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ON IMPROVEMENTS OF SOME INTEGRAL INEQUALITIES
( Mahir Kadakal ),( İmdat İşcan ),( HURIYE KADAKAL ),( KERIM BEKAR ) 호남수학회 2021 호남수학학술지 Vol.43 No.3
In this paper, improved power-mean integral inequality, which provides a better approach than power-mean integral inequality, is proved. Using Hölder-İşcan integral inequality and improved power-mean integral inequality, some inequalities of Hadamard’s type for functions whose derivatives in absolute value at certain power are quasi-convex are given. In addition, the results obtained are compared with the previous ones. Then, it is shown that the results obtained together with identity are better than those previously obtained.
ON TRIGONOMETRICALLY QUASI-CONVEX FUNCTIONS
( Selim Numan ),( İmdat İşcan ) 호남수학회 2021 호남수학학술지 Vol.43 No.1
In this paper, we introduce and study the concept of trigono-metrically quasi-convex function. We prove Hermite-Hadamard type in- equalities for the newly introduced class of functions and obtain some new Hermite-Hadamard inequalities for functions whose first derivative in absolute value, raised to a certain power which is greater than one, respectively at least one, is trigonometrically quasi-convex convex. We also extend our initial results to functions of several variables. Next, we point out some applications of our results to give estimates for the approximation error of the integral the function in the trapezoidal formula.