Research Article
Year 2020,
Volume: 41 Issue: 4, 862 - 874, 29.12.2020
Abstract
References
- [1] Dragomir S.S., Pearce C.E.M., Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.
- [2] Maden S., Kadakal H., Kadakal M. and İşcan İ., Some new integral inequalities for n-times differentiable convex and concave functions, Journal of Nonlinear Sciences and Applications, 10(12) (2017) 6141-6148.
- [3] Dragomir S.S., Agarwal R.P. and Cerone P., On Simpson’s inequality and applications, J. of Inequal. Appl., 5 (2000) 533-579.
- [4] İşcan İ., Bekar K. and Numan S., Hermite-Hadamard and Simpson type inequalities for differentiable quasi-geometrically convex functions, Turkish Journal of Analysis and Number Theory, 2 (2) (2014) 42-46.
- [5] Kadakal M., Kadakal H. and İşcan İ., Some new integral inequalities for n-times differentiable s-convex functions in the first sense, Turkish Journal of Analysis and Number Theory, 5(2) (2017) 63-68.
- [6] Set E., Ozdemir M.E. and Sarikaya M.Z., On new inequalities of Simpson’s type for quasi-convex functions with applications, Tamkang Journal of Mathematics, 43(3) (2012) 357–364.
- [7] Varosanec S., On h-convexity, J. Math. Anal. Appl., 326 (2007) 303-311.
- [8] Kadakal H., Hermite-Hadamard type inequalities for trigonometrically convex functions, Scientific Studies and Research. Series Mathematics and Informatics, 28 (2) (2018) 19-28.
- [9] Kadakal M., Better results for trigonometrically convex functions via hölder-iscan and improved power-mean inequalities, Universal Journal of Mathematics and Applications, 3(1) (2020) 38-43.
- [10] Bekar K., Hermite–Hadamard Type Inequalities for Trigonometrically P Functions. Comptes Rendus de l’Académie Bulgare des Sciences, 72 (11) (2019) 1449-1457.
- [11] Mitrinovic D.S., Pecaric J.E. and Fink A.M., Classical and New Inequalities in Analysis, The Netherlands: Kluwer Academic Publishers, 1993.
- [12] İşcan İ., New refinements for integral and sum forms of Hölder inequality, Journal of Inequalities and Applications, 304 (2019) 1-11.
- [13] Kadakal M., İşcan İ., Kadakal H., and Bekar K., On improvements of some integral inequalities, Researchgate, (2019) https://doi.org/10.13140/RG.2.2.15052.46724. [14] Sarikaya M.Z., Set, E. and Ozdemir, M.E. On new inequalities of Simpson’s type for s-convex functions. Computers & Mathematics with Applications, 60(8) (2010) 2191-2199.
Year 2020,
Volume: 41 Issue: 4, 862 - 874, 29.12.2020
Abstract
The aim of this article is to define a special case of h- convex function, namely the notion of a trigonometrically convex function. Using the Hölder, Hölder-İşcan integral inequality and the power-mean, improved power-mean integral inequalities, and together with an integral identity, some new Simpson-type inequalities have been obtained for trigonometric convex functions. We also give some applications for special means.
Keywords
Convex function trigonometrically convex function Simpson type inequality Hölder inequality Power mean inequality.
References
- [1] Dragomir S.S., Pearce C.E.M., Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.
- [2] Maden S., Kadakal H., Kadakal M. and İşcan İ., Some new integral inequalities for n-times differentiable convex and concave functions, Journal of Nonlinear Sciences and Applications, 10(12) (2017) 6141-6148.
- [3] Dragomir S.S., Agarwal R.P. and Cerone P., On Simpson’s inequality and applications, J. of Inequal. Appl., 5 (2000) 533-579.
- [4] İşcan İ., Bekar K. and Numan S., Hermite-Hadamard and Simpson type inequalities for differentiable quasi-geometrically convex functions, Turkish Journal of Analysis and Number Theory, 2 (2) (2014) 42-46.
- [5] Kadakal M., Kadakal H. and İşcan İ., Some new integral inequalities for n-times differentiable s-convex functions in the first sense, Turkish Journal of Analysis and Number Theory, 5(2) (2017) 63-68.
- [6] Set E., Ozdemir M.E. and Sarikaya M.Z., On new inequalities of Simpson’s type for quasi-convex functions with applications, Tamkang Journal of Mathematics, 43(3) (2012) 357–364.
- [7] Varosanec S., On h-convexity, J. Math. Anal. Appl., 326 (2007) 303-311.
- [8] Kadakal H., Hermite-Hadamard type inequalities for trigonometrically convex functions, Scientific Studies and Research. Series Mathematics and Informatics, 28 (2) (2018) 19-28.
- [9] Kadakal M., Better results for trigonometrically convex functions via hölder-iscan and improved power-mean inequalities, Universal Journal of Mathematics and Applications, 3(1) (2020) 38-43.
- [10] Bekar K., Hermite–Hadamard Type Inequalities for Trigonometrically P Functions. Comptes Rendus de l’Académie Bulgare des Sciences, 72 (11) (2019) 1449-1457.
- [11] Mitrinovic D.S., Pecaric J.E. and Fink A.M., Classical and New Inequalities in Analysis, The Netherlands: Kluwer Academic Publishers, 1993.
- [12] İşcan İ., New refinements for integral and sum forms of Hölder inequality, Journal of Inequalities and Applications, 304 (2019) 1-11.
- [13] Kadakal M., İşcan İ., Kadakal H., and Bekar K., On improvements of some integral inequalities, Researchgate, (2019) https://doi.org/10.13140/RG.2.2.15052.46724. [14] Sarikaya M.Z., Set, E. and Ozdemir, M.E. On new inequalities of Simpson’s type for s-convex functions. Computers & Mathematics with Applications, 60(8) (2010) 2191-2199.
There are 13 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Natural Sciences |
| Authors | |
| Publication Date | December 29, 2020 |
| Submission Date | June 9, 2020 |
| Acceptance Date | September 18, 2020 |
| Published in Issue | Year 2020Volume: 41 Issue: 4 |