Some integral inequalities for the product of $s$-convex functions in the fourth sense

[1] M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, New York, Dover, 1972.

[2] G. Adilov and S. Kemali, Abstract convexity and Hermite-Hadamard type inequalities, J. Inequal. Appl. 2009 (2009).

[3] G. Adilov, G. Tinaztepe and R. Tinaztepe, On the global minimization of increasing positively homogeneous functions over the unit simplex, Int. J. Comput. Math. 87 (2010), 2733–2746.

[4] G. Adilov and I. Yesilce, B−1-convex Sets and B −1-measurable Maps, Numer. Funct. Anal. Optim. 33 (2012), no. 2, 131–141.

[5] G. Adilov and I. Yesilce, On Generalizations of the concept of convexity, Hacettepe J. Math. Statist. 41 (2012), no. 5, 723–730.

[6] M. Alomari and M. Darus, Co-ordinated s-convex functions in the first sense with some Hadamard-type inequalities, Int. J. Contemp. Math. Sci. 3 (2008), 1557-1567.

[7] D. Bertsimas and I. Popescu, Optimal inequalities in probability theory, A Convex Optimization Approach Sloan WP #4025, June, 1998.

[8] W.W. Breckner, Stetigkeitsaussagen fur eine Klasse verallgemekterter konvexer Funktionen in topologischen linearen Raumen. Publ. Inst. Math. 23 (1978), 13–20.

[9] W.Briech and C. Horvath, B-convexity, Optim. 53 (2004), no. 2, 103–127.

[10] H. Budak and Y. Bakis, On Fejer type inequalities for products convex and s-convex functions, Mathematica 2020 (2020), 165.

[11] F.X. Chen and S.H. Wu, Several complementary inequalities to inequalities of Hermite-Hadamard type for s-convex functions, J. Nonlinear Sci. Appl. 9 (2016), no. 2, 705–716.

[12] Y.M. Chu, M.A. Khan, T. Ali and S.S. Dragomir, Inequalities for α-fractional differentiable functions, J. Inequal. Appl. 2017 (2017), no. 1, 1–12.

[13] Y.M. Chu, M.A. Khan, T.U. Khan and T. Ali, Generalizations of Hermite-Hadamard type inequalities for MT-convex functions, J. Nonlinear Sci. Appl. 9 (2016), no. 5, 4305–4316.

[14] S.S. Dragomir and C.E.M. Pierce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA, Victoria University, 2000, Monographs.

[15] Z. Eken, S. Sezer, G. Tinaztepe and G. Adilov, s-convex functions in the fourth sense and some of their properties, Konuralp J. Math. 9 (2021), no. 2, 260–267.

[16] N.N. Hue and D.Q. Huy, Some inequalities of the Hermite-Hadamard type for product of two functions, J. New Theory 13 (2016), 26–37.

[17] J. Jensen and T. Gronwall, An elementary exposition of the theory of the Gamma function, Ann. Math. Soc. 17 (1916),
no. 3, 124–166.

[18] H. Kara, H. Budak, M.A. Ali, M.Z. Sarikaya and Y.M. Chu, Weighted Hermite–Hadamard type inclusions for products of
co-ordinated convex interval-valued functions, Adv. Difference Equ. 2021 (2021), no. 1, 1–16.

[19] S. Kemali, I. Yesilce and G. Adilov, B-convexity, B−1-convexity, and their comparison, Numer. Funct. Anal. Optim. 36 (2015), no. 2, 133–146.

[20] S. Kemali, Hermite-Hadamard type inequality for s-convex functions in the fourth sense, Turk. J. Math. Comput. Sci. 13 (2021), no. 2, 287–293.

[21] U.S. Kirmaci, M. Klaricic Bakula, M.E. Ozdemir and J. Pecaric, Hadamard-type inequalities for s-convex functions, Appl.
Math. Comput. 193 (2007), no. 1, 26–35.

[22] M.A. Khan, T. Ali, S.S. Dragomir and M.Z. Sarikaya, Hermite–Hadamard type inequalities for conformable fractional integrals, Rev. R. Acad. Cienc. Exactas Fis. Nat. (Esp.) 112 (2018), no. 4, 1033–1048.

[23] M.A. Khan, G.A. Khan, T. Ali and A. Kilicman, On the refinement of Jensen’s inequality, Appl. Math. Comput. 262 (2015), 128–135.

[24] M.A. Khan, Y. Khurshid, T. Ali and N. Rehman, Inequalities for three times differentiable functions, Punjab Univ. J. Math. 48 (2016), no. 2, 35–48.

[25] K. Lange, Convexity, optimization and inequalities, Appl. Prob. p. 55-73, Springer, New York, 2010.

[26] B. Meftah, M. Benssaad, W. Kaidouchi and S. Ghomrani, Confortable Fractional Hermite-Hadamard Type Inequalities for Product of two Harmonic s-Convex Functions, Proc. Amer. Math. Soc. 149 (2021), no. 4, 1495–1506.

[27] T. Nawaz and M.A. Memon, Hermite-Hadamard-Type inequalities for product of functions by using convex functions, J. Math. 2021 (2021).

[28] W. Orlicz, A note on modular spaces I, Bull. Acad. Polon. Soi. Ser. Math. Astronom Phys. 9 (1961), 157–162.

[29] M.E. Ozdemir, M.A. Latif and A.O. Akdemir, On some Hadamard-type inequalities for product of two s-convex functions on the co-ordinates, J. Inequal. Appl. 2012 (2012), no. 1, 1–13.

[30] B.G. Pachpatte, On some inequalities for convex functions, RGMIA Res. Rep. Coll, 6 (2003), no. 1. 1–9.

[31] B.G. Pachpatte, A note on integral inequalities involving the product of two functions, J. Inequal. Pure Appl. Math. 7 (2006), no. 2, Article 78.

[32] A.M. Rubinov, Abstract convexity and global optimization, Kluwer Academic Publishers, Dordrecht, 2000.

[33] S. Sezer, The Hermite-Hadamard inequality for s-Convex functions in the third sense, AIMS Math. 6 (2021), no. 7, 7719–7732.

[34] I. Singer, Abstract convex analysis, John Wiley & Sons., New York, 1997.

[35] G. Tinaztepe, S. Kemali, S. Sezer, Z. Eken, The sharper form of Brunn-Minkowski type inequality for boxes, Hacettepe J. Math. Statist. 31 (2020), no. 47, 1–10.

[36] G. Tinaztepe, The sharpening H¨older inequality via abstract convexity. Turk. J. Math. 40 (2016), no. 2, 438–444.

[37] R. Webster, Convexity, Oxford University Press, 1994.

[38] M.L.J. Van De Vel, Theory of convex structures, North Holland Mathematical Library, 50. North-Holland Publishing Co., Amsterdam, 1993.

[39] I. Yesilce and G. Adilov, Hermite-Hadamard inequalities for B-convex and B−1-convex functions, Int. J. Nonlinear Anal.Appl. 8 (2017), no. 1, 225–233.