Refinements of the majorization-type inequalities via green and fink identities and related results
-
Sadia Khalid
,
Josip Pečarić
Abstract
In this work, the Green’s function of order two is used together with Fink’s approach in Ostrowski’s inequality to represent the difference between the sides of the Sherman’s inequality. Čebyšev, Grüss and Ostrowski-type inequalities are used to obtain several bounds of the presented Sherman-type inequality. Further, we construct a new family of exponentially convex functions and Cauchy-type means by looking to the linear functionals associated with the obtained inequalities.
Communicated by Ján Borsík
References
[1] Agarwal, R. P.—Bradanović, S. I.—Pečarić, J.: Generalizations of Sherman’s inequality by Lidstone’s interpolating polynomial, J. Inequal. Appl. (2016), 1–18.10.1186/s13660-015-0935-6Search in Google Scholar
[2] Agarwal, R. P.—Wong, P. J. Y.: Error Inequalities in Polynomial Interpolation and Their Applications, Kluwer Academic Publishers, Dordrecht / Boston / London, 1993.10.1007/978-94-011-2026-5Search in Google Scholar
[3] Cerone, P.—Dragomir, S. S.: Some new Ostrowski-type bounds for the Čebyšev functional and applications, J. Math. Inequal. 8 (2014), 159–170.10.7153/jmi-08-10Search in Google Scholar
[4] Fink, A. M.: Bounds of the deviation of a function from its avereges, Czechoslovak Math. J. 42 (1992), 289–310.10.21136/CMJ.1992.128336Search in Google Scholar
[5] Fuchs, L.: A new proof of an inequality of Hardy-Littlewood-Pólya, Mat. Tidsskr. B (1947), 53–54.Search in Google Scholar
[6] Khalid, S.—Pečarić, J.—Vukelić, A.: Refinements of the majorization theorems via Fink identity and related results, J. Classical. Anal. 7 (2015), 129–154.10.7153/jca-07-12Search in Google Scholar
[7] Khan, M. A.—Latif, N.—Perić, I.—Pečarić, J.: On majorization for matrices, Math. Balkanica (N.S.) 27 (2013), Fasc 1–2, 3–19.Search in Google Scholar
[8] Pečarić, J.: On some inequalities for functions with nondecreasing increments, J. Math. Anal. Appl. 98 (1984), 188–197.10.1016/0022-247X(84)90287-7Search in Google Scholar
[9] Pečarić, J.-Perić, J.: Improvements of the Giaccardi and the Petrović inequality and related Stolarsky type means, An. Univ. Craiova Ser. Mat. Inform. 39 (2012), 65–75.Search in Google Scholar
[10] Pečarić, J.—Praljak, M.: Hermite interpolation and inequalities involving weighted averages of n-convex functions, Math. Inequal. Appl. 19 (2016), 1169–1180.10.7153/mia-19-86Search in Google Scholar
[11] Pečarić, J.—Proschan, F.—Tong, Y. L.: Convex Functions, Partial Orderings, and Statistical Applications, Academic Press, New York, 1992.Search in Google Scholar
© 2018 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- A multi-parameter generalization of the symmetric algorithm
- Single identities forcing lattices to be Boolean
- Weighted uniform density ideals
- A generalized class of restricted Stirling and Lah numbers
- The Riemann hypothesis and universality of the Riemann zeta-function
- Distance functions on the sets of ordinary elliptic curves in short Weierstrass form over finite fields of characteristic three
- The drazin inverse of the sum of two matrices
- Refinements of the majorization-type inequalities via green and fink identities and related results
- Characterizations and properties of graphs of Baire functions
- Some improvements of the young mean inequality and its reverse
- On characteristic of bounded analytic functions involving hyperbolic derivative
- A uniqueness problem for entire functions related to Brück’s conjecture
- System of nonlocal resonant boundary value problems involving p-Laplacian
- Construction of a unique mild solution of one-dimensional Keller-Segel systems with uniformly elliptic operators having variable coefficients
- Infinitely many solutions for non-homogeneous Neumann problems in Orlicz-Sobolev spaces
- Characterization of rough weighted statistical limit set
- Approximation by Baskakov-Durrmeyer operators based on (p, q)-integers
- On generalized 4-th root metrics of isotropic scalar curvature
- Compactifications from generators and relations
- Diophantine quadruples with values in k-generalized Fibonacci numbers
