We describe for any Riemannian manifold M a certain scheme ML, lying in between the first and second neighbourhood of the diagonal of M . Semiconformal maps between Riemannian manifolds are then analyzed as those maps that preserve ML; harmonic maps are analyzed as those that preserve the (LeviCivita-) mirror image formation inside ML. Introduction For any Riemannian manifold M , we describe a ...

This work aims to generalize the Banach contraction theorem M-fuzzy cone metric spaces. We construct generalized contractive conditions for three self mappings with which they have a unique common fixed point.

Trapezoid maps are a kind of continuous and piecewise linear maps with a flat top. By the conjugacy relationship, we present a complete classification for four families of trapezoid maps. Firstly, using an extension method, we construct all homeomorphic solutions of conjugacy equation φ ◦ f = g ◦ φ for some non-monotone continuous maps f and g. Secondly, using an iterative construction method a...

Abstract In this paper, the generalized Kannan-type contraction in cone metric spaces over Banach algebras is introduced. The fixed point theorems satisfying contractive conditions are obtained, without appealing to completeness of X or normality cone. continuity mapping relaxed. Furthermore, we prove that necessary if has a . These results greatly generalize several well-known comparable liter...

Let H(B) be the space of all holomorphic functions on the unit ball B in CN , and S(B) the collection of all holomorphic self-maps of B . Let φ ∈ S(B) and g ∈ H(B) with g(0) = 0 , the generalized composition operator is defined by C φ ( f )(z) = ∫ 1 0 R f (φ(tz))g(tz) dt t , Here, we characterize the boundedness and compactness of the generalized composition operator acting from Bloch-type spac...

Let g be a finite dimensional real Lie algebra. Let ρ : g → End(V ) be a representation of g in a finite dimensional real vector space. Let CV = ( End(V )⊗S(g) )g be the algebra of End(V )-valued invariant differential operators with constant coefficients on g. Let U be an open subset of g. We consider the problem of determining the space of generalized functions φ on U with values in V which a...