arXiv subjects
Publications and source records attributed to Marija Rasajski.
In this paper the double-sided Talor's approximations are used to obtain generalisations and improvements of some trigonometric inequalities.
In this paper the double-sided Taylor's approximations are studied. A short proof of a well-known theorem on the double-sided Taylor's approximations is introduced. Also, two new theorems are proved regarding the monotonicity of such approximations. Then we present some new applications of the double-sided Taylor's approximations in the theory of analytic inequalities.
In this paper we prove some exponential inequalities involving the sinc function. We analyze and prove inequalities with constant exponents as well as inequalities with certain polynomial exponents. Also, we establish intervals in which these inequalities hold.
In this paper we propose and prove some generalizations and sharpenings of certain inequalities of Wilker;'s and Shafer-Fink's type. Application of the Wu-Debnath theorem enabled us to prove some double sided inequalities.
In this paper we propose a new method for sharpening and refinements of some trigonometric inequalities. We apply these ideas to some inequalities of Wilker-Cusa-Huygens's type.
In this paper we give some sharper refinements and generalizations of inequalities related to Shafer's inequality for the arctangent function, stated in Theorems 1, 2 and 4 in [1], by C. Mortici and H.M. Srivastava.
Eigenvalues of a graph are the eigenvalues of the corresponding (0,1)-adjacency matrix. The second largest eigenvalue lambda_2 provides significant information on characteristics and structure of graphs. Therefore, finding bounds for lambda_2 is a topic of interest in many fields. So far we have studied the graphs with the property lambda_2 is less or equal to 2, so-called reflexive graphs. The original RS-theorem is about them. In this paper we generalize that concept and introduce the arbitrary bounds. The Generalized RS-theorem gives us an answer whether the second largest eigenvalue of a graph is greater than, less than, or equal to a, a>0, within some classes of connected graphs with a cut-vertex. After removing the cut-vertex u of the given graph G, we examine the indices of the components of G-u. The information on these indices is used to make conclusions about the second largest eigenvalue of the graph G. In the RS-theorem a=2. Here, we state and prove the Generalized RS-theorem, one corollary, and, also, give some useful lemmas.