$\left(m_{1},m_{2}\right) $-Geometric Arithmetically Convex Functions and Related Inequalities
$\left(m_{1},m_{2}\right) $-Geometric Arithmetically Convex Functions and Related Inequalities
In this manuscript, we introduce and study the concept of $\left( m_{1},m_{2}\right) $-geometric arithmetically (GA) convex functions and their some algebric properties. In addition, we obtain Hermite-Hadamard type inequalities for the newly introduced this type of functions whose derivatives in absolute value are the class of $\left( m_{1},m_{2}\right) $ -GA-convex functions by using both well-known power mean and Hölder's integral inequalities.
Keywords:
Convex function, m-convex function, (m1;m2)-GA convex function Hermite-Hadamard inequality,
___
- [1] Bakula, MK., Özdemir, ME. and Peˇcari´c, J., Hadamard type inequalities for m-convex and (alpha;m)-convex functions, J. Inequal. Pure Appl. Math. 9 (4) (2008), Art. 96, 12 pages.
- [2] Dragomir SS. and Pearce, CEM., Selected Topics on Hermite-Hadamard Inequalities and Its Applications, RGMIA Monograph, 2002.
- [3] Dragomir, SS. Peˇcari´c, J. and Persson, LE., Some inequalities of Hadamard Type, Soochow Journal of Mathematics, 21(3) (2001), pp. 335-341.
- [4] Hadamard, J., Étude sur les propriétés des fonctions entières en particulier d’une fonction considérée par Riemann, J. Math. Pures Appl. 58(1893), 171-215.
- [5] Hudzik, H., Maligranda, L. Some remarks on s-convex functions, Aequationes Math., 48(1) (1994), 100–111.
- [6] Kadakal, H., Hermite-Hadamard type inequalities for trigonometrically convex functions, Scientific Studies and Research. Series Mathematics and Informatics, 28(2) (2018), 19-28.
- [7] Kadakal, H., New Inequalities for Strongly r-Convex Functions, Journal of Function Spaces, Volume 2019, Article ID 1219237, 10 pages, 2019.
- [8] Kadakal, H., (m1;m2)-convexity and some new Hermite-Hadamard type inequalities, International Journal of Mathematical Modelling and Computations, (Submitted to journal), 2020.
- [9] Kadakal, M. Kadakal, H. and ˙I ¸scan, ˙I., 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.
- [10] Maden, S. Kadakal, H., Kadakal, M. and ˙I¸scan, ˙I., Some new integral inequalities for n-times differentiable convex and concave functions, Journal of Nonlinear Sciences and Applications, 10(12) (2017), 6141-6148.
- [11] Niculescu, CP., Convexity according to the geometric mean, Math. Inequal. Appl. 3 (2) (2000), 155-167.
- [12] Niculescu, CP., Convexity according to means, Math. Inequal. Appl. 6 (4) (2003), 571-579.
- [13] Özcan, S., Some Integral Inequalities for Harmonically ( ; s)-Convex Functions, Journal of Function Spaces, Volume 2019, Article ID 2394021, 8 pages (2019).
- [14] Özcan, S. and ˙I¸scan, ˙I., Some new Hermite-Hadamard type inequalities for s-convex functions and their applications, Journal of Inequalities and Applications, Article number: 2019:201 (2019).
- [15] Toader, G., Some generalizations of the convexity, Proc. Colloq. Approx. Optim., Univ. Cluj Napoca, Cluj-Napoca, 1985, 329-338.
- [16] Ji, AP. Zhang, TY. Qi, F., Integral inequalities of Hermite-Hadamard type for ( ;m)-GA-convex functions, arXiv preprint arXiv:1306.0852, 4 June 2013.
- [17] Varošanec, V., On h-convexity, J. Math. Anal. Appl. 326 (2007) 303-311.
- ISSN: 2147-6268
- Yayın Aralığı: Yılda 4 Sayı
- Başlangıç: 2013
- Yayıncı: -