steffensen’s inequality
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Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1462
Author(s):  
Ksenija Smoljak Kalamir

The aim of this paper is to study the q-Steffensen inequality and to prove some weaker conditions for this inequality in quantum calculus. Further, we prove q-analogues of some frequently used generalizations of Steffensen’s inequality and obtain some refinements of q-Steffensen’s inequality and its generalizations.


2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Saad Ihsan Butt ◽  
Asfand Fahad ◽  
Adil Naseer ◽  
Josip Pečarić

2019 ◽  
Vol 27 (2) ◽  
pp. 121-137
Author(s):  
Josip Pečarić ◽  
Anamarija Perušić Pribanić ◽  
Ksenija Smoljak Kalamir

Abstract Using two-point Abel-Gontscharoff interpolating polynomial some new generalizations of Steffensen’s inequality for n−convex functions are obtained and some Ostrowski-type inequalities related to obtained generalizations are given. Furthermore, using the Čebyšev functional some new bounds for the remainder in obtained generalizations are proven and related Grüss-type inequalities are given.


Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 329
Author(s):  
Asfand Fahad ◽  
Saad Butt ◽  
Josip Pečarić

By using Fink’s Identity, Green functions, and Montgomery identities we prove some identities related to Steffensen’s inequality. Under the assumptions of n-convexity and n-concavity, we give new generalizations of Steffensen’s inequality and its reverse. Generalizations of some inequalities (and their reverse), which are related to Hardy-type inequality. New bounds of Gr u ¨ ss and Ostrowski-type inequalities have been proved. Moreover, we formulate generalized Steffensen’s-type linear functionals and prove their monotonicity for the generalized class of ( n + 1 ) -convex functions at a point. At the end, we present some applications of our study to the theory of exponentially convex functions. .


2019 ◽  
Vol 43 (3) ◽  
pp. 293-307
Author(s):  
Josip Pečarić ◽  
Anamarija Perušić Pribanić ◽  
Ana Vukelić

2018 ◽  
Vol 73 (4) ◽  
Author(s):  
Julije Jakšetić ◽  
Josip Pečarić ◽  
Ksenija Smoljak Kalamir

2018 ◽  
Vol 16 (1) ◽  
pp. 420-428
Author(s):  
Andrea Aglić Aljinović ◽  
Josip Pečarić ◽  
Anamarija Perušić Pribanić

AbstractIn this paper, we obtained new generalizations of Steffensen’s inequality for n-convex functions by using extension of Montgomery identity via Taylor’s formula. Since 1-convex functions are nondecreasing functions, new inequalities generalize Stefensen’s inequality. Related Ostrowski type inequalities are also provided. Bounds for the reminders in new identities are given by using the Chebyshev and Grüss type inequalities.


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