In this article, we studied the necessary conditions for univalence of integral operators that involve two functions: generalized Bessel function and a from well-known class normalized analytic functions in open unit disk. The main tools our discussions were Kudriasov univalency functions, as well functional inequalities functions. We included Bessel, modified spherical special cases. Furthermo...

We present Voevodsky’s construction of a model univalent type theory in the category simplicial sets. To this end, we first give general technique for constructing categorical models dependent theory, using universes to obtain coherence. then construct (weakly) universal Kan fibration, and use it exhibit Lastly, introduce Univalence Axiom, several equivalent formulations, show that holds our mo...

Cubical type theory provides a constructive justification to certain aspects of homotopy type theory such as Voevodsky’s univalence axiom. This makes many extensionality principles, like function and propositional extensionality, directly provable in the theory. This paper describes a constructive semantics, expressed in a presheaf topos with suitable structure inspired by cubical sets, of some...

Cubical type theory is an extension of Martin-Löf type theory recently proposed by Cohen, Coquand, Mörtberg and the author which allows for direct manipulation of n-dimensional cubes and where Voevodsky’s Univalence Axiom is provable. In this paper we prove canonicity for cubical type theory: any natural number in a context build from only name variables is judgmentally equal to a numeral. To a...

Let N be the set of all meromorphic functions f deened in the unit disc D that satisfy Nehari's univalence criterion (1 ? jzj 2) 2 jSf(z)j 2. In this paper we investigate certain properties of the class N. We obtain sharp estimates for the spherical distortion, and also a two-point distortion theorem that actually characterizes the set N. Finally, we study some aspects of the boundary behavior ...