We prove the existence of fixed points of p-tupling renormalization operators for interval and circle mappings having a critical point of arbitrary real degree r > 1. Some properties of the resulting maps are studied: analyticity, univalence, behavior as r tends to infinity.

It is sometimes convenient or useful in mathematics to treat isomorphic structures as the same. The recently proposed Univalence Axiom for the foundations of mathematics elevates this idea to a foundational principle in the setting of Homotopy Type Theory. It states, roughly, that isomorphic structures can be identified. We explore the motivations and consequences, both mathematical and philoso...

In this paper, we obtain a new univalence criterion for analytic functions defined outside of the unit disk. Relevant connections of the results, which are presented in this paper with various known results are also considered. 2000 Mathematics Subject Classification: Primary 30C45.

In this paper, we consider the subclasses Tj , Tj,μ and Sj(p) (j = 2, 3, . . .), and generalize univalence conditions for integral operator Fα1,α2,...,αn,β of the analytic function f belonging to the classes T2, T2,μ and S(p). 2000 Mathematics Subject Classification: 30C45.

* Correspondence: maslina@ukm. my School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600 Selangor D. Ehsan, Malaysia Abstract An attempt has been made to give a criteria to a family of functions defined in the space of analytic functions to be univalent. Such criteria extended earlier univalence criteria of Pescar’s-type of analytic funct...

For analytic functions f, g in the open unit disk U, we define two new integral operators. The main object of this paper is to obtain the univalence conditions for the integral operators. Several corollaries of the main results are also considered.

Reasoning modulo equivalences is natural for everyone, including mathematicians. Unfortunately, in proof assistants based on type theory, which are frequently used to mechanize mathematical results and carry out program verification efforts, equality appallingly syntactic, as a result, exploiting cumbersome at best. Parametricity univalence two major concepts that have been explored the literat...

We will give a detailed account of why the simplicial sets model of the univalence axiom due to Voevodsky also models W-types. In addition, we will discuss W-types in categories of simplicial presheaves and an application to models of set theory.