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Journal articles on the topic 'Steffensen's inequality'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Fahad, Asfand, Josip Pečarić, and Marjan Praljak. "Generalized Steffensen's inequality." Journal of Mathematical Inequalities, no. 2 (2015): 481–87. http://dx.doi.org/10.7153/jmi-09-41.

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2

Mercer, Peter R. "Extensions of Steffensen's Inequality." Journal of Mathematical Analysis and Applications 246, no. 1 (2000): 325–29. http://dx.doi.org/10.1006/jmaa.2000.6822.

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3

El-Khatib, Mohammed S., Atta A. K. Abu Hany, Mohammed M. Matar, Manar A. Alqudah, and Thabet Abdeljawad. "On Cerone's and Bellman's generalization of Steffensen's integral inequality via conformable sense." AIMS Mathematics 8, no. 1 (2023): 2062–82. http://dx.doi.org/10.3934/math.2023106.

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<abstract><p>By making use of the conformable integrals, we establish some new results on Cerone's and Bellman's generalization of Steffensen's integral inequality. In fact, we provide a variety of generalizations of Steffensen's integral inequality by using conformable calculus.</p></abstract>

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4

Awan, K. M., Josip Pečarić, and Atiq Ur Rehman. "Steffensen's generalization of Čebyšev inequality." Journal of Mathematical Inequalities, no. 1 (2015): 155–63. http://dx.doi.org/10.7153/jmi-09-15.

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5

Jakšetić, Julije, and Josip Pečarić. "Steffensen's inequality for positive measures." Mathematical Inequalities & Applications, no. 3 (2015): 1159–70. http://dx.doi.org/10.7153/mia-18-90.

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6

Jakšetić, Julije, Josip Pečarić, and Ksenija Smoljak Kalamir. "Some measure theoretic aspects of Steffensen's and reversed Steffensen's inequality." Journal of Mathematical Inequalities, no. 2 (2016): 459–69. http://dx.doi.org/10.7153/jmi-10-36.

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7

Pearce, C. E. M., and J. Peĉarić. "On an extension of Hölder's inequality." Bulletin of the Australian Mathematical Society 51, no. 3 (1995): 453–58. http://dx.doi.org/10.1017/s0004972700014271.

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8

Ozkan, Umut Mutlu, and Hüseyin Yildirim. "Steffensen's Integral Inequality on Time Scales." Journal of Inequalities and Applications 2007 (2007): 1–11. http://dx.doi.org/10.1155/2007/46524.

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9

Pečarić, Josip E. "A companion to Jensen-Steffensen's inequality." Journal of Approximation Theory 44, no. 3 (1985): 289–91. http://dx.doi.org/10.1016/0021-9045(85)90099-1.

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10

Hong, Dug Hun, Eunho L. Moon, and Jae Duck Kim. "Steffensen's Integral Inequality for the Sugeno Integral." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 22, no. 02 (2014): 235–41. http://dx.doi.org/10.1142/s0218488514500111.

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In this paper we consider Steffensen's integral inequality for the Sugeno integral [Formula: see text] where f is a nonincreasing and convex function defined on [0, 1] with f(0) = 1, f(1) = 0 and g is a nonincreasing function defined on [0, 1] where 0 ≤ g(t) ≤ 1 for all t ∈ [a, b] with [Formula: see text]

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11

Iddrisu, Mohammed Muniru, Christopher A. Okpoti, and Kazeem A. Gbolagade. "Refinement of Steffensen's inequality for superquadratic functions." International Journal of Mathematical Analysis 8 (2014): 611–17. http://dx.doi.org/10.12988/ijma.2014.4250.

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12

Gauchman, Hillel. "On a further generalization of Steffensen's inequality." Journal of Inequalities and Applications 2000, no. 5 (2000): 925921. http://dx.doi.org/10.1155/s1025583400000291.

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13

Abramovich, Shoshana, Slavica Ivelic, and Josip E. Pecaric. "Improvement of Jensen--Steffensen's inequality for superquadratic functions." Banach Journal of Mathematical Analysis 4, no. 1 (2010): 159–69. http://dx.doi.org/10.15352/bjma/1272374678.

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14

Liu, Zheng. "A simple proof of the discrete Steffensen's inequality." Tamkang Journal of Mathematics 35, no. 4 (2004): 281–83. http://dx.doi.org/10.5556/j.tkjm.35.2004.185.

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15

Aglić Aljinović, A., Josip Pečarić, and Anamarija Perušić ribanić. "Generalizations of Steffensen's inequality via weighted Montgomery identity." Mathematical Inequalities & Applications, no. 2 (2014): 779–99. http://dx.doi.org/10.7153/mia-17-57.

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16

Mitrinović, Dragoslav S., and Josip E. Pečarić. "On the Bellman generalization of Steffensen's inequality, III." Journal of Mathematical Analysis and Applications 135, no. 1 (1988): 342–45. http://dx.doi.org/10.1016/0022-247x(88)90158-8.

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17

Fahad, Asfand, and Josip Pečarić. "Generalized Steffensen's inequality by Montgomery identities and Green functions." Mathematical Inequalities & Applications, no. 4 (2019): 1303–17. http://dx.doi.org/10.7153/mia-2019-22-89.

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18

PECARIC, JOSIP, та KSENIJA SMOLJAK KALAMIR. "On some Bounds for the Parameter λ in Steffensen's Inequality". Kyungpook mathematical journal 55, № 4 (2015): 969–81. http://dx.doi.org/10.5666/kmj.2015.55.4.969.

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19

Abramovich, S., M. Klaričić Bakula, M. Matić, and J. Pečarić. "A variant of Jensen–Steffensen's inequality and quasi-arithmetic means." Journal of Mathematical Analysis and Applications 307, no. 1 (2005): 370–86. http://dx.doi.org/10.1016/j.jmaa.2004.10.027.

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20

Pečarić, Josip, Anamarija Perušić ribanić, and Ksenija Smoljak Kalamir. "Integral error representation of Hermite interpolating polynomials and related generalizations of Steffensen's inequality." Mathematical Inequalities & Applications, no. 4 (2019): 1177–91. http://dx.doi.org/10.7153/mia-2019-22-81.

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21

Smoljak Kalamir, Ksenija. "Weaker Conditions for the q-Steffensen Inequality and Some Related Generalizations." Mathematics 8, no. 9 (2020): 1462. http://dx.doi.org/10.3390/math8091462.

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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.

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22

Fahad, Asfand, Saad Ihsaan Butt, Josip Pečarić, and Marjan Praljak. "Generalized Taylor’s Formula and Steffensen’s Inequality." Mathematics 11, no. 16 (2023): 3570. http://dx.doi.org/10.3390/math11163570.

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New Steffensen-type inequalities are obtained by combining generalized Taylor expansions, Rabier and Pečarić extensions of Steffensen’s inequality and Faà di Bruno’s formula for higher order derivatives of the composition.

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23

Fahad, Asfand, Saad Butt, and Josip Pečarić. "Generalized Steffensen’s Inequality by Fink’s Identity." Mathematics 7, no. 4 (2019): 329. http://dx.doi.org/10.3390/math7040329.

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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

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24

Pečarić, Josip, Anamarija Perušić Pribanić, and Ksenija Smoljak Kalamir. "Generalizations of Steffensen’s inequality via some Euler-type identities." Acta Universitatis Sapientiae, Mathematica 8, no. 1 (2016): 103–26. http://dx.doi.org/10.1515/ausm-2016-0007.

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Abstract Using Euler-type identities some new generalizations of Steffensen’s inequality for n–convex functions are obtained. Moreover, the Ostrowski-type inequalities related to obtained generalizations are given. Furthermore, using inequalities for the Čebyšev functional in terms of the first derivative some new bounds for the remainder in identities related to generalizations of Steffensen’s inequality are proven.

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25

Butt, Saad Ihsan, Milica Klaričić Bakula, and Josip Pečarić. "Steffensen-Grüss inequality." Journal of Mathematical Inequalities, no. 2 (2021): 799–810. http://dx.doi.org/10.7153/jmi-2021-15-56.

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26

Pečarić, Josip, Anamarija Perušić, and Ksenija Smoljak. "Cerone’s Generalizations of Steffensen’s Inequality." Tatra Mountains Mathematical Publications 58, no. 1 (2014): 53–75. http://dx.doi.org/10.2478/tmmp-2014-0006.

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Abstract In this paper, generalizations of Steffensen’s inequality with bounds involving any two subintervals motivated by Cerone’s generalizations are given. Furthermore, weaker conditions for Cerone’s generalization as well as for new generalizations obtained in this paper are given. Moreover, functionals defined as the difference between the left-hand and the right-hand side of these generalizations are studied and new Stolarsky type means related to them are obtained.

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27

Niezgoda, Marek. "On Sherman-Steffensen type inequalities." Filomat 32, no. 13 (2018): 4627–38. http://dx.doi.org/10.2298/fil1813627n.

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In this work, Sherman-Steffensen type inequalities for convex functions with not necessarily non-negative coefficients are established by using Steffensen?s conditions. The Brunk, Bellman and Olkin type inequalities are derived as special cases of the Sherman-Steffensen inequality. The superadditivity of the Jensen-Steffensen functional is investigated via Steffensen?s condition for the sequence of the total sums of all entries of the involved vectors of coeffecients. Some results of Baric et al. [2] and of Krnic et al. [11] on the monotonicity of the functional are recovered. Finally, a Sherm

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28

Klaričić Bakula, Milica, and Josip Pečarić. "Chebyshev-Steffensen Inequality Involving the Inner Product." Mathematics 10, no. 1 (2022): 122. http://dx.doi.org/10.3390/math10010122.

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In this paper, we prove the Chebyshev-Steffensen inequality involving the inner product on the real m-space. Some upper bounds for the weighted Chebyshev-Steffensen functional, as well as the Jensen-Steffensen functional involving the inner product under various conditions, are also given.

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29

Bullen, P. S. "The Jensen-Steffensen inequality." Mathematical Inequalities & Applications, no. 3 (1998): 391–401. http://dx.doi.org/10.7153/mia-01-38.

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30

Ivelić, S., M. Klaričić Bakula, and J. Pečarić. "Converse Jensen–Steffensen inequality." Aequationes mathematicae 82, no. 3 (2011): 233–46. http://dx.doi.org/10.1007/s00010-011-0076-z.

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31

Pečarić, Josip, Anamarija Perušić Pribanić, and Ksenija Smoljak Kalamir. "Weighted Hermite–Hadamard-Type Inequalities by Identities Related to Generalizations of Steffensen’s Inequality." Mathematics 10, no. 9 (2022): 1505. http://dx.doi.org/10.3390/math10091505.

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32

Jakšetić, Julije. "GENERALISATIONS OF STEFFENSEN’S INEQUALITY BY HERMITE’S POLYNOMIAL." Математички билтен/BULLETIN MATHÉMATIQUE DE LA SOCIÉTÉ DES MATHÉMATICIENS DE LA RÉPUBLIQUE MACÉDOINE, no. 2 (2014): 53–68. http://dx.doi.org/10.37560/matbil14200053j.

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33

Pečarić, J., A. Perušić, and K. Smoljak. "Generalizations of Steffensen’s Inequality by Lidstone’s Polynomials." Ukrainian Mathematical Journal 67, no. 11 (2016): 1721–38. http://dx.doi.org/10.1007/s11253-016-1185-6.

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34

Rubab, Faiza, Hira Nabi, and Asif R. Khan. "GENERALIZATION AND REFINEMENTS OF JENSEN INEQUALITY." Journal of Mathematical Analysis 12, no. 5 (2021): 1–27. http://dx.doi.org/10.54379/jma-2021-5-1.

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We give generalizations and refinements of Jensen and Jensen− Mercer inequalities by using weights which satisfy the conditions of Jensen and Jensen− Steffensen inequalities. We also give some refinements for discrete and integral version of generalized Jensen−Mercer inequality and shown to be an improvement of the upper bound for the Jensen’s difference given in [32]. Applications of our work include new bounds for some important inequalities used in information theory, and generalizing the relations among means.

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35

Aljinović, Andrea Aglić, Josip Pečarić, and Anamarija Perušić Pribanić. "Generalizations of Steffensen’s inequality via the extension of Montgomery identity." Open Mathematics 16, no. 1 (2018): 420–28. http://dx.doi.org/10.1515/math-2018-0039.

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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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36

Srivastava, Hari Mohan, Pshtiwan Othman Mohammed, Ohud Almutairi, Artion Kashuri та Y. S. Hamed. "Some Integral Inequalities in 𝒱-Fractional Calculus and Their Applications". Mathematics 10, № 3 (2022): 344. http://dx.doi.org/10.3390/math10030344.

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We consider the Steffensen–Hayashi inequality and remainder identity for V-fractional differentiable functions involving the six parameters truncated Mittag–Leffler function and the Gamma function. In view of these, we obtain some integral inequalities of Steffensen, Hermite–Hadamard, Chebyshev, Ostrowski, and Grüss type to the V-fractional calculus.

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37

Yıldırım, Emrah. "Some generalizations on q-Steffensen inequality." Journal of Mathematical Inequalities, no. 4 (2022): 1333–45. http://dx.doi.org/10.7153/jmi-2022-16-88.

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38

NICULESCU, CONSTANTIN P. "The Abel-Steffensen inequality in higher dimensions." Carpathian Journal of Mathematics 35, no. 1 (2019): 69–78. http://dx.doi.org/10.37193/cjm.2019.01.08.

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39

Aglić Aljinović, Andrea. "GENERALIZATIONS OF STEFFENSEN’S INEQUALITY VIA n WEIGHT FUNCTIONS." Математички билтен/BULLETIN MATHÉMATIQUE DE LA SOCIÉTÉ DES MATHÉMATICIENS DE LA RÉPUBLIQUE MACÉDOINE, no. 2 (2014): 31–35. http://dx.doi.org/10.37560/matbil14200031a.

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40

Wu, Shan-He, and H. M. Srivastava. "Some improvements and generalizations of Steffensen’s integral inequality." Applied Mathematics and Computation 192, no. 2 (2007): 422–28. http://dx.doi.org/10.1016/j.amc.2007.03.020.

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41

Pečarić, Josip, Anamarija Perušić, and Ksenija Smoljak. "Mercer and Wu–Srivastava generalisations of Steffensen’s inequality." Applied Mathematics and Computation 219, no. 21 (2013): 10548–58. http://dx.doi.org/10.1016/j.amc.2013.04.028.

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42

Bibi, Rabia, Ammara Nosheen, and Josip Pečarić. "Extensions in Time Scales Integral Inequalities of Jensen’s Type via Fink’s Identity." Mathematica Slovaca 73, no. 3 (2023): 657–74. http://dx.doi.org/10.1515/ms-2023-0048.

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ABSTRACT In this paper, using Fink’s identity and Green’s function, we obtain several extensions of Jensen’s inequality, Jensen–Steffensen inequality, and the converse of Jensen’s inequality for diamond integrals. Functions involved in these extensions are n-convex functions, n ∈ ℤ + . Some bounds for related identities are also part of the discussion. An improved Hölder’s inequality is obtained as an application of improved Jensen’s inequality.

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43

Pečarić, Josip, Anamarija Perušić Pribanić, and Ksenija Smoljak Kalamir. "Generalizations of Steffensen’s inequality via two-point Abel-Gontscharoff polynomial." Analele Universitatii "Ovidius" Constanta - Seria Matematica 27, no. 2 (2019): 121–37. http://dx.doi.org/10.2478/auom-2019-0023.

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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.

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44

Shi, Huan-Nan, and Shan-He Wu. "MAJORIZED PROOF AND IMPROVEMENT OF THE DISCRETE STEFFENSEN’S INEQUALITY." Taiwanese Journal of Mathematics 11, no. 4 (2007): 1203–8. http://dx.doi.org/10.11650/twjm/1500404813.

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45

Sulaiman, W. "Some New Generalizations of Steffensen´s Inequality." British Journal of Mathematics & Computer Science 2, no. 3 (2012): 176–86. http://dx.doi.org/10.9734/bjmcs/2012/1146.

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46

Song, Ying-Qing, Muhammad Adil Khan, Syed Zaheer Ullah, and Yu-Ming Chu. "Integral Inequalities Involving Strongly Convex Functions." Journal of Function Spaces 2018 (June 11, 2018): 1–8. http://dx.doi.org/10.1155/2018/6595921.

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We study the notions of strongly convex function as well as F-strongly convex function. We present here some new integral inequalities of Jensen’s type for these classes of functions. A refinement of companion inequality to Jensen’s inequality established by Matić and Pečarić is shown to be recaptured as a particular instance. Counterpart of the integral Jensen inequality for strongly convex functions is also presented. Furthermore, we present integral Jensen-Steffensen and Slater’s inequality for strongly convex functions.

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47

Horváth, László. "Integral Jensen–Mercer and Related Inequalities for Signed Measures with Refinements." Mathematics 13, no. 3 (2025): 539. https://doi.org/10.3390/math13030539.

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In this paper, we give necessary and sufficient conditions for the integral Jensen–Mercer inequality and closely related inequalities to be satisfied for finite signed measures. As applications, we obtain new special inequalities that are related to the integral Jensen–Steffensen inequality. We also provide refinements of the majorization-type inequality associated with the Jensen–Mercer inequality for finite signed measures. Using the result obtained, we extend a known refinement. The majorization-type inequalities needed for the proofs are interesting in themselves.

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48

Smoljak Kalamir, Ksenija. "Steffensen Type Inequalites for Convex Functions on Borel σ-Algebra". Mathematics 9, № 24 (2021): 3276. http://dx.doi.org/10.3390/math9243276.

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In the paper, we prove Steffensen type inequalities for positive finite measures by using functions which are convex in point. Further, we prove Steffensen type inequalities on Borel σ-algebra for the function of the form f/h which is convex in point. We conclude the paper by showing that these results also hold for convex functions.

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49

El-Deeb, Ahmed A., Osama Moaaz, Dumitru Baleanu, and Sameh S. Askar. "A variety of dynamic $ \alpha $-conformable Steffensen-type inequality on a time scale measure space." AIMS Mathematics 7, no. 6 (2022): 11382–98. http://dx.doi.org/10.3934/math.2022635.

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<abstract><p>The main objective of this work is to establish several new alpha-conformable of Steffensen-type inequalities on time scales. Our results will be proved by using time scales calculus technique. We get several well-known inequalities due to Steffensen, if we take $ \alpha = 1 $. Some cases we get continuous inequalities when $ \mathbb{T} = \mathbb{R} $ and discrete inequalities when $ \mathbb{T} = \mathbb{Z} $.</p></abstract>

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50

Wilbert, Asambo Awini, Mohammed Muniru Iddrisu, and Benedict Barnes. "Convexity Properties in Non-Newtonian Calculus and Their Applications." European Journal of Mathematical Analysis 4 (October 28, 2024): 19. http://dx.doi.org/10.28924/ada/ma.4.19.

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The study presented some results on convexity properties in non-Newtonian calculus. Also presented is the Jensen-Steffensen inequality in non-Newtonian calculus and some applications. The research was mainly on positive real numbers.

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