Open Access

Continued Fraction Representations of the Generalized Operator Entropy


Cite

ANDO, T.: Topics on operator inequalities, Ryukyu University. Lecture Note Series, 1978. Search in Google Scholar

AGLER, J.—MCCARTHY, J. E.—YOUNG, N. J.: Operator monotone functions and Löwner functions of several variables, Ann. Math. 176 (2012), 1783–1826. Search in Google Scholar

DINH, T. H.—DUMITRU, R.—FRANCO, J. A.: The matrix power means and interpolations, Adv. Oper. Theory 3 (2018), 647–654. Search in Google Scholar

HIGHAM, N. J.: Functions of Matrices: Theory and Computation.University of Manchister, SIAM, 2008. Search in Google Scholar

ISA, H.—ITO, M.—KAMEI, E.—TOHYAMA, H.—WATANEBE, M.: Relative operator entropy, operator divergence and Shannon inequality, Sci. Math. Japan. 75 (2012), no. 3, 289–298. Search in Google Scholar

JONES, W. B.—THRON, W. J.: Continued Fractions. Analytic Theory and Applications. (With a foreword by Felix E. Browder. With an introduction by Peter Henrici.) Encyclopedia of Mathematics and its Applications Vol. 11, Addison-Wesley Publishing Co., Reading, Mass., 1980. Search in Google Scholar

KACHA, A.—OUNIR, B.—SALHI, S.: Continued fraction expansion of the relative operator entropy and the Tsallis relative entropy, ISOR J. Of Math. Issue 6 (2016), 19–31. Search in Google Scholar

KIM, S.: Operator entropy and fidelity associated with the geometric mean, Linear Algebra Appl. 438 (2013), 2475–2483. Search in Google Scholar

KHOVANSKI, A. N.: The Aplications of Continued Fractions and their Generalisation to Problemes in Approximation Theory. Noordhoff, Groningen, The Netherlands, 1963. Search in Google Scholar

LORENTZEN, L.—WADELAND, H.: Continued Fractions with Applications. Studies in Computational Mathematics Vol 3. North-Holland Publishing Co., Amsterdam, 1992. Search in Google Scholar

MENNOU, S.—CHILLALI, A.—KACHA, A.: Matrix continued fractions expansions of the error function 31. Commun. Math. 1 (2023), 257–271. Search in Google Scholar

MURPHY, G. J.: C-Algebras and Operators Theory, Chapter 2, Academic press, INC Harcourt Brace Jovanovich publishers, 1990. Search in Google Scholar

NETTLER, G.: On transcendental numbers whose sum, difference, quotient and product are transcendental numbers, Math. Student 41 (1974), no. 3–4, 339–348. Search in Google Scholar

PETZ, D.: Bregman divergence as relative operator entropy, Acta Math. Hungar. 116 (2007), 127–131. Search in Google Scholar

RAISSOULI, M.—KACHA, A.—SALHI, S: . The continued fractions expansions of real powers of positive definite matrices with applications to matrix means, Arab. J. Sci. Eng. 31 (2006), no.1, 41–56. Search in Google Scholar

SABABHEH, M.: Convexity and matrix means, Linear Algebra Appl. 506 (2016), 588–602. Search in Google Scholar

eISSN:
1338-9750
Language:
English
Publication timeframe:
3 times per year
Journal Subjects:
Mathematics, General Mathematics