Hermite-Hadamard Type Inequalities for Sub-Topical Functions

Document Type : Research Paper

Author

Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.

10.22072/wala.2023.2000551.1419

Abstract

In this paper, we study Hermite-Hadamard type inequalities for sub-topical (increasing and plus sub-homogeneous) functions in the framework of abstract convexity. Some examples of such inequalities for functions defined on special domains are given.

Keywords


[1] G.R. Adilov and S. Kemali, Hermite-Hadamard type inequalities for increasing positively homogeneous functions, J. 
      Inequal. Appl., 2007(1) (2007), 1-10.
[2] M.H. Daryaei and  A. Doagooei, Topical functions: Hermite-Hadamard type inequalities and Kantorovich duality, Math. 
     Inequal. Appl., 21(3) (2018), 779-793.
[3] S.S. Dragomir, J. Dutta and A.M. Rubinov, Hermite-Hadamard type inequalities for increasing convex-along-rays 
     functions, Analysis, 24(2) (2004), 171-181.
[4] S.S. Dragomir, J. Pe\v{c}ari\'{c} and L.-E. Persson, Some inequalities of Hadamard type, Soochow Journal of 
     Mathematics, 21(3) (1995), 335-341.
[5] A. Doagooei, Maximal elements of sub-topical functions with applications to global optimization, Bull. Iranian Math. 
     Soc., 42 (2016), 31-41.
[6] A. Doagooei, Sub-topical functions and plus-co-radiant sets, Optimization, 65 (2016), 107-119.
[7] H. Mohebi and M. Samet, Abstract convexity of topical functions, J. Global Optim., 58 (2014), 365-375.
[8] Ch.EM. Pearce and A.M. Rubinov, P-functions, quasi-convex functions, and Hadamard-type inequalities, J. Math. Anal. 
      Appl., 240(1) (1999), 92-104.
[9] A.M. Rubinov, Abstract Convexity and Global Optimization, Kluwer Academic Publishers, Dordrecht, 2000.
[10] A.M. Rubinov and I. Singer, Topical and sub-topical functions, downward sets and abstract convexity, Optimization
       50 (2001), 307-351.
[11] I. Yesilce and G. Adilov, Hermite-Hadamard inequalities for $\mathbb{B}$-convex and $\mathbb{B}^{-1}$-convex 
       functions, International Journal of Nonlinear Analysis and Applications, 8(1) (2017), 225-233.