Araştırma Makalesi
BibTex RIS Kaynak Göster

New General Inequalities For Exponential Type Convex Function

Yıl 2023, Cilt: 8 Sayı: 1, 11 - 18, 03.05.2023
https://izlik.org/JA32FT63BD

Öz

In this paper, we introduce the concept of an exponential type convex function. We establish new integral inequalities of the Hermite-Hadamard type by using the Power-Mean and Hölder Inequalities. Additionally, we give the Riemann-Liouville fractional integrals definitions. We use these Riemann-Liouville fractional integrals to establish a new integral inequality for exponential type convex function.

Kaynakça

  • Alomari M.W., Dragomir S.S. and Kirmaci U.S., Generalizations of the Hermite-Hadamard type inequalities for functions whose derivatives are s-convex, Acta Commen. Uni. Tartu. Math., 17 (2), 2013.
  • Kadakal M., İşçan İ., Exponential Type Convexity and Some Related Inequalities. Journal of Inequalities and Application,
  • Özdemir M.E. and Kırmacı U. S. Two new theorem on mappings uniformly continuous and convex with applications to quadrature rules and means, Appl. Math. Comp., 2003, 143: 269--274.
  • Hadamard J.: Êtude sur les propriêtês des fonctions entiêres en particullier d'une fonction considêrêê par Riemann. J. Math. Pures Appl. 58, 171-215 (1893)
  • Özdemir, M.E., Bayraktar, B., Butt. S.I. and Akdemir, A.O., Some New Hermite-Hadamard type inequalities Via Non-Conformable Fractional Integrals, Turkish J. Ineq., 5 (2) (2021), 48 --60.
  • Set, E., Akdemir, A.O., Karaoğlan, A., Abdeljawad, T. and Shatanawi, W., On New Generalizations of Hermite-Hadamard Type Inequalities via Atangana-Baleanu Fractional Integral Operators, Axioms, 10(3)(2021), 223.
  • Özdemir, M. E., New Refinements of Hadamard Integral inequlaity via k-Fractional Integrals for p-Convex Function, Turkish Jour. Sci., 6 (1)(2021), 1-5.
  • Ekinci, A., Akdemir, A.O. and Özdemir, M.E., Integral Inequalities for Different Kinds of Convexity via Classical Inequalities, Turkish Jour. Sci, 5 (3)(2020), 305-313.
  • Ekinci, A., Özdemir, M.E. and Set, E., New Integral Inequalities of Ostrowski Type for Quasi-Convex Functions with Applications, Turkish Jour. Sci, 5 (3)(2020), 290-304.
  • Yıldız, Ç., Gürbüz, M. and Akdemir, A.O. The Hadamard Type Inequalities for M- Convex Functions. Konuralp Jour. Math., 1(1)(2013), 40-47.
  • Chu, Y.M., Khan, M.A., Khan, T.U. and Ali, T., Generalizations of Hermite-Hadamard type inequalities for MT-convex functions, J. Nonlinear Sci. Appl., 9(5)(2016), 4305-4316.
  • Khan, M.A., Chu, Y., Khan, T.U. and Khan, J., Some new inequalities of Hermite-Hadamard type for s-convex functions with applications, Open Mathematics, 15(1)(2017), 1414-1430.
  • R. Gorenflo, F. Mainardi, Fractional calculus: integral and differential equations of fractional order, Springer Verlag, Wien (1997), 223-276.
  • Özdemir, M.E., Dragomir, S.S. and Yıldız, Ç., The Hadamard Inequality For Convex Function Via Fractional Integrals, Acta Math. Sci., 33(5) (2013), 1293-1299.
  • İşcan, İ., New refinements for integral and sum forms of Hölder inequality, J. Inequal. Appl., 2019:304 (2019).

Yıl 2023, Cilt: 8 Sayı: 1, 11 - 18, 03.05.2023
https://izlik.org/JA32FT63BD

Öz

Kaynakça

  • Alomari M.W., Dragomir S.S. and Kirmaci U.S., Generalizations of the Hermite-Hadamard type inequalities for functions whose derivatives are s-convex, Acta Commen. Uni. Tartu. Math., 17 (2), 2013.
  • Kadakal M., İşçan İ., Exponential Type Convexity and Some Related Inequalities. Journal of Inequalities and Application,
  • Özdemir M.E. and Kırmacı U. S. Two new theorem on mappings uniformly continuous and convex with applications to quadrature rules and means, Appl. Math. Comp., 2003, 143: 269--274.
  • Hadamard J.: Êtude sur les propriêtês des fonctions entiêres en particullier d'une fonction considêrêê par Riemann. J. Math. Pures Appl. 58, 171-215 (1893)
  • Özdemir, M.E., Bayraktar, B., Butt. S.I. and Akdemir, A.O., Some New Hermite-Hadamard type inequalities Via Non-Conformable Fractional Integrals, Turkish J. Ineq., 5 (2) (2021), 48 --60.
  • Set, E., Akdemir, A.O., Karaoğlan, A., Abdeljawad, T. and Shatanawi, W., On New Generalizations of Hermite-Hadamard Type Inequalities via Atangana-Baleanu Fractional Integral Operators, Axioms, 10(3)(2021), 223.
  • Özdemir, M. E., New Refinements of Hadamard Integral inequlaity via k-Fractional Integrals for p-Convex Function, Turkish Jour. Sci., 6 (1)(2021), 1-5.
  • Ekinci, A., Akdemir, A.O. and Özdemir, M.E., Integral Inequalities for Different Kinds of Convexity via Classical Inequalities, Turkish Jour. Sci, 5 (3)(2020), 305-313.
  • Ekinci, A., Özdemir, M.E. and Set, E., New Integral Inequalities of Ostrowski Type for Quasi-Convex Functions with Applications, Turkish Jour. Sci, 5 (3)(2020), 290-304.
  • Yıldız, Ç., Gürbüz, M. and Akdemir, A.O. The Hadamard Type Inequalities for M- Convex Functions. Konuralp Jour. Math., 1(1)(2013), 40-47.
  • Chu, Y.M., Khan, M.A., Khan, T.U. and Ali, T., Generalizations of Hermite-Hadamard type inequalities for MT-convex functions, J. Nonlinear Sci. Appl., 9(5)(2016), 4305-4316.
  • Khan, M.A., Chu, Y., Khan, T.U. and Khan, J., Some new inequalities of Hermite-Hadamard type for s-convex functions with applications, Open Mathematics, 15(1)(2017), 1414-1430.
  • R. Gorenflo, F. Mainardi, Fractional calculus: integral and differential equations of fractional order, Springer Verlag, Wien (1997), 223-276.
  • Özdemir, M.E., Dragomir, S.S. and Yıldız, Ç., The Hadamard Inequality For Convex Function Via Fractional Integrals, Acta Math. Sci., 33(5) (2013), 1293-1299.
  • İşcan, İ., New refinements for integral and sum forms of Hölder inequality, J. Inequal. Appl., 2019:304 (2019).
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Çetin Yıldız 0000-0002-8302-343X

Emre Bakan 0000-0002-6881-5711

Hüseyin Dönmez 0000-0002-6799-1270

Yayımlanma Tarihi 3 Mayıs 2023
IZ https://izlik.org/JA32FT63BD
Yayımlandığı Sayı Yıl 2023 Cilt: 8 Sayı: 1

Kaynak Göster

APA Yıldız, Ç., Bakan, E., & Dönmez, H. (2023). New General Inequalities For Exponential Type Convex Function. Turkish Journal of Science, 8(1), 11-18. https://izlik.org/JA32FT63BD
AMA 1.Yıldız Ç, Bakan E, Dönmez H. New General Inequalities For Exponential Type Convex Function. TJOS. 2023;8(1):11-18. https://izlik.org/JA32FT63BD
Chicago Yıldız, Çetin, Emre Bakan, ve Hüseyin Dönmez. 2023. “New General Inequalities For Exponential Type Convex Function”. Turkish Journal of Science 8 (1): 11-18. https://izlik.org/JA32FT63BD.
EndNote Yıldız Ç, Bakan E, Dönmez H (01 Mayıs 2023) New General Inequalities For Exponential Type Convex Function. Turkish Journal of Science 8 1 11–18.
IEEE [1]Ç. Yıldız, E. Bakan, ve H. Dönmez, “New General Inequalities For Exponential Type Convex Function”, TJOS, c. 8, sy 1, ss. 11–18, May. 2023, [çevrimiçi]. Erişim adresi: https://izlik.org/JA32FT63BD
ISNAD Yıldız, Çetin - Bakan, Emre - Dönmez, Hüseyin. “New General Inequalities For Exponential Type Convex Function”. Turkish Journal of Science 8/1 (01 Mayıs 2023): 11-18. https://izlik.org/JA32FT63BD.
JAMA 1.Yıldız Ç, Bakan E, Dönmez H. New General Inequalities For Exponential Type Convex Function. TJOS. 2023;8:11–18.
MLA Yıldız, Çetin, vd. “New General Inequalities For Exponential Type Convex Function”. Turkish Journal of Science, c. 8, sy 1, Mayıs 2023, ss. 11-18, https://izlik.org/JA32FT63BD.
Vancouver 1.Yıldız Ç, Bakan E, Dönmez H. New General Inequalities For Exponential Type Convex Function. TJOS [Internet]. 01 Mayıs 2023;8(1):11-8. Erişim adresi: https://izlik.org/JA32FT63BD