Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2021, Cilt: 13 Sayı: 2, 287 - 293, 31.12.2021
https://doi.org/10.47000/tjmcs.925182

Öz

Kaynakça

  • [1] Abramowitz, M., Stegun, I.A., (Eds), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathematics Series 55, Washington, 1970.
  • [2] Adilov, G., Rubinov, A.M., $B-$convex sets and functions. Numerical Functional Analysis and Optimization, 27(3-4)(2006), 237–257.
  • [3] Adilov, G., Yesilce, I., On Generalizations of the concept of convexity, Hacettepe Journal of Mathematics and Statistics, 41(5)(2012), 723–730.
  • [4] Adilov, G., Kemali, S., Abstract convexity and Hermite-Hadamard type inequalities, Journal of Inequalities and Applications, 2009(2009), 943534.
  • [5] Alomari, M.W., Darus, M., Kirmaci, U.S., Some inequalities of Hermite-Hadamard type for s-convex functions, Acta Mathematica Scientia, 31(4)(2011), 1643–1652.
  • [6] Dragomir, S.S., Agarwal, R.P.,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.
  • [7] Dragomir, S.S., Pierce, C.E.M., On some inequalities for differentiable convex functions and applications, preprint, (2000).
  • [8] Dragomir, S.S., Pierce, C.E.M., Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA, Victoria University, 2000.
  • [9] Dragomir S.S., Fitzpatrick, S., The Hadamard’s inequality for s-convex functions in the second sense, Demonstratio Math., 32(4)(1999), 687–696.
  • [10] Eken, Z., Sezer, S., Tınaztepe, G., Adilov, G., s-convex functions in the fourth sense and their some properties. Submitted.
  • [11] Hudzik, H., Maligranda, L., Some remarks on s-convex functions. Aequ. Math. 48(1994), 100–111.
  • [12] Khan, M., Hanif, M.A., Khan, A.H., et al, Association of Jensen’s inequality for s-convex function with Csiszar divergence, J Inequal 162(2019).
  • [13] Kırmacı, U.S., Bakula, M.K., Ozdemir, M.E., Pecaric, J., Hadamard-type inequalities for s-convex functions, Appl. Math. Comput., 193(2007), 26–35.
  • [14] Kemali, S., Sezer, S., Tınaztepe, G., Adilov, G., s-Convex function in the third sense, Korean J. Math., 29(3)(2021), 593-602.
  • [15] Kemali, S., Yesilce, I., Adilov, G., $B$-Convexity, $B^{-1}$-Convexity, and their comparison, Numerical Functional Analysis and Optimization, 36(2)(2015), 133–146.
  • [16] Orlicz, W., A note on modular spaces I. Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys, 9(1961), 157–162.
  • [17] Özcan, S., İşcan, I., Some new Hermite–Hadamard type inequalities for s-convex functions and their applications, Journal of Inequalities and Applications, Article, 201, (2019).
  • [18] Pearce C.E.M., Pecaric, J., Inequalities for differentiable mappings with application to special means and quadrature formula, Applied Mathematics Letters 13(2)(2000), 51–55.
  • [19] Sezer, S., Eken, Z., Tınaztepe, G., Adilov, G., p-Convex functions and some of their properties, Numerical Functional Analysis and Optimization, 42(4)(2021), 443–459.
  • [20] Sezer, S., The Hermite-Hadamard inequality for s-Convex functions in the third sense AIMS Mathematics, 6(7), (2021), 7719–7732.
  • [21] Tinaztepe, G. Yesilce, I., Adilov, G., Separation of $B^{-1}$-convex sets by $B^{-1}$-measurable Maps, Journal of Convex Analysis, 21(2)(2014), 571–580.
  • [22] Yeşilce, İ., Adilov, G., Hermite-Hadamard inequalities for $B$-convex and $B^{-1}$-convex functions. International Journal of Nonlinear Analysis and Applications, 8(1)(2017), 225–233.
  • [23] Zhang, K.S., Wan, J.P., p-Convex functions and their properties, Pure and Applied Mathematics, 1(23)2007), 130–133.

Hermite-Hadamard Type Inequality for s-Convex Functions in the Fourth Sense

Yıl 2021, Cilt: 13 Sayı: 2, 287 - 293, 31.12.2021
https://doi.org/10.47000/tjmcs.925182

Öz

In this study, firstly, Hermite-Hadamard type inequalities are examined for functions whose first derivative is $s$-convex functions in the fourth sense. In addition, Hermite-Hadamard type inequalities are examined for functions whose second derivative is $s$-convex functions in the fourth sense. Finally, some application examples including special tools and digamma functions are presented.

Kaynakça

  • [1] Abramowitz, M., Stegun, I.A., (Eds), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathematics Series 55, Washington, 1970.
  • [2] Adilov, G., Rubinov, A.M., $B-$convex sets and functions. Numerical Functional Analysis and Optimization, 27(3-4)(2006), 237–257.
  • [3] Adilov, G., Yesilce, I., On Generalizations of the concept of convexity, Hacettepe Journal of Mathematics and Statistics, 41(5)(2012), 723–730.
  • [4] Adilov, G., Kemali, S., Abstract convexity and Hermite-Hadamard type inequalities, Journal of Inequalities and Applications, 2009(2009), 943534.
  • [5] Alomari, M.W., Darus, M., Kirmaci, U.S., Some inequalities of Hermite-Hadamard type for s-convex functions, Acta Mathematica Scientia, 31(4)(2011), 1643–1652.
  • [6] Dragomir, S.S., Agarwal, R.P.,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.
  • [7] Dragomir, S.S., Pierce, C.E.M., On some inequalities for differentiable convex functions and applications, preprint, (2000).
  • [8] Dragomir, S.S., Pierce, C.E.M., Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA, Victoria University, 2000.
  • [9] Dragomir S.S., Fitzpatrick, S., The Hadamard’s inequality for s-convex functions in the second sense, Demonstratio Math., 32(4)(1999), 687–696.
  • [10] Eken, Z., Sezer, S., Tınaztepe, G., Adilov, G., s-convex functions in the fourth sense and their some properties. Submitted.
  • [11] Hudzik, H., Maligranda, L., Some remarks on s-convex functions. Aequ. Math. 48(1994), 100–111.
  • [12] Khan, M., Hanif, M.A., Khan, A.H., et al, Association of Jensen’s inequality for s-convex function with Csiszar divergence, J Inequal 162(2019).
  • [13] Kırmacı, U.S., Bakula, M.K., Ozdemir, M.E., Pecaric, J., Hadamard-type inequalities for s-convex functions, Appl. Math. Comput., 193(2007), 26–35.
  • [14] Kemali, S., Sezer, S., Tınaztepe, G., Adilov, G., s-Convex function in the third sense, Korean J. Math., 29(3)(2021), 593-602.
  • [15] Kemali, S., Yesilce, I., Adilov, G., $B$-Convexity, $B^{-1}$-Convexity, and their comparison, Numerical Functional Analysis and Optimization, 36(2)(2015), 133–146.
  • [16] Orlicz, W., A note on modular spaces I. Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys, 9(1961), 157–162.
  • [17] Özcan, S., İşcan, I., Some new Hermite–Hadamard type inequalities for s-convex functions and their applications, Journal of Inequalities and Applications, Article, 201, (2019).
  • [18] Pearce C.E.M., Pecaric, J., Inequalities for differentiable mappings with application to special means and quadrature formula, Applied Mathematics Letters 13(2)(2000), 51–55.
  • [19] Sezer, S., Eken, Z., Tınaztepe, G., Adilov, G., p-Convex functions and some of their properties, Numerical Functional Analysis and Optimization, 42(4)(2021), 443–459.
  • [20] Sezer, S., The Hermite-Hadamard inequality for s-Convex functions in the third sense AIMS Mathematics, 6(7), (2021), 7719–7732.
  • [21] Tinaztepe, G. Yesilce, I., Adilov, G., Separation of $B^{-1}$-convex sets by $B^{-1}$-measurable Maps, Journal of Convex Analysis, 21(2)(2014), 571–580.
  • [22] Yeşilce, İ., Adilov, G., Hermite-Hadamard inequalities for $B$-convex and $B^{-1}$-convex functions. International Journal of Nonlinear Analysis and Applications, 8(1)(2017), 225–233.
  • [23] Zhang, K.S., Wan, J.P., p-Convex functions and their properties, Pure and Applied Mathematics, 1(23)2007), 130–133.
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Serap Kemali 0000-0001-5804-4127

Yayımlanma Tarihi 31 Aralık 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 13 Sayı: 2

Kaynak Göster

APA Kemali, S. (2021). Hermite-Hadamard Type Inequality for s-Convex Functions in the Fourth Sense. Turkish Journal of Mathematics and Computer Science, 13(2), 287-293. https://doi.org/10.47000/tjmcs.925182
AMA Kemali S. Hermite-Hadamard Type Inequality for s-Convex Functions in the Fourth Sense. TJMCS. Aralık 2021;13(2):287-293. doi:10.47000/tjmcs.925182
Chicago Kemali, Serap. “Hermite-Hadamard Type Inequality for S-Convex Functions in the Fourth Sense”. Turkish Journal of Mathematics and Computer Science 13, sy. 2 (Aralık 2021): 287-93. https://doi.org/10.47000/tjmcs.925182.
EndNote Kemali S (01 Aralık 2021) Hermite-Hadamard Type Inequality for s-Convex Functions in the Fourth Sense. Turkish Journal of Mathematics and Computer Science 13 2 287–293.
IEEE S. Kemali, “Hermite-Hadamard Type Inequality for s-Convex Functions in the Fourth Sense”, TJMCS, c. 13, sy. 2, ss. 287–293, 2021, doi: 10.47000/tjmcs.925182.
ISNAD Kemali, Serap. “Hermite-Hadamard Type Inequality for S-Convex Functions in the Fourth Sense”. Turkish Journal of Mathematics and Computer Science 13/2 (Aralık 2021), 287-293. https://doi.org/10.47000/tjmcs.925182.
JAMA Kemali S. Hermite-Hadamard Type Inequality for s-Convex Functions in the Fourth Sense. TJMCS. 2021;13:287–293.
MLA Kemali, Serap. “Hermite-Hadamard Type Inequality for S-Convex Functions in the Fourth Sense”. Turkish Journal of Mathematics and Computer Science, c. 13, sy. 2, 2021, ss. 287-93, doi:10.47000/tjmcs.925182.
Vancouver Kemali S. Hermite-Hadamard Type Inequality for s-Convex Functions in the Fourth Sense. TJMCS. 2021;13(2):287-93.