Some New Integral Inequalities for n-Times Differentiable Godunova-Levin Functions
Year 2017,
, 1 - 5, 08.12.2017
Huriye Kadakal
,
Mahir Kadakal
,
İmdat Iscan
Abstract
In this work, by using an integral identity together with the Hölder
integral inequality we establish several new inequalities for n-times
differentiable Godunova-Levin functions
References
- [1]. Akdemir A.O., Özdemir M. E., “Some Hadamard-Type Inequalities For Coordinated P−Convex Functions and Godunova-Levin Functions”, arXiv:1012.5880v2 [math.CA] 24 Mar 2011.
- [2]. Cerone P., Dragomir S.S., Roumeliotis J., “Some Ostrowski type inequalities for n-time differentiable mappings and applications”, Demonstratio Math., 32 (4) (1999), 697-712.
- [3]. Cerone P., Dragomir S.S., Roumeliotis J., Šunde J., “A new generalization of the trapezoid formula for n-time differentiable mappings and applications”, Demonstratio Math., 33 (4) (2000), 719-736.
- [4]. Hwang D.Y.,“Some Inequalities for n-time Differentiable Mappings and Applications”, Kyung. Math. Jour., 43 (2003), 335-343.
- [5]. İşcan İ., “Some Generalized Hermite-Hadamard Type Inequalities for Quasi-Geometrically Convex Functions”, American Journal of Mathematical Analysis, 2013, Vol. 1, No. 3, 48-52.
- [6]. İşcan İ., “Some new general integral inequalities for h-convex and h-concave functions”, Adv. Pure Appl. Math. 5 (1), 21-29 (2014).
- [7]. İşcan İ., “Hermite-Hadamard type inequalities for harmonically convex functions”, Hacettepe Journal of Mathematics and Statistics, Volume 43 (6) (2014), 935-942.
- [8]. İşcan İ., “Hermite-Hadamard type inequalities for GA-s-convex functions”, Le Matematiche, Vol. LXIX (2014) Fasc. II, pp. 129-146.
- [9]. İşcan İ., Numan S., “Ostrowski type inequalities for harmonically quasi-convex functions”, Electronic Journal of Mathematical Analysis and Applications, Vol. 2(2) July 2014, pp. 189-198.
- [10]. İşcan İ., “On new general integral inequalities for quasi-convex functions and their applications”, Palestine Journal of Mathematics. 4(1) (2015), 21-29.
- [11]. Jiang W.D., Niu D.W., Hua Y., Qi F., “Generalizations of Hermite-Hadamard inequality to n-time differentiable function which are s -convex in the second sense”, Analysis (Munich), 32 (2012), 209-220.
- [12]. Kırmacı U.S., Bakula M.K., Özdemir M.E., Pećarić J., “Hadamard-type inequalities for s -convex functions”, Appl. Math. and Comp., 193 (2007), 26-35.
- [13]. Li M., Andweiwei J., “Some Fractional Hermite-Hadamard Inequalities for Convex and Godunova-Levin Functions”, Ser. Math. Inform. Vol. 30, No 2 (2015), 195-208.
- [14]. Maden S., Kadakal H., Kadakal M., İşcan İ., “Some new integral inequalities for n-times differentiable convex and concave functions”. https://www.researchgate.net/publication/312529563, (Submitted).
- [15]. Noor M.A., Noor K.I., Awan M.U., “Fractional Ostrowski Inequalities for s-Godunova-Levin Functions”, International Journal of Analysis and Applications, Volume 5, Number 2 (2014), 167-173.
- [16]. Noor M.A., Noor K.I., Awan M.U., Khan S., “Fractional Hermite-Hadamard Inequalities for some New Classes of Godunova-Levin Functions”, Appl. Math. Inf. Sci. 8, No. 6, 2865-2872, (2014).
- [17]. Özdemir M.E., Yıldız Ç., “New Inequalities for n-time differentiable functions”, Arxiv:1402.4959v1.
- [18]. Özdemir M.E., “Some inequalities for the s-Godunova–Levin type functions”, Math Sci (2015) 9:27-32.
- [19]. Set E., Özdemir M.E., Dragomir S.S., “On Hadamard-Type Inequalities Involving Several Kinds of Convexity”, Jour. of Ineq. and Appl., 2010, 286845.
- [20]. Wang S.H., Xi B.Y., Qi F., “Some new inequalities of Hermite-Hadamard type for n-time differentiable functions which are m-convex”, Analysis (Munich), 32 (2012), 247-262.
- [21]. Xi B. Y., Qi F., “Some Integral Inequalities of Hermite-Hadamard Type for Convex Functions with Applications to Means”, J. Funct. Spaces Appl (2012) 14 pages
n-kere Türevlenebilen Godunova-Levin Fonksiyonları için Bazı Yeni İntegral Eşitsizlikler
Year 2017,
, 1 - 5, 08.12.2017
Huriye Kadakal
,
Mahir Kadakal
,
İmdat Iscan
Abstract
Bu
çalışmada, Hölder integral eşitsizliği ile birlikte bir integral eşitliği
kullanılarak n-kere türevlenebilen Godunova-Levin Fonksiyonları için bir kaç
yeni eşitsizlik bulunmuştur.
References
- [1]. Akdemir A.O., Özdemir M. E., “Some Hadamard-Type Inequalities For Coordinated P−Convex Functions and Godunova-Levin Functions”, arXiv:1012.5880v2 [math.CA] 24 Mar 2011.
- [2]. Cerone P., Dragomir S.S., Roumeliotis J., “Some Ostrowski type inequalities for n-time differentiable mappings and applications”, Demonstratio Math., 32 (4) (1999), 697-712.
- [3]. Cerone P., Dragomir S.S., Roumeliotis J., Šunde J., “A new generalization of the trapezoid formula for n-time differentiable mappings and applications”, Demonstratio Math., 33 (4) (2000), 719-736.
- [4]. Hwang D.Y.,“Some Inequalities for n-time Differentiable Mappings and Applications”, Kyung. Math. Jour., 43 (2003), 335-343.
- [5]. İşcan İ., “Some Generalized Hermite-Hadamard Type Inequalities for Quasi-Geometrically Convex Functions”, American Journal of Mathematical Analysis, 2013, Vol. 1, No. 3, 48-52.
- [6]. İşcan İ., “Some new general integral inequalities for h-convex and h-concave functions”, Adv. Pure Appl. Math. 5 (1), 21-29 (2014).
- [7]. İşcan İ., “Hermite-Hadamard type inequalities for harmonically convex functions”, Hacettepe Journal of Mathematics and Statistics, Volume 43 (6) (2014), 935-942.
- [8]. İşcan İ., “Hermite-Hadamard type inequalities for GA-s-convex functions”, Le Matematiche, Vol. LXIX (2014) Fasc. II, pp. 129-146.
- [9]. İşcan İ., Numan S., “Ostrowski type inequalities for harmonically quasi-convex functions”, Electronic Journal of Mathematical Analysis and Applications, Vol. 2(2) July 2014, pp. 189-198.
- [10]. İşcan İ., “On new general integral inequalities for quasi-convex functions and their applications”, Palestine Journal of Mathematics. 4(1) (2015), 21-29.
- [11]. Jiang W.D., Niu D.W., Hua Y., Qi F., “Generalizations of Hermite-Hadamard inequality to n-time differentiable function which are s -convex in the second sense”, Analysis (Munich), 32 (2012), 209-220.
- [12]. Kırmacı U.S., Bakula M.K., Özdemir M.E., Pećarić J., “Hadamard-type inequalities for s -convex functions”, Appl. Math. and Comp., 193 (2007), 26-35.
- [13]. Li M., Andweiwei J., “Some Fractional Hermite-Hadamard Inequalities for Convex and Godunova-Levin Functions”, Ser. Math. Inform. Vol. 30, No 2 (2015), 195-208.
- [14]. Maden S., Kadakal H., Kadakal M., İşcan İ., “Some new integral inequalities for n-times differentiable convex and concave functions”. https://www.researchgate.net/publication/312529563, (Submitted).
- [15]. Noor M.A., Noor K.I., Awan M.U., “Fractional Ostrowski Inequalities for s-Godunova-Levin Functions”, International Journal of Analysis and Applications, Volume 5, Number 2 (2014), 167-173.
- [16]. Noor M.A., Noor K.I., Awan M.U., Khan S., “Fractional Hermite-Hadamard Inequalities for some New Classes of Godunova-Levin Functions”, Appl. Math. Inf. Sci. 8, No. 6, 2865-2872, (2014).
- [17]. Özdemir M.E., Yıldız Ç., “New Inequalities for n-time differentiable functions”, Arxiv:1402.4959v1.
- [18]. Özdemir M.E., “Some inequalities for the s-Godunova–Levin type functions”, Math Sci (2015) 9:27-32.
- [19]. Set E., Özdemir M.E., Dragomir S.S., “On Hadamard-Type Inequalities Involving Several Kinds of Convexity”, Jour. of Ineq. and Appl., 2010, 286845.
- [20]. Wang S.H., Xi B.Y., Qi F., “Some new inequalities of Hermite-Hadamard type for n-time differentiable functions which are m-convex”, Analysis (Munich), 32 (2012), 247-262.
- [21]. Xi B. Y., Qi F., “Some Integral Inequalities of Hermite-Hadamard Type for Convex Functions with Applications to Means”, J. Funct. Spaces Appl (2012) 14 pages