Araştırma Makalesi
Yıl 2020, Cilt 69, Sayı 2, 1111 - 1118, 31.12.2020

### Kaynakça

• Amir, D., Characterizations of inner product spaces, Birkhauser Verlag, 1986.
• Bauschke, H.H., Combettes, P.L., Convex Analysis and Monotone Operator Theory in Hilbert Spaces, Springer, New York, 2011.
• Bhatia, R., Sharma, R., Some inequalities for positive linear maps, Linear Algebra Appl., 436(6) (2012), 1562--1571.
• Cheung, W.S., Pečarić, J., Bohr's inequalities for Hilbert space operators, J. Math. Anal. Appl., 323(1) (2006), 403--412.
• Choi, M.D., Hadwin, D., Nordgren, E., Radjavi, H., Rosenthal, P., On positive linear maps preserving invertibility, J. Funct. Anal. 59(3) (1984), 462--469.
• Cvetkovski, Z., Inequalities: Theorems, Techniques and Selected Problems, Springer Science & Business Media, 2012.
• Evans, D.E., Positive linear maps on operator algebras, Comm. Math. Phys., 48(1) (1976), 15--22.
• Fu, X., Some generalizations of operator inequalities, J. Math. Inequal., 9(1) (2015), 101--105.
• Fujii, M., Zuo, H., Matrix order in Bohr inequality for operators, Banach J. Math. Anal., 1 (2010), 21--27.
• Furuta, T., Mićić Hot, J., Pečarić, J., Seo, Y., Mond-Pečarić method in operator inequalities, Monographs in Inequalities, Zagreb, 2005.
• Gumus I.H., A note on a conjecture about Wielandt's inequality, Linear Multilinear Algebra, 63(9) (2015), 1909--1913.
• Hirzallah, O., Non-commutative operator Bohr inequality, J. Math. Anal. Appl., 282(2) (2003), 578--583.
• Lin, M., On an operator Kantorovich inequality for positive linear maps, J. Math. Anal. Appl., 402(1) (2013), 127--132.
• Størmer, E., Positive linear maps of operator algebras, Acta Math., 110(1) (1963), 233--278.
• Zhang, P., More operator inequalities for positive linear maps, Banach J. Math. Anal., 9(1) (2015), 166--172.

### Some results around quadratic maps

Yıl 2020, Cilt 69, Sayı 2, 1111 - 1118, 31.12.2020

### Öz

This paper dedicated to study quadratic maps. We present some new operator equalities and inequalities by using quadratic map in the framework of B(H). Applications for particular case of interest are also provided. The parallelogram law is recovered  and some other interesting operator equalities are established. Afterward,   we get an extension of some well known inequalities such as, triangle  inequality. Especially, Bohr's inequality is generalized to the context of quadratic map. Some results concerning this inequality are surveyed.  We give an application of our results in the previous sections. We show that our results are a generalization of some well known works due to Fujii and Hirzallah.

### Kaynakça

• Amir, D., Characterizations of inner product spaces, Birkhauser Verlag, 1986.
• Bauschke, H.H., Combettes, P.L., Convex Analysis and Monotone Operator Theory in Hilbert Spaces, Springer, New York, 2011.
• Bhatia, R., Sharma, R., Some inequalities for positive linear maps, Linear Algebra Appl., 436(6) (2012), 1562--1571.
• Cheung, W.S., Pečarić, J., Bohr's inequalities for Hilbert space operators, J. Math. Anal. Appl., 323(1) (2006), 403--412.
• Choi, M.D., Hadwin, D., Nordgren, E., Radjavi, H., Rosenthal, P., On positive linear maps preserving invertibility, J. Funct. Anal. 59(3) (1984), 462--469.
• Cvetkovski, Z., Inequalities: Theorems, Techniques and Selected Problems, Springer Science & Business Media, 2012.
• Evans, D.E., Positive linear maps on operator algebras, Comm. Math. Phys., 48(1) (1976), 15--22.
• Fu, X., Some generalizations of operator inequalities, J. Math. Inequal., 9(1) (2015), 101--105.
• Fujii, M., Zuo, H., Matrix order in Bohr inequality for operators, Banach J. Math. Anal., 1 (2010), 21--27.
• Furuta, T., Mićić Hot, J., Pečarić, J., Seo, Y., Mond-Pečarić method in operator inequalities, Monographs in Inequalities, Zagreb, 2005.
• Gumus I.H., A note on a conjecture about Wielandt's inequality, Linear Multilinear Algebra, 63(9) (2015), 1909--1913.
• Hirzallah, O., Non-commutative operator Bohr inequality, J. Math. Anal. Appl., 282(2) (2003), 578--583.
• Lin, M., On an operator Kantorovich inequality for positive linear maps, J. Math. Anal. Appl., 402(1) (2013), 127--132.
• Størmer, E., Positive linear maps of operator algebras, Acta Math., 110(1) (1963), 233--278.
• Zhang, P., More operator inequalities for positive linear maps, Banach J. Math. Anal., 9(1) (2015), 166--172.

### Ayrıntılar

Birincil Dil İngilizce Matematik Research Article Mohsen ERFANİAN OMİDVAR> (Sorumlu Yazar) Department of Mathematics, Mashhad Branch, Islamic Azad University 0000-0002-5395-8170 Iran Shiva SHEYBANİ Bu kişi benim Mashhad Branch, Islamic Azad University 0000-0002-7285-1571 Iran Mahnaz KHANEHGIR Bu kişi benim Mashhad Branch, Islamic Azad University 0000-0002-7435-7307 Iran Sever DRAGOMIR> Victoria University of Technology 0000-0003-2902-6805 Australia 31 Aralık 2020 15 Aralık 2019 2 Mayıs 2020 Yıl 2020, Cilt 69, Sayı 2