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Some New Integral Inequalities for n-Times Differentiable Godunova-Levin Functions

Year 2017, , 1 - 5, 08.12.2017

Huriye Kadakal , Mahir Kadakal , İmdat Iscan

https://doi.org/10.17776/csj.358766
Cited By: 4

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 

Keywords

Convex function Godunova-Levin function Hölder Integral inequality Hölder Integral inequality

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

https://doi.org/10.17776/csj.358766
Cited By: 4

Abstract

Bu
çalışmada, Hölder integral eşitsizliği ile birlikte bir integral eşitliği
kullanılarak n-kere türevlenebilen Godunova-Levin Fonksiyonları için bir kaç
yeni eşitsizlik bulunmuştur.

Keywords

Konveks fonksiyon Godunova-Levin fonksiyonu Hölder İntegral eşitsizliği Hölder İntegral eşitsizliği

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
There are 21 citations in total.

Details

Journal Section Natural Sciences
Authors

Huriye Kadakal

Mahir Kadakal

İmdat Iscan

Publication Date December 8, 2017
Submission Date February 24, 2017
Acceptance Date September 25, 2017
Published in Issue Year 2017

Cite

APA Kadakal, H., Kadakal, M., & Iscan, İ. (2017). Some New Integral Inequalities for n-Times Differentiable Godunova-Levin Functions. Cumhuriyet Science Journal, 38(4), 1-5. https://doi.org/10.17776/csj.358766

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Integral Inequalities for n-Times Differentiable h-Convex and h-Concave Functions
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