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Year 2020, Volume: 8 Issue: 2, 313 - 321, 27.10.2020

Huriye Kadakal Kerim Bekar

Abstract

References

  • [1] S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Its Applications, RGMIA Monograph, 2002.
  • [2] S.S. Dragomir, J. Pecaric and LE.Persson, Some inequalities of Hadamard Type, Soochow Journal of Mathematics, 21(3)(2001), pp. 335-341.
  • [3] J. Hadamard, Etude sur les proprietes des fonctions entieres en particulier d’une fonction conside´re´e par Riemann, J. Math. Pures Appl. 58(1893), 171-215.
  • [4] İ. İşcan, Some new Hermite-Hadamard type inequalities for geometrically convex functions, Mathematics and Statistics 1(2): 86-91, 2013.
  • [5] İ. İşcan, New refinements for integral and sum forms of H¨older inequality, Journal of Inequalities and Applications, (2019) 2019:304.
  • [6] İ. İşcan, A new improvement of H¨older inequality via isotonic linear functionals, AIMS Mathematics, 5(3) (2020) 1720-1728.
  • [7] İ. İşcan and M. Kunt, Hermite-Hadamard-Fejer type inequalities for quasi-geometrically convex functions via fractional integrals, Journal of Mathematics, Volume 2016, Article ID 6523041, 7 pages.
  • [8] İ. İşcan, and S. Turhan. Generalized Hermite-Hadamard-Fejer type inequalities for GA-convex functions via Fractional integral, Moroccan Journal of Pure and Applied Analysis 2(1) (2016): 34-46.
  • [9] H. Kadakal, New Inequalities for Strongly r-Convex Functions, Journal of Function Spaces, Volume 2019, Article ID 1219237, 10 pages, 2019.
  • [10] M. Kadakal, $\left( m_{1},m_{2}\right) $-geometric arithmetically convex functions and related inequalities, Mathematical Sciences and Applications E-Notes, (Submitted to journal), 2020.
  • [11] H. Kadakal, $\left( m_{1},m_{2}\right) $-convexity and some new Hermite-Hadamard type inequalities, International Journal of Mathematical Modelling and Computations, 09(04), Fall (2019), 297-309.
  • [12] M. Kadakal, İ. İşcan, H. Kadakal and K. Bekar, On improvements of some integral inequalities, Researchgate, DOI: 10.13140/RG.2.2.15052.46724, Preprint, January 2019.
  • [13] M. Kadakal, H. Kadakal and İ. İşcan, Some new integral inequalities for n-times differentiable s-convex functions in the first sense, Turkish Journal of Analysis and Number Theory, 5(2) (2017), 63-68.
  • [14] C.P. Niculescu, Convexity according to the geometric mean, Math. Inequal. Appl. 3 (2) (2000), 155-167.
  • [15] S. Özcan, Some Integral Inequalities for Harmonically (a; s)-Convex Functions, Journal of Function Spaces, Volume 2019, Article ID 2394021, 8 pages (2019).
  • [16] S. Özcan, and İ. İşcan, Some new Hermite-Hadamard type inequalities for s-convex functions and their applications, Journal of Inequalities and Applications, Article number: 2019:201 (2019).
  • [17] J. Park, Some generalized inequalities of Hermite-Hadamard type for (a;m)-geometric-arithmetically convex functions, Applied Mathematical Sciences, 7.95 (2013): 4743-4759.
  • [18] G. Toader, Some generalizations of the convexity, Proc. Colloq. Approx. Optim., Univ. Cluj Napoca, Cluj-Napoca, 1985, 329-338.
  • [19] T. Toplu, M. Kadakal and İ. İşcan, On n-Polynomial convexity and some related inequalities AIMS Mathematics, 5(2) (2020), 1304.
  • [20] F. Usta, H. Budak and M. Z. Sarıkaya, Montgomery identities and Ostrowski type inequalities for fractional integral operators, Revista de la Real Academia de Ciencias Exactas, F´ısicas y Naturales. Serie A. Matematicas, 113(2) (2019), 1059-1080
  • [21] F. Usta, H. Budak and M. Z. Sarıkaya, Some New Chebyshev Type Inequalities Utilizing Generalized Fractional Integral Operators, AIMS Mathematics, 5(2) (2020) 1147-1161.
  • [22] F. Usta, H. Budak, M. Z. Sarıkaya and E. Set, On generalization of trapezoid type inequalities for s-convex functions with generalized fractional integral operators, Filomat, 32(6) (2018), 2153-2171.
  • [23] AP Ji, TY Zhang, F Qi, Integral inequalities of Hermite-Hadamard type for (a;m)-GA-convex functions, arXiv preprint arXiv:1306.0852, 4 June 2013.
  • [24] T.Y. Zhang, A.P. Ji, & F. Qi, Some inequalities of Hermite-Hadamard type for GA-convex functions with applications to means. Le Matematiche, 68(1) (2013), 229-239.

$\left(m_{1},m_{2}\right)$-GG Convex Functions and Related Inequalities

Year 2020, Volume: 8 Issue: 2, 313 - 321, 27.10.2020

Huriye Kadakal Kerim Bekar

Abstract

In this manuscript, we introduce and study the concept of $\left( m_{1},m_{2}\right) $-GG convex functions and some algebraic properties of them. In addition, we obtain Hermite-Hadamard type inequalities for the newly introduced class of functions by using an identity and Hölder, Hölder-İşcan, power-mean and improved power-mean integral inequalities.                                                                                                                                                                                                                                                                                                                                                          

Keywords

Convex function geometric convexity GG-convex function (m1;m2)-GG convex function Hermite-Hadamard type inequalities

References

  • [1] S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Its Applications, RGMIA Monograph, 2002.
  • [2] S.S. Dragomir, J. Pecaric and LE.Persson, Some inequalities of Hadamard Type, Soochow Journal of Mathematics, 21(3)(2001), pp. 335-341.
  • [3] J. Hadamard, Etude sur les proprietes des fonctions entieres en particulier d’une fonction conside´re´e par Riemann, J. Math. Pures Appl. 58(1893), 171-215.
  • [4] İ. İşcan, Some new Hermite-Hadamard type inequalities for geometrically convex functions, Mathematics and Statistics 1(2): 86-91, 2013.
  • [5] İ. İşcan, New refinements for integral and sum forms of H¨older inequality, Journal of Inequalities and Applications, (2019) 2019:304.
  • [6] İ. İşcan, A new improvement of H¨older inequality via isotonic linear functionals, AIMS Mathematics, 5(3) (2020) 1720-1728.
  • [7] İ. İşcan and M. Kunt, Hermite-Hadamard-Fejer type inequalities for quasi-geometrically convex functions via fractional integrals, Journal of Mathematics, Volume 2016, Article ID 6523041, 7 pages.
  • [8] İ. İşcan, and S. Turhan. Generalized Hermite-Hadamard-Fejer type inequalities for GA-convex functions via Fractional integral, Moroccan Journal of Pure and Applied Analysis 2(1) (2016): 34-46.
  • [9] H. Kadakal, New Inequalities for Strongly r-Convex Functions, Journal of Function Spaces, Volume 2019, Article ID 1219237, 10 pages, 2019.
  • [10] M. Kadakal, $\left( m_{1},m_{2}\right) $-geometric arithmetically convex functions and related inequalities, Mathematical Sciences and Applications E-Notes, (Submitted to journal), 2020.
  • [11] H. Kadakal, $\left( m_{1},m_{2}\right) $-convexity and some new Hermite-Hadamard type inequalities, International Journal of Mathematical Modelling and Computations, 09(04), Fall (2019), 297-309.
  • [12] M. Kadakal, İ. İşcan, H. Kadakal and K. Bekar, On improvements of some integral inequalities, Researchgate, DOI: 10.13140/RG.2.2.15052.46724, Preprint, January 2019.
  • [13] M. Kadakal, H. Kadakal and İ. İşcan, Some new integral inequalities for n-times differentiable s-convex functions in the first sense, Turkish Journal of Analysis and Number Theory, 5(2) (2017), 63-68.
  • [14] C.P. Niculescu, Convexity according to the geometric mean, Math. Inequal. Appl. 3 (2) (2000), 155-167.
  • [15] S. Özcan, Some Integral Inequalities for Harmonically (a; s)-Convex Functions, Journal of Function Spaces, Volume 2019, Article ID 2394021, 8 pages (2019).
  • [16] S. Özcan, and İ. İşcan, Some new Hermite-Hadamard type inequalities for s-convex functions and their applications, Journal of Inequalities and Applications, Article number: 2019:201 (2019).
  • [17] J. Park, Some generalized inequalities of Hermite-Hadamard type for (a;m)-geometric-arithmetically convex functions, Applied Mathematical Sciences, 7.95 (2013): 4743-4759.
  • [18] G. Toader, Some generalizations of the convexity, Proc. Colloq. Approx. Optim., Univ. Cluj Napoca, Cluj-Napoca, 1985, 329-338.
  • [19] T. Toplu, M. Kadakal and İ. İşcan, On n-Polynomial convexity and some related inequalities AIMS Mathematics, 5(2) (2020), 1304.
  • [20] F. Usta, H. Budak and M. Z. Sarıkaya, Montgomery identities and Ostrowski type inequalities for fractional integral operators, Revista de la Real Academia de Ciencias Exactas, F´ısicas y Naturales. Serie A. Matematicas, 113(2) (2019), 1059-1080
  • [21] F. Usta, H. Budak and M. Z. Sarıkaya, Some New Chebyshev Type Inequalities Utilizing Generalized Fractional Integral Operators, AIMS Mathematics, 5(2) (2020) 1147-1161.
  • [22] F. Usta, H. Budak, M. Z. Sarıkaya and E. Set, On generalization of trapezoid type inequalities for s-convex functions with generalized fractional integral operators, Filomat, 32(6) (2018), 2153-2171.
  • [23] AP Ji, TY Zhang, F Qi, Integral inequalities of Hermite-Hadamard type for (a;m)-GA-convex functions, arXiv preprint arXiv:1306.0852, 4 June 2013.
  • [24] T.Y. Zhang, A.P. Ji, & F. Qi, Some inequalities of Hermite-Hadamard type for GA-convex functions with applications to means. Le Matematiche, 68(1) (2013), 229-239.
There are 24 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Huriye Kadakal

Kerim Bekar 0000-0002-7531-9345

Publication Date October 27, 2020
Submission Date February 25, 2020
Acceptance Date July 13, 2020
Published in Issue Year 2020 Volume: 8 Issue: 2

Cite

APA Kadakal, H., & Bekar, K. (2020). $\left(m_{1},m_{2}\right)$-GG Convex Functions and Related Inequalities. Konuralp Journal of Mathematics, 8(2), 313-321.
AMA Kadakal H, Bekar K. $\left(m_{1},m_{2}\right)$-GG Convex Functions and Related Inequalities. Konuralp J. Math. October 2020;8(2):313-321.
Chicago Kadakal, Huriye, and Kerim Bekar. “$\left(m_{1},m_{2}\right)$-GG Convex Functions and Related Inequalities”. Konuralp Journal of Mathematics 8, no. 2 (October 2020): 313-21.
EndNote Kadakal H, Bekar K (October 1, 2020) $\left(m_{1},m_{2}\right)$-GG Convex Functions and Related Inequalities. Konuralp Journal of Mathematics 8 2 313–321.
IEEE H. Kadakal and K. Bekar, “$\left(m_{1},m_{2}\right)$-GG Convex Functions and Related Inequalities”, Konuralp J. Math., vol. 8, no. 2, pp. 313–321, 2020.
ISNAD Kadakal, Huriye - Bekar, Kerim. “$\left(m_{1},m_{2}\right)$-GG Convex Functions and Related Inequalities”. Konuralp Journal of Mathematics 8/2 (October 2020), 313-321.
JAMA Kadakal H, Bekar K. $\left(m_{1},m_{2}\right)$-GG Convex Functions and Related Inequalities. Konuralp J. Math. 2020;8:313–321.
MLA Kadakal, Huriye and Kerim Bekar. “$\left(m_{1},m_{2}\right)$-GG Convex Functions and Related Inequalities”. Konuralp Journal of Mathematics, vol. 8, no. 2, 2020, pp. 313-21.
Vancouver Kadakal H, Bekar K. $\left(m_{1},m_{2}\right)$-GG Convex Functions and Related Inequalities. Konuralp J. Math. 2020;8(2):313-21.
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