Integral inequalities of Ostrowski type for two kinds of s-logarithmically convex functions
-
Bo-Yan Xi
,
Shu-Hong Wang
und
Feng Qi
Abstract
In the paper, the authors establish several integral inequalities of the Ostrowski type for s-logarithmically convex functions. These integral inequalities modify the conditions and correct errors in two main theorems of the paper [A. O. Akdemir and M. Tunç, Ostrowski type inequalities for s-logarithmically convex functions in the second sense with applications, Georgian Math. J. 22 (2015), no. 1, 1–7].
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 12361013
Funding statement: This work was partially supported by the National Natural Science Foundation of China (Grant No. 12361013).
Acknowledgements
The authors appreciate anonymous referees for their careful corrections and valuable comments on the original version of this paper.
References
[1] A. O. Akdemir and M. Tunç, On some integral inequalities for s-logarithmically convex functions and their applications, preprint (2012), https://arxiv.org/abs/1212.1584. Suche in Google Scholar
[2] A. O. Akdemir and M. Tunç, Ostrowski type inequalities for s-logarithmically convex functions in the second sense with applications, Georgian Math. J. 22 (2015), no. 1, 1–7. 10.1515/gmj-2014-0061Suche in Google Scholar
[3] M. Alomari and M. Darus, Some Ostrowski type inequalities for convex functions with applications, RGMIA Res. Rep. Coll. 13 (2010), no. 2, Paper No. 3. Suche in Google Scholar
[4] M. Alomari, M. Darus, S. S. Dragomir and P. Cerone, Ostrowski type inequalities for functions whose derivatives are s-convex in the second sense, Appl. Math. Lett. 23 (2010), no. 9, 1071–1076. 10.1016/j.aml.2010.04.038Suche in Google Scholar
[5]
R.-F. Bai, F. Qi and B.-Y. Xi,
Hermite–Hadamard type inequalities for the m- and
[6] W. W. Breckner, Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer Funktionen in topologischen linearen Räumen, Publ. Inst. Math. (Beograd) (N. S.) 23(37) (1978), 13–20. Suche in Google Scholar
[7] T. Du and Y. Peng, Hermite–Hadamard type inequalities for multiplicative Riemann–Liouville fractional integrals, J. Comput. Appl. Math. 440 (2024), Article ID 115582. 10.1016/j.cam.2023.115582Suche in Google Scholar
[8] H. Hudzik and L. Maligranda, Some remarks on s-convex functions, Aequationes Math. 48 (1994), no. 1, 100–111. 10.1007/BF01837981Suche in Google Scholar
[9] K. Mehrez and P. Agarwal, New Hermite–Hadamard type integral inequalities for convex functions and their applications, J. Comput. Appl. Math. 350 (2019), 274–285. 10.1016/j.cam.2018.10.022Suche in Google Scholar
[10] W. Orlicz, A note on modular spaces. I, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 9 (1961), 157–162. Suche in Google Scholar
[11] J. E. Pečarić, F. Proschan and Y. L. Tong, Convex Functions, Partial Orderings, and Statistical Applications, Math. Sci. Eng. 187, Academic Press, Boston, 1992. Suche in Google Scholar
[12] Y. Peng, H. Fu and T. Du, Estimations of bounds on the multiplicative fractional integral inequalities having exponential kernels, Commun. Math. Stat. (2022), 10.1007/s40304-022-00285-8. 10.1007/s40304-022-00285-8Suche in Google Scholar
[13]
M. Tunç and A. Açikel,
On
[14] Y. Wu and F. Qi, Discussions on two integral inequalities of Hermite–Hadamard type for convex functions, J. Comput. Appl. Math. 406 (2022), Article ID 114049. 10.1016/j.cam.2021.114049Suche in Google Scholar
[15] B.-Y. Xi and F. Qi, Inequalities of Hermite–Hadamard type for extended s-convex functions and applications to means, J. Nonlinear Convex Anal. 16 (2015), no. 5, 873–890. Suche in Google Scholar
[16] B. Y. Xi and F. Qi, Some integral inequalities of Hermite–Hadamard type for s-logarithmically convex functions, Acta Math. Sci. Ser. A (Chinese Ed.) 35 (2015), no. 3, 515–524. Suche in Google Scholar
[17] B.-Y. Xi and F. Qi, Some integral inequalities of Hermite–Hadamard type for s-logarithmically convex functions, preprint (2015), https://doi.org/10.13140/RG.2.1.4385.9044. Suche in Google Scholar
© 2024 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Fractional p-Laplacian elliptic Dirichlet problems
- Group invertibility of the sum in rings and its applications
- σ-symmetric amenability of Banach algebras
- Generalized Stockwell transforms: Spherical mean operators and applications
- Existence of positive weak solutions for stationary fractional Laplacian problem by using sub-super solutions
- Capacity in Besov and Triebel–Lizorkin spaces with generalized smoothness
- Existence of solutions for (p(y),q(y))-Laplacian elliptic problem on an exterior domain
- Degeneration phenomenon in linear ordinary differential equations
- Weak type estimates of genuine Calderón–Zygmund operators on the local Morrey spaces associated with ball quasi-Banach function spaces
- Generalized derivation on semiprime and prime Banach algebras
- Weak positive solutions to singular quasilinear elliptic equation
- Constructions and characterizations of mixed reverse-order laws for the Moore–Penrose inverse and group inverse
- Integral inequalities of Ostrowski type for two kinds of s-logarithmically convex functions
- On the polar dualities and star dualities of the quasi Lp -intersection bodies
- New estimates for the Berezin number of Hilbert space operators
- Addendum to On Kuratowski partitions in the Marczewski and Laver structures and Ellentuck topology
Artikel in diesem Heft
- Frontmatter
- Fractional p-Laplacian elliptic Dirichlet problems
- Group invertibility of the sum in rings and its applications
- σ-symmetric amenability of Banach algebras
- Generalized Stockwell transforms: Spherical mean operators and applications
- Existence of positive weak solutions for stationary fractional Laplacian problem by using sub-super solutions
- Capacity in Besov and Triebel–Lizorkin spaces with generalized smoothness
- Existence of solutions for (p(y),q(y))-Laplacian elliptic problem on an exterior domain
- Degeneration phenomenon in linear ordinary differential equations
- Weak type estimates of genuine Calderón–Zygmund operators on the local Morrey spaces associated with ball quasi-Banach function spaces
- Generalized derivation on semiprime and prime Banach algebras
- Weak positive solutions to singular quasilinear elliptic equation
- Constructions and characterizations of mixed reverse-order laws for the Moore–Penrose inverse and group inverse
- Integral inequalities of Ostrowski type for two kinds of s-logarithmically convex functions
- On the polar dualities and star dualities of the quasi Lp -intersection bodies
- New estimates for the Berezin number of Hilbert space operators
- Addendum to On Kuratowski partitions in the Marczewski and Laver structures and Ellentuck topology
