2 citations · 7 across the 19 of their papers we have counts for
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A comparison of the weakest contractive conditions for Banach and Kannan mappings
Shunya Hashimoto, Misako Kikkawa, Shuji Machihara +1
We study the weakest convergence-type conditions for fixed point results for Banach and Kannan mappings. Building on Suzuki's weakest condition for Banach mappings and our previous…
On the weakest conditions for the existence of fixed points of Kannan and Chatterjea type contractions
Shunya Hashimoto, Misako Kikkawa, Shuji Machihara +1
In this paper, we study the weakest possible conditions for fixed point theorems involving two classes of mappings defined by Kannan and Chatterjea. Our approach relies on the so-c…
Revisiting the Rellich inequality
Neal Bez, Shuji Machihara, Tohru Ozawa
We revisit the Rellich inequality from the viewpoint of isolating the contributions from radial and spherical derivatives. This naturally leads to a comparison of the norms of the…
On the compactness of the (non)radial Sobolev spaces
Shuji Machihara, Megumi Sano
In this note, we give the affirmative answer of the question in [18], which is a compactness result of the non-radial Sobolev spaces. As an application, we show the existence of an…
A supersolutions perspective on hypercontractivity
Yosuke Aoki, Jonathan Bennett, Neal Bez +3
The purpose of this article is to expose an algebraic closure property of supersolutions to certain diffusion equations. This closure property quickly gives rise to a monotone quan…