@article{Cvetković_Milovanović_Stanić_2015, title={Positive Solutions of a Class of Operator Equations}, volume={67}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/1977}, abstractNote={ Positive solutions of a class of matrix equations were studied by Bhatia, et al., <em class="EmphasisTypeItalic ">Bull. London Math. Soc.</em>, 32, 214 (2000), <em class="EmphasisTypeItalic ">SIAM J. Matrix Anal. Appl.</em>, 14, 132 (1993) and 27, 103–114 (2005), by Kwong, <em class="EmphasisTypeItalic ">Linear Algebra Appl.</em>, 108, 177–197 (1988), and by Cvetkovi? and Milovanovi?, [<em class="EmphasisTypeItalic ">Linear Algebra Appl.</em&gt;, 429, 2401–2414 (2008)]. Following the idea used in the last paper, we study a class of operator equations in infinite-dimensional spaces and prove that the positivity of solutions can be established for this class of equations under the condition that a certain rational function is positive semidefinite.}, number={2}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Cvetković, A. S. and Milovanović, G. V. and Stanić, M. P.}, year={2015}, month={Feb.}, pages={245-260} }