Öz
Kaynakça
- Ando, T. 1979, Concavity of certain maps on positive definite matrices and applications to Hadamard products, Lin. Alg. & Appl. 26, 203-241. google scholar
- Araki, H., Hansen, F. 2000, Jensen’s operator inequality for functions of several variables, Proc. Amer. Math. Soc. 128 No. 7, 2075-2084. google scholar
- Aujila, J. S., Vasudeva, H. L. 1995, Inequalities involving Hadamard product and operator means, Math. Japon. 42 265-272. google scholar
- Cerone, P., Dragomir, S. S. 2000, Trapezoidal-type rules from an inequalities point of view, in Handbook of Analytic-Computational Methods in Applied Mathematics, G. Anastassiou (Ed.), CRC Press, NY, 65-134. google scholar
- Dragomir, S. S. 2006, Bounds for the normalized Jensen functional, Bull. Austral. Math. Soc. 74(3), 417-478. google scholar
- Dragomir, S. S. 2022, Some tensorial Hermite-Hadamard type inequalities for convex functions of selfadjoint operators in Hilbert spaces, Preprint RGMIA Res. Rep. Coll. 25 , Art. 90, 14 pp. [Online https://rgmia.org/papers/v25/v25a90.pdf]. google scholar
- Korányi, A. 1961, On some classes of analytic functions of several variables. Trans. Amer. Math. Soc., 101, 520–554. google scholar
- Ebadian, A., Nikoufar, I., Gordji, M. E. 2011, Perspectives of matrix convex functions, Proc. Natl. Acad. Sci. USA, 108, no. 18, 7313–7314. google scholar
- Fujii, J. I. 1995, The Marcus-Khan theorem for Hilbert space operators. Math. Jpn. 41, 531-535 google scholar
- Furuta, T., Mićić Hot, J., Pečarić, J., Seo, Y. 2005, Mond-Pečarić method in operator inequalities. inequalities for bounded selfadjoint operators on a Hilbert space, Element, Zagreb. google scholar
- Kitamura, K., Seo, Y. 1998, Operator inequalities on Hadamard product associated with Kadison’s Schwarz inequalities, Scient. Math. 1, No. 2, 237-241. google scholar
- Wada, S. 2007, On some refinement of the Cauchy-Schwarz Inequality, Lin. Alg. & Appl. 420, 433-440. google scholar
A Trapezoid Type Tensorial Norm Inequality for Continuous Functions of Selfadjoint Operators in Hilbert Spaces
Öz
Generalized trapezoid and trapezoid rules play an important role in approximating the Lebesgue integral in the case of scalarvalued functions defined on a finite interval. Motivated by this reason, in this paper we provided several norm error bounds in approximation the integral of continuous function of the convex combination of some tensorial products in terms of the corresponding tensorial generalized and trapezoid rules. The case of continuously differentiable functions is analysed in detail in the case when the derivative is bounded on a finite interval. Related results for the case when the absolute value of the derivative is convex is also provided. The important particular case for the operator exponential function is also considered and the corresponding norm inequalities revealed.
Anahtar Kelimeler
tensorial product selfadjoint operators operator norm trapezoid rule convex functions
Kaynakça
- Ando, T. 1979, Concavity of certain maps on positive definite matrices and applications to Hadamard products, Lin. Alg. & Appl. 26, 203-241. google scholar
- Araki, H., Hansen, F. 2000, Jensen’s operator inequality for functions of several variables, Proc. Amer. Math. Soc. 128 No. 7, 2075-2084. google scholar
- Aujila, J. S., Vasudeva, H. L. 1995, Inequalities involving Hadamard product and operator means, Math. Japon. 42 265-272. google scholar
- Cerone, P., Dragomir, S. S. 2000, Trapezoidal-type rules from an inequalities point of view, in Handbook of Analytic-Computational Methods in Applied Mathematics, G. Anastassiou (Ed.), CRC Press, NY, 65-134. google scholar
- Dragomir, S. S. 2006, Bounds for the normalized Jensen functional, Bull. Austral. Math. Soc. 74(3), 417-478. google scholar
- Dragomir, S. S. 2022, Some tensorial Hermite-Hadamard type inequalities for convex functions of selfadjoint operators in Hilbert spaces, Preprint RGMIA Res. Rep. Coll. 25 , Art. 90, 14 pp. [Online https://rgmia.org/papers/v25/v25a90.pdf]. google scholar
- Korányi, A. 1961, On some classes of analytic functions of several variables. Trans. Amer. Math. Soc., 101, 520–554. google scholar
- Ebadian, A., Nikoufar, I., Gordji, M. E. 2011, Perspectives of matrix convex functions, Proc. Natl. Acad. Sci. USA, 108, no. 18, 7313–7314. google scholar
- Fujii, J. I. 1995, The Marcus-Khan theorem for Hilbert space operators. Math. Jpn. 41, 531-535 google scholar
- Furuta, T., Mićić Hot, J., Pečarić, J., Seo, Y. 2005, Mond-Pečarić method in operator inequalities. inequalities for bounded selfadjoint operators on a Hilbert space, Element, Zagreb. google scholar
- Kitamura, K., Seo, Y. 1998, Operator inequalities on Hadamard product associated with Kadison’s Schwarz inequalities, Scient. Math. 1, No. 2, 237-241. google scholar
- Wada, S. 2007, On some refinement of the Cauchy-Schwarz Inequality, Lin. Alg. & Appl. 420, 433-440. google scholar
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Temel Matematik (Diğer) |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Yayımlanma Tarihi | 17 Aralık 2023 |
| Yayımlandığı Sayı | Yıl 2023 Cilt: 1 Sayı: 2 |
