Some remarks on Cîrtoaje’s conjecture

Abstract

In this paper, we give new conditions under which the Cîrtoaje's conjecture is also valid. We also show that a certain generalization of the Cîrtoaje's inequality fulfils an interesting property.MSC: Primary 26D10; secondary 26D15

Next generalization of Cîrtoaje’s inequality

“…The conjecture was proved by Matejíčka [ 3 ]. Matejíčka also proved ( 1 ) under other conditions in [ 4 , 5 ]. For example, he showed that ( 1 ) is also valid for .…”

“…For example, he showed that ( 1 ) is also valid for . In [ 5 ], one interesting property of the generalized Cîrtoaje’s inequality (CI) was found. In [ 6 ], a classification of sets of solutions of (CI) was made.…”

Una nueva prueba para una conjetura de Özban

“…que fue probada de forma independiente por Laub-Ilani [6,5] y Zeikii-Cirtoaje-Berndt [17,2]. Para obtener detalles importantes sobre generalizaciones, extensiones y desigualdades relacionadas con (2), consultar las referencias [4,3,1,7,8,9,10,12,13,14,16]. Además, se observa que la prueba de (1) desarrollada por Matejíčka en [11] se basa en métodos de análisis matemático y numérico.…”

On the Generalization for Some Power-Exponential-Trigonometric Inequalities

“…In recent years, an increasing amount of attention has been paid to the study of power-exponential inequalities [1][2][3][4][5][6][7][8][9][10]. A review of some problems and historical landmarks are given in [2,11].…”