The sharper version for generalized power mean inequalities with negative exponent

In this study, the generalized power mean inequalities with a negative parameter are refined using an optimality theorem on the generator function. The optimality theorem requires the study of different cases for the exponents and yields a refinement of the inequality in a neighbourhood of the vectors for which the equality occurs. Then, these local inequalities are generalized to all positive vectors by an appropriate selection of parameters. Also, some of the results are exemplified by numerical calculations

The Development of a Mathematics Self-Report Inventory for Turkish Elementary Students

The purpose of the current study is to develop a mathematics self-report inventory (MSRI) to measure Turkish elementary students' mathematics expectancy beliefs and task values based on the expectancy-value theory of achievement motivation. In Study-1 (n = 1,315), exploratory factor analysis (EFA) and reliability analysis are used to evaluate the MSRI. EFA results suggest a five-factor model that consists of interest value, extrinsic-utility value, importance value, personal cost, and expectancy beliefs. In Study-2 (n = 1,343), confirmatory factor analysis (CFA) and convergent, discriminant, and subgroup validity results are also used to examine construct validity for the MSRI. The results indicate that (a) elementary students' scores on the MSRI did not significantly differ by gender; (b) elementary students' scores on the MSRI were significantly influenced by grade level; and (c) a significant, positive, and strong relationship existed between students' scores on the MSRI and students' achievement scores from the Level Determination Exam. The findings of this study showed that, with a few exceptions, the MSRI is a reliable and valid psychological tool for use with the elementary students in Turkey and may be regarded as beneficial in guiding subsequent study goals by explaining students' achievement-related beliefs grounded in the expectancy value theory.WoSScopu

Some integral inequalities for the product of s-convex functions in the fourth sense

n this paper, several novel inequalities are examined for the product of two s-convex functions in the fourth sense. Also, some applications regarding special means and digamma functions are presented