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New General Inequalities For Exponential Type Convex Function

Yıl 2023, Cilt: 8 Sayı: 1, 11 - 18, 03.05.2023

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

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 Volume VIII Issue I
Yazarlar

Çetin Yıldız 0000-0002-8302-343X

Emre Bakan 0000-0002-6881-5711

Hüseyin Dönmez 0000-0002-6799-1270

Yayımlanma Tarihi 3 Mayıs 2023
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.
AMA Yıldız Ç, Bakan E, Dönmez H. New General Inequalities For Exponential Type Convex Function. TJOS. Mayıs 2023;8(1):11-18.
Chicago Yıldız, Çetin, Emre Bakan, ve Hüseyin Dönmez. “New General Inequalities For Exponential Type Convex Function”. Turkish Journal of Science 8, sy. 1 (Mayıs 2023): 11-18.
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 Ç. Yıldız, E. Bakan, ve H. Dönmez, “New General Inequalities For Exponential Type Convex Function”, TJOS, c. 8, sy. 1, ss. 11–18, 2023.
ISNAD Yıldız, Çetin vd. “New General Inequalities For Exponential Type Convex Function”. Turkish Journal of Science 8/1 (Mayıs 2023), 11-18.
JAMA 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, 2023, ss. 11-18.
Vancouver Yıldız Ç, Bakan E, Dönmez H. New General Inequalities For Exponential Type Convex Function. TJOS. 2023;8(1):11-8.