Authors:
Muhammad Bilal,Asif R. Khan,DOI NO:
https://doi.org/10.26782/jmcms.2021.07.00008Keywords:
Hermite–Hadamard dual inequality,p–convex function,quasi-convex function,P–convex function,Abstract
In this article, we would like to introduce some new types of convex function, which we named quasi convex function and convex function. With the help of these new notions we would also state the well-known Hermite Hadamard dual inequalities which we call Hermite Hadamard dual inequality for quasi convex function and convex function, respectively. In this way various new results related to Hermite Hadamard inequalities would be obtained and some would be captured as special cases by varying different values of .Refference:
I. Ambreen Arshad and Asif Raza Khan, Hermite-Hadamard-Fejer type inequalities for s-p-convex functions of several senses, TJMM, 11 (2019), 25–40.
II. Asif Raza Khan, Inam Ullah Khan and Siraj Muhammad, Hermite-Hadamard type fractional inequalities for s-convex functions of mixed kind, TMCS, 1 (2021), 25–37.
III. Charles Hermite, Sur deux limites d’une inte ́grale de ́finie, Mathesis, 3 (1883), 82.
IV. Edwin Ford Beckenback, Convex Functions, Bull. Amer. Math. Soc., 54 (1948), 439–460.
V. I ̇mdat Iscan, Hermite-Hadamard and Simpson like inequalities for differentiable harmonically convex functions, J. Math., 2014, (2014), Article 346305.
VI. I ̇mdat Iscan, Hermite-Hadamard type inequality for p-convex functions, Int. J. Anal. App., 11(2), (2016), 137–145.
VII. I ̇mdat Iscan, Selim Nauman and Kerim Bekar, Hermaite-Hadamard and Simpson type inequalities for differentiable harmonically P-convex functions, British. J. Math. & Comp., 4 (14) (2014), 1908–1920.
VIII. Jaekeun Park, Hermite-Hadamard and Simpson-like type inequalities for differentiable Harmonically Quasi-convex functions, Int. J. Math. Anal., 8(33), (2014), 1692–1645.
IX. Mehmet Kunt and I ̇mdat Iscan, Hermite-Hadamard-Fejer type inequalities for p-convex functions, Arab. J. Math., 23(1), (2017), 215–230.
X. Muhammad Aslam Noor, Khalida Inayat Noor, Marcela Mihai and Muhammad Uzair Awan, Hermite-Hadamard inequalities for differentiable p-convex functions using hypergeometric functions, Publications de L’Institut Mathematique, 100(114), (2015), 251–257.
XI. Muhammad Bilal and Asif Raza Khan, New Generalized Hermite-Hadamard Inequalities for p-convex functions in the mixed kind, EJPAM (Accepted), 2021.
XII. Muhammad Bilal, Muhammad Imtiaz Asif Raza Khan, Ihsan Ullah Khan and Muhammad Zafran, Generalized Hermite-Hadamard inequalities for s-convex functions in mixed kind, (Submitted), (2021).
XIII. Murat Emin O ̈zdemi ́r, Merve Avci and Havva Kavurmaci, Hermaite-Hadamard type inequalities via (α, m) convexity, Comp. Math. App., 61, (2011), 2614–2620.
XIV. Mehmood Faraz, Asif R. Khan, & M. Azeem Ullah Siddique. : ‘SOME RESULTS RELATED TO CONVEXIFIABLE FUNCTIONS’. J. Mech. Cont.& Math. Sci., Vol.-15, No.-12, December (2020) pp 36-45. DOI : 10.26782/jmcms.2020.12.00004
XV. Silvestru Sever Dragomir, Josip Pec ̌aric ́ and Lars-Erik Persson, Some inequalities of Hadamard type, Soochow J. Math., 21(3) (1995), 335–341.