition: D(xy) = xDy + (Dx)y for x,y belonging to the domain of D. If logarithmic mappings exist in X, then cosine and sine elements C(x) and S(x) defined by means of antilogarithmic mappings satisfy the Trigonometric Identity, i.e. [ C ( x ) ] 2 + [ S ( x ) ] 2 = e whenever x belongs to the domain of these mappings. The following question arises: Do there exist non-Leibniz algebras with logarithms such that...

Nonlinear mixed Volterra-Fredholm integrodifferential equation with nonlocal condition

Haribhau L. Tidke, Machindra B. Dhakne (2012)

Applications of Mathematics

The aim of the present paper is to investigate the global existence of mild solutions of nonlinear mixed Volterra-Fredholm integrodifferential equations, with nonlocal condition. Our analysis is based on an application of the Leray-Schauder alternative and rely on a priori bounds of solutions.

On first order impulsive semilinear functional differential inclusions

Mouffak Benchohra, Johnny Henderson, Sotiris K. Ntouyas (2003)

Archivum Mathematicum

In this paper the Leray-Schauder nonlinear alternative for multivalued maps combined with the semigroup theory is used to investigate the existence of mild solutions for first order impulsive semilinear functional differential inclusions in Banach spaces.

On functional differential inclusions in Hilbert spaces

Myelkebir Aitalioubrahim (2012)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We prove the existence of monotone solutions, of the functional differential inclusion ẋ(t) ∈ f(t,T(t)x) +F(T(t)x) in a Hilbert space, where f is a Carathéodory single-valued mapping and F is an upper semicontinuous set-valued mapping with compact values contained in the Clarke subdifferential ∂ c V ( x ) of a uniformly regular function V.

Currently displaying 121 – 140 of 199