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Existence of Periodic Solutions for Nonlinear Neutral Dynamic Equations with Functional Delay on a Time Scale

Abdelouaheb Ardjouni, Ahcène Djoudi (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Let 𝕋 be a periodic time scale. The purpose of this paper is to use a modification of Krasnoselskii’s fixed point theorem due to Burton to prove the existence of periodic solutions on time scale of the nonlinear dynamic equation with variable delay x ▵ t = - a t h x σ t + c ( t ) x ▵ ˜ t - r t + G t , x t , x t - r t , t ∈ 𝕋 , where f ▵ is the ▵ -derivative on 𝕋 and f ▵ ˜ is the ▵ -derivative on ( i d - r ) ( 𝕋 ) . We invert the given equation to obtain an equivalent integral equation from which we define a fixed point mapping written as a sum of a large contraction and a compact map. We show...

Extensional subobjects in categories of Ω -fuzzy sets

Jiří Močkoř (2007)

Czechoslovak Mathematical Journal

Two categories 𝕊𝕖𝕥 ( Ω ) and 𝕊𝕖𝕥𝔽 ( Ω ) of fuzzy sets over an M V -algebra Ω are investigated. Full subcategories of these categories are introduced consisting of objects ( s u b ( A , δ ) , σ ) , where s u b ( A , δ ) is a subset of all extensional subobjects of an object ( A , δ ) . It is proved that all these subcategories are quasi-reflective subcategories in the corresponding categories.

Extensions of fuzzy connectives on ACDL

Hui Liu, Bin Zhao (2019)

Kybernetika

The main goal of this paper is to construct fuzzy connectives on algebraic completely distributive lattice(ACDL) by means of extending fuzzy connectives on the set of completely join-prime elements or on the set of completely meet-prime elements, and discuss some properties of the new fuzzy connectives. Firstly, we present the methods to construct t-norms, t-conorms, fuzzy negations valued on ACDL and discuss whether De Morgan triple will be kept. Then we put forward two ways to extend fuzzy implications...

Extensions of group retractions.

Byrd, Richard D., Lloyd, Justin T., Mena, Roberto A., Teller, J.Roger (1980)

International Journal of Mathematics and Mathematical Sciences

Extensions of partially ordered partial abelian monoids

Sylvia Pulmannová (2006)

Czechoslovak Mathematical Journal

The notion of a partially ordered partial abelian monoid is introduced and extensions of partially ordered abelian monoids by partially ordered abelian groups are studied. Conditions for the extensions to exist are found. The cases when both the above mentioned structures have the Riesz decomposition property, or are lattice ordered, are treated. Some applications to effect algebras and MV-algebras are shown.

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