We consider the Dirac-type operators D + a, a is a paravector in the Clifford algebra. For this operator we state a Cauchy-Green formula in the spaces and . Further, we consider the Cauchy problem for this operator.
In this work, we establish new Furi–Pera type fixed point theorems for the sum and the product of abstract nonlinear operators in Banach algebras; one of the operators is completely continuous and the other one is -Lipchitzian. The Kuratowski measure of noncompactness is used together with recent fixed point principles. Applications to solving nonlinear functional integral equations are given. Our results complement and improve recent ones in [10], [11], [17].
The paper is concerned with the Nemitskii operator in Hölder spaces. Namely conditions are given to ensure acting, continuity, Lipschitz and differentiability properties.
In the paper, three different ways of constructing distances between vaguely described objects are shown: a generalization of the classic distance between subsets of a metric space, distance between membership functions of fuzzy sets and a fuzzy metric introduced by generalizing a metric space to fuzzy-metric one. Fuzzy metric spaces defined by Zadeh’s extension principle, particularly to are dealt with in detail.