[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5831/HMJ.2021.43.1.130

ON TRIGONOMETRICALLY QUASI-CONVEX FUNCTIONS

Numan, Selim (Department of Mathematics, Faculty of Arts and Sciences, Giresun University)
Iscan, Imdat (Department of Mathematics, Faculty of Arts and Sciences, Giresun University)

Publication Information

Honam Mathematical Journal / v.43, no.1, 2021 , pp. 130-140 More about this Journal

Abstract

In this paper, we introduce and study the concept of trigonometrically quasi-convex function. We prove Hermite-Hadamard type inequalities 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.

Keywords

Convex function; trigonometrically convex function; trigonometrically quasi-convex functions; Hermite-Hadamard inequality;

Citations & Related Records

Reference

1	H. Kadakal, Hermite-Hadamard type inequalities for trigonometrically convex functions, Scientific Studies and Research. Series Mathematics and Informatics, 28(2) (2018), 19-28.
2	G. Zabandan, A new refinement of the Hermite-Hadamard inequality for convex functions, J. Inequal. Pure Appl. Math. 10(2) (2009), Article ID 45, 7 pages.
3	SS. Dragomir and RP. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett. 11(5) (1998), 91-95. DOI
4	SS. Dragomir and CEM. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Its Applications, RGMIA Monograph 2002.
5	SS. Dragomir, J. Pecaric and LE.Persson, Some inequalities of Hadamard Type, Soochow Journal of Mathematics, 21(3) (1995), pp. 335-341.
6	J. Hadamard, Etude sur les proprietes des fonctions entieres en particulier d'une fonction consideree par Riemann, J. Math. Pures Appl. 58 (1893), 171-215.
7	DA. Ion, Some estimates on the Hermite-Hadamard inequality through quasi-convex functions, An. Univ. Craiova Math. Comp. Sci. Ser. 34 (2007), 82-87.
8	I. Iscan, Generalization of different type integral inequalities via fractional integrals for functions whose second derivatives absolute values are quasi-convex, Konuralp journal of Mathematics, 1(2) (2013), 67-79.
9	I. Iscan, New general integral inequalities for quasi-geometrically convex functions via fractional integrals, Journal of Inequalities and Applications, 2013 (2013):491, 15 pages. DOI
10	I. Iscan, On generalization of different type inequalities for harmonically quasi-convex functions via fractional integrals, Applied Mathematics and Computation, 275 (2016), 287-298. DOI
11	I. Iscan, S. Turhan and S. Maden, Hermite-Hadamard and Simpson-like type inequalities for differentiable p-quasi-convex functions, Filomat, 31(19) (2017), 5945-5953. DOI
12	I. Iscan and M. Kunt, Hermite-Hadamard-Fejer type inequalities for quasi-geometrically convex functions via fractional integrals, Journal of Mathematics, 2016, (2016), Article ID 6523041, 7 pages.