45 citations · 134 across the 6 of their papers we have counts for
7 papers
The Ptolemy-Alhazen problem and spherical mirror reflection
Masayo Fujimura, Parisa Hariri, Marcelina Mocanu +1
An ancient optics problem of Ptolemy, studied later by Alhazen, is discussed. This problem deals with reflection of light in spherical mirrors. Mathematically this reduces to the s…
Local convexity of metric balls
Parisa Hariri, Riku Klén, Matti Vuorinen
We study local convexity properties of the triangular ratio metric balls in proper subdomains of the real coordinate space. We also study inclusion properties of the visual angle m…
Comparison theorems for hyperbolic type metrics
Oleksiy Dovgoshey, Parisa Hariri, Matti Vuorinen
The connection between several hyperbolic type metrics is studied in subdomains of the Euclidean space. In particular, a new metric is introduced and compared to the distance ratio…
Some remarks on the Cassinian metric
Parisa Hariri, Riku Klen, Matti Vuorinen +1
Some sharp inequalities between the triangular ratio metric and the Cassinian metric are proved in the unit ball.
Inequalities and bilipschitz conditions for triangular ratio metric
Parisa Hariri, Matti Vuorinen, Xiaohui Zhang
Let be a domain and let and be two metrics on . We compare the geometries defined by the two metrics to each other for several pairs of m…
Some remarks on the visual angle metric
Parisa Hariri, Matti Vuorinen, Gendi Wang
We show that the visual angle metric and the triangular ratio metric are comparable in convex domains. We also find the extremal points for the visual angle metric in the half spac…
Lipschitz conditions, triangular ratio metric, and quasiconformal maps
Jiaolong Chen, Parisa Hariri, Riku Klén +1
The triangular ratio metric is studied in subdomains of the complex plane and Euclidean -space. Various inequalities are proven for it. The main results deal with the behavior o…