Can Sobolev Inequality Be Written for Sharma-Mittal Entropy?

Akturk, O.; Akturk, E.; Tomak, M.

doi:10.1007/s10773-008-9766-2

Can Sobolev Inequality Be Written for Sharma-Mittal Entropy?

Atıf İçin Kopyala

Akturk O. U., Akturk E., Tomak M.

INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, cilt.47, sa.12, ss.3310-3320, 2008 (SCI-Expanded)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 47 Sayı: 12
Basım Tarihi: 2008
Doi Numarası: 10.1007/s10773-008-9766-2
Dergi Adı: INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Sayfa Sayıları: ss.3310-3320
Hacettepe Üniversitesi Adresli: Evet

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.