Strongly M_φM_ψ-convex functions, the Hermite-Hadamard-Fejér inequality and related results



Abstract

We present Hermite-Hadamard-Fejér type inequalities for strongly MφMψ-convex functions. Some refinements of them and bounds for the integral mean of the product of two functions are also obtained.


Keywords

MN-convex function; strongly M_φM_ψ-convex function; the Hermite-Hadamard-Fejér inequality; quasi-arithmetic mean

M.W. Alomari, Some properties of h-MN-convexity and Jensen’s type inequalities, J . Interdiscip. Math. 22 (2019), no. 8, 1349–1395.

A. Azócar, K. Nikodem, and G. Roa, Fejér-type inequalities for strongly convex functions, Ann. Math. Sil. 26 (2012), 43–54.

M. Bombardelli and S. Varošanec, M_φM_ψ-convexity and separation theorems, J. Inequal. Appl. 2022 (2022), Paper No. 65, 7 pp.

M. Bracamonte, J. Giménez, and J. Medina, Sandwich theorem for reciprocally strongly convex functions, Rev. Colombiana Mat. 52 (2018), no. 2, 171–184.

A. El Farissi, Simple proof and refinement of Hermite–Hadamard inequality, J. Math. Inequal. 4 (2010), no. 3, 365–369.

M. Feng, J. Ruan, and X. Ma, Hermite–Hadamard type inequalities for multidimensional strongly h-convex functions, Math. Inequal. Appl. 24 (2021), no. 4, 897–911.

J.-B. Hiriart-Urruty, C. Lemaréchal, Fundamentals of Convex Analysis, Springer-Verlag, Berlin, 2001.

N. Merentes and K. Nikodem, Remarks on strongly convex functions, Aequationes Math. 80 (2010), no. 1-2, 193–199.

F.C. Mitroi and C.I. Spiridon, Hermite–Hadamard type inequalities of convex functions with respect to a pair of quasi-arithmetic means, Math. Rep. (Bucur.) 14(64) (2012), no. 3, 91–295.

C. Niculescu and L.-E. Persson, Convex Functions and their Applications. A Contemporary Approach, CMS Books in Mathematics, 23, Springer, New York, 2006.

M.A. Noor, K.I. Noor, and S. Iftikhar, Hermite–Hadamard inequalities for strongly harmonic convex functions, J. Inequal. Spec. Funct. 7 (2016), no. 3, 99–113.

B.T. Polyak, Existence theorems and convergence of minimizing sequences in extremum problems with restictions, Soviet Math. Dokl. 7 (1966), 72–75.

T. Rajba and Sz. Wąsowicz, Probabilistic characterization of strong convexity, Opuscula Math. 31 (2011), no. 1, 97–103.

S. Turhan, A.K. Demirel, S. Maden, and I. Iscan, Hermite–Hadamard type integral inequalities for strongly GA-convex functions, Proc. International Conference on Mathematics and Mathematics Education (ICMME 2018), Turk. J. Math. Comput. Sci. 10 (2018), 178–183.

S. Turhan, A.K. Demirel, S. Maden, and I. Iscan, Hermite–Hadamard type integral inequalities for strongly p-convex functions, Proc. International Conference on Mathematics and Mathematics Education (ICMME 2018), Turk. J. Math. Comput. Sci. 10 (2018), 184–189.

S. Turhan, M. Kunt, and İ. İşcan, Hermite–Hadamard type inequalities for M_φA-convex functions, International Journal of Mathematical Modelling & Computations 10 (2020), no. 1, 57–75.

S. Turhan, S. Maden, A.K. Demirel, and I. Iscan, Hermite–Hadamard type inequality for M_φA-strongly convex functions, New Trends Math. Sci. 6 (2018), no. 4, 127–133.

S. Varošanec, M_φA-h-convexity and Hermite–Hadamard type inequalities, Int. J. Anal. Appl. 20 (2022), Paper No. 36, 14 pp.

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Published : 2023-11-22


BombardelliM., & VarošanecS. (2023). Strongly M_φM_ψ-convex functions, the Hermite-Hadamard-Fejér inequality and related results. Annales Mathematicae Silesianae. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/15453

Mea Bombardelli 
Department of Mathematics, Faculty of Science, University of Zagreb  Croatia
Sanja Varošanec  varosans@math.hr
Department of Mathematics, Faculty of Science, University of Zagreb  Croatia
https://orcid.org/0000-0002-9358-1830



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