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Bicategories in Univalent Foundations [PDF]
We develop bicategory theory in univalent foundations. Guided by the notion of univalence for (1-)categories studied by Ahrens, Kapulkin, and Shulman, we define and study univalent bicategories.
B. Ahrens+3 more
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Univalence for convolutions [PDF]
The radius of univalence is found for the convolution f∗g of functions f∈S (normalized univalent functions) and g∈C (close-to-convex functions). A lower bound for the radius of univalence is also determined when f and g range over all of S.
Herb Silverman
doaj +4 more sources
Univalent functions with univalent Gelfond-Leontev derivatives [PDF]
We investigate functions of the form f(z) = z/(1 + 5 0 0 Sne Onz")=2 + E n s O n e " that are analytic in the unitary circle U. Necessary and sufficient conditions in terms of {n}for a trinomial f and the bounds of br, 1 § n 5 4 for a particular form
V. SRINIVAS
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Univalent functions with univalent derivatives. II [PDF]
S. M. Shah, S. Y. Trimble
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Univalency of Certain Transform of Univalent Functions
We consider univalency problem in the unit disc $$\mathbb{D}$$ of the function \[g(z)=\frac{(z/f(z))-1}{-a_{2}}, \] where $$f$$ belongs to some classes of univalent functions in $$\mathbb{D}$$ and $$a_{2}=\frac{f''(0)}{2}\neq 0$$.
Obradović, Milutin, Tuneski, Nikola
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We review the concept of a univalent fibration and show by elementary means that every Kan fibration in simplicial sets can be embedded in a univalent Kan fibration.
van den Berg, B., Moerdijk, I.
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In this article, by making use of the q-Srivastava-Attiya operator, we introduce and investigate a new family SWΣ(δ,γ,λ,s,t,q,r) of normalized holomorphic and bi-univalent functions in the open unit disk U, which are associated with the Bazilevič ...
H. Srivastava, A. Wanas, R. Srivastava
semanticscholar +1 more source
In the present investigation, our aim is to define a generalized subclass of analytic and bi-univalent functions associated with a certain $q$-integral operator in the open unit disk $\mathbb{U}$.
B. Khan+5 more
semanticscholar +1 more source
The Marriage of Univalence and Parametricity [PDF]
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 is appallingly syntactic, and as a result, exploiting equivalences is cumbersome at best ...
Tabareau, Nicolas+2 more
openaire +6 more sources