On some new observations on Kurepa's left factorial

Nicola Fabiano; Nikola Mirkov; Zoran D. Mitrovic; Stojan Radenovic

Volume 4, Issue 3 , June 2022, , Pages 1-8


  After a brief historical excursus, we prove in a simple way some properties of Kurepa's function, the left factorial. We introduce Kurepa's hypothesis,  propose a new description, and the relation to Bezout's parameters and the Diophantine equation. A numerical analysis supports Kurepa's hypothesis ...  Read More

Some critical remarks of recent results on F-contractions in b-metric spaces

Mudasir Younis; Nicola Fabiano; Mirjana Pantovic; Stojan Radenovic

Volume 4, Issue 2 , April 2022, , Pages 1-10


  In this paper, we analyze, generalize and correct some recent results on F-contractions within b-metric spaces. In all results, our only assumption is the strict growth of the function F: $\left( 0,+\infty \right) \rightarrow \left( -\infty ,+\infty \right) .$  Read More

On various types of compatible Jungck--Rhoades pairs of mappings in C*-algebra valued metric spaces

Parveen Kumar; Nicola Fabiano; Ljiljana Paunovic

Volume 3, Issue 3 , September 2021, , Pages 1-25


  In this paper, among other things, we have established four different types of compatible mappings that work in the context of C*-algebra valued metric spaces. The obtained types of mappings generalize from previously known ones within ordinary metric spaces. We have shown by examples ...  Read More

A proof of the Cauchy--Schwarz inequality from the change of reference frame

Nicola Fabiano

Volume 3, Issue 1 , February 2021, , Pages 46-47


  Inspired by [1] a proof of the Cauchy--Schwarz inequality is given by considering the transformation between two different inertial reference frames.  Read More