Eur. Phys. J. Plus (2022) 137: 320
https://doi.org/10.1140/epjp/s13360-022-02555-4

Regular Article

The R_κκ function and its applications: disentropy, image processing and the κ-diode

Laboratory of Quantum Information Technology, Department of Teleinformatic Engineering (DETI), Federal University of Ceara (UFC), C.P. 6007, Campus do Pici, 60455-970, Fortaleza, CE, Brazil

^c rubens.ramos@ufc.br

Received: 2 June 2021
Accepted: 3 March 2022
Published online: 9 March 2022

Abstract

Three generalizations of the Lambert W function were recently discussed in the literature: the Lambert–Tsallis W_q function, the R_qq function and the Lambert–Kaniadakis W_κ function. All of them have been used in interesting problems in physics and engineering. In this direction, the present work introduces a fourth generalization, the new function R_κκ(z), solution of the equation R_κκ(z) × _κ exp_κ(R_κκ(z)) = z. In this work, it is shown this new function can be used to construct a new disentropy as well it is used to model the κ-diode, a hypothetical electronic device whose electrical current depends κ-exponentially on the voltage between its terminals. Analytical and numerical results for R_κκ, the new disentropy and κ-diode are presented.