Can Sobolev Inequality Be Written for Sharma-Mittal Entropy?


Akturk O. U. , Akturk E., TOMAK M.

INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, cilt.47, ss.3310-3320, 2008 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 47 Konu: 12
  • Basım Tarihi: 2008
  • Doi Numarası: 10.1007/s10773-008-9766-2
  • Dergi Adı: INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
  • Sayfa Sayıları: ss.3310-3320

Özet

In this paper, we focus on Sobolev inequality in the context of Sharma-Mittal entropy. Using this new inequality, generalized entropic uncertainty relation in accordance with Sharma-Mittal entropy is derived and the pseudoadditivity relation has been obtained. This new entropic uncertainty relation has then been applied to physical examples such as one dimensional harmonic oscillator and Posch-Teller potential. Finally, it has been shown that for certain values of the parameters of Sharma-Mittal measure, the present results reduce to the corresponding results of Shannon, Renyi and Tsallis measures.