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http://dx.doi.org/10.11568/kjm.2019.27.3.803

ON STEFFENSEN INEQUALITY IN p-CALCULUS  

Yadollahzadeh, Milad (School of Mathematics Shahid Sattari Aeronautical University of Science and Technology)
Tourani, Mehdi (Department of Mathematics Faculty of Mathematical Sciences, University of Mazandaran)
Karamali, Gholamreza (School of Mathematics Shahid Sattari Aeronautical University of Science and Technology)
Publication Information
Korean Journal of Mathematics / v.27, no.3, 2019 , pp. 803-817 More about this Journal
Abstract
In this paper, we provide a new version of Steffensen inequality for p-calculus analogue in [17, 18] which is a generalization of previous results. Also, the conditions for validity of reverse to p-Steffensen inequalities are given. Lastly, we will obtain a generalization of p-Steffensen inequality to the case of monotonic functions.
Keywords
p-derivative; p-integral; Steffensen inequality;
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1 M.H. Annaby and Z.S. Mansour, q-Fractional Calculus and Equations, Springer-Verlag, Berlin Heidelberg, 2012.
2 A. Aral, V. Gupta, and R.P. Agarwal, Applications of q-Calculus in Operator Theory, New York, Springer, 2013.
3 J.A. Bergh, Generalization of Steffensen inequality, J. Math. Anal. Appl. 41, (1973), 187-191.   DOI
4 P.S. Bullen, The Steffensen inequality, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No. 320-328, (1970), 59-63.
5 P. Cerone, Special functions: approximations and bounds, Appl. Anal. Discrete Math. 1 (1) (2007), 72-91.   DOI
6 B. Choczewski, I. Corovei, and A. Matkowska, On some functional equations related to Steffensen inequality, Ann. Univ. Paedagog. Crac. Stud. Math. 4 (2004), 31-37.
7 T. Ernst, A comprehensive treatment of q-Calculus, Springer Science, Business Media, 2012.
8 L. Gajek and A. Okolewski, Sharp bounds on moments of generalized order statistics, Metrika 52 (1) (2000), 27-43.   DOI
9 A.M. Fink, Steffensen type inequalities, Rocky Mountain J. Math. 12 (1982), 785-793.   DOI
10 L. Gajek and A. Okolewski, Steffensen-type inequalites for order and record statistics, Ann. Univ. Mariae Curie-Sk lodowska, Sect. A 51 (1) (1997), 41-59.
11 L. Gajek and A. Okolewski, Improved Steffensen type bounds on expectations of record statistics, Statist. Probab. Lett. 55 (2) (2001), s205-212.   DOI
12 H. Gauchman, Integral Inequalities in q-Calculus, Comp. Math. with Applics. 47 (2004), 281-300   DOI
13 F.H. Jackson, On q-functions and a certain difference operator, Trans. Roy Soc. Edin. 46 (1908), 253-281.   DOI
14 V. Kac and P. Cheung, Quantum calculus, Springer Science, Business Media, 2002.
15 E. Koelink, Eight lectures on quantum groups and q-special functions, Revista colombiana de Matematicas. 30 (1996), 93-180.
16 J.F. Steffensen, On certain inequalities between mean values, and their application to actuarial problems, Skand. Aktuarietidskr. 1 (1918), 82-97.
17 T.H. Koornwinder and R.F. Swarttow, On q-analogues of the Fourier and Hankel transforms, Trans. Amer. Math. Soc. 333 (1992), 445-461.   DOI
18 A. Neamaty and M. Tourani, The presentation of a new type of quantum calculus, Tbilisi Mathematical Journal-De Gruyter 10 (2) (2017) 15-28.   DOI
19 A. Neamaty and M. Tourani, Some results on p-calculus, Tbilisi Mathematical Journal-De Gruyter 11 (1) (2018), 159-168.   DOI
20 K.R. Parthasarathy, An introduction to quantum stochastic calculus, Springer Science, Business Media, 2012.
21 P.M. Vasic and J.E. Pecaric, Note on the Steffensen inequality, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No. 716-734, (1981), 80-82.