International Journal of Nonlinear Analysis and Applications
Inequalities for $tgs$-convex functions via some conformable fractional integrals
Document Type : Research Paper
Authors
1 School of Natural Sciences, National University of Sciences and Technology, sector H-12, Islamabad, Pakistan
2 School of Natural Sciences, National University of Sciences and Technology, Islamabad, Pakistan.
Abstract
In this research article, we establish several Hermite-Hadamard type inequalities for tgs-convex functions via conformable fractional integrals and new fractional conformable integral operators.
Keywords
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[22] I. Iscan, Hermite-Hadamard type inequalities for harmonically convex functions, Hacet. J. Math. Stat. 43(6) (2014) 935–942.
[23] E. Set, M. Z. Sarikaya, A. G¨ozpnar, Some Hermite-Hadamard type inequalities for convex functions via conformable fractional integrals and related inequalities, preprint, 26 (2016) 221–229.
[24] M. Tunc, E. Gov, U. S¸anal, On tgs-convex function and their inequalities, Facta Univ. Ser. Math. Inf. 30(5) (2015) 679–691.
[25] S. Ullah, G. Farid , K. A. Khan, A. Waheed and S. Mehmood, Generalized fractional inequalities for quasi-convex functions, Adv. Difference Equ. 2019 (2019) p. 15.
[26] K. S. Zhang and J. P. Wan, p-convex functions and their properties, Pure Appl. Math. 23(1) (2007) 130–133.
[8] J. Hadamard, Etude sur les propri´et´es des fonctions enti`eres et en particulier d’une fonction consid´er´ee par ´ Riemann, J. Math. Pures Appl. (1893) 171–215.
[9] Ch. Hermite, Sur deux limites d’une in´tegrale ´denie, Mathesis 3 (1883) 82.
[10] F. Jarad, E. Ugurlu, T. Abdeljawad and D. Baleanu, On a new class of fractional operators, Adv. Difference Equ. 2017 (2017).
[11] S. M. Kang, G. Farid, W. Nazeer and S. Mehmood, (h, m)-convex functions and associated fractional Hadamard and Fej´er-Hadamard inequalities via an extended generalized Mittag-Leffler function, J. Inequal. Appl. 2019 (2019) p. 78.
[12] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential equations, Elsevier Science B. V., Amsterdam, 2006.
[13] S. Mehmood, G. Farid, K. A. Khan and M. Yussouf, New fractional Hadamard and Fej´er-Hadamard inequalities associated with exponentially (h, m)-convex functions, Eng. Appl. Sci. Lett. 3(2) (2020) 9–18.
[14] S. Mehmood, G. Farid, K. A. Khan and M. Yussouf, New Hadamard and Fej´er-Hadamard fractional inequalities for exponentially m-convex function, Eng. Appl. Sci. Lett. 3(1) (2020) 45–55.
[15] N. Mehreen and M. Anwar, Hermite-Hadamard type inequalities via exponentially (p, h)-convex functions. IEEE Access, 8 (2020) 37589–37595
[16] N. Mehreen and M. Anwar, Hermite-Hadamard and Hermite-Hadamard-Fej´er type inequalities for p-convex functions via conformable fractional integrals, J. Inequal. Appl. 2020 (2020) p. 107.
[17] N. Mehreen and M. Anwar, Hermite-Hadamard and Hermite-Hadamard-Fej´er type inequalities for p-convex functions via new fractional conformable integral operators, J. Math. Compt. Sci. 19 (2019) 230–240.
[18] N. Mehreen and M. Anwar, Hermite-Hadamard type inequalities via exponentially p-convex functions and exponentially s-convex functions in second sense with applications, J. Inequal. Appl. 2019 (2019), p. 92.
[19] N. Mehreen and M. Anwar, Integral inequalities for some convex functions via generalized fractional integrals, J. Inequal. Appl. 2018 (2018) p. 208.
[20] N. Mehreen and M. Anwar, Some inequalities via ψ-Riemann-Liouville fractional integrals, AIMS Math. 4(5) (2019) 1403–1415.
[21] N. Mehreen and M. Anwar, On some Hermite-Hadamard type inequalities for tgs-convex functions via generalized fractional integrals, Adv. Differnce Equ. 2020 (2020) p. 6.
[22] I. Iscan, Hermite-Hadamard type inequalities for harmonically convex functions, Hacet. J. Math. Stat. 43(6) (2014) 935–942.
[23] E. Set, M. Z. Sarikaya, A. G¨ozpnar, Some Hermite-Hadamard type inequalities for convex functions via conformable fractional integrals and related inequalities, preprint, 26 (2016) 221–229.
[24] M. Tunc, E. Gov, U. S¸anal, On tgs-convex function and their inequalities, Facta Univ. Ser. Math. Inf. 30(5) (2015) 679–691.
[25] S. Ullah, G. Farid , K. A. Khan, A. Waheed and S. Mehmood, Generalized fractional inequalities for quasi-convex functions, Adv. Difference Equ. 2019 (2019) p. 15.
[26] K. S. Zhang and J. P. Wan, p-convex functions and their properties, Pure Appl. Math. 23(1) (2007) 130–133.
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Volume 12, Issue 2
November 2021Pages 425-436
- Receive Date: 08 February 2020
- Revise Date: 06 May 2020
- Accept Date: 08 May 2020