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Year 2024, Volume: 7 Issue: 1, 1 - 11, 31.03.2024

Sever Dragomır

https://doi.org/10.33401/fujma.1362681

Abstract

References

  • [1] P.R. Beesack and J.E. Pecaric, On Jessen’s inequality for convex functions, J. Math. Anal. Appl.110 (1985), 536-552. $\href{https://doi.org/10.1016/0022-247X(85)90315-4}{[\mbox{CrossRef}]} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-0001542604&origin=resultslist&sort=plf-f&src=s&sid=4cc854a753b93f4c5fe2d4fbfcda623d&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22On+Jessen%27s+inequality+for+convex+functions%22%29&sl=78&sessionSearchId=4cc854a753b93f4c5fe2d4fbfcda623d&relpos=2}{[\mbox{Scopus}]} %\href{https://www.webofscience.com/wos/woscc/full-record/WOS:000513943500001}{[\mbox{Web of Science}]}$
  • [2] J.E. Pecaric, On Jessen’s inequality for convex functions (III), J. Math. Anal. Appl., 156 (1991), 231-239. $\href{https://doi.org/10.1016/0022-247X(91)90393-E}{[\mbox{CrossRef}]} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-5644248294&origin=resultslist&sort=plf-f&src=s&sid=81fa61a1532600f63071f79cd12df452&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22On+Jessen%27s+inequality+for+convex+functions%22%29&sl=67&sessionSearchId=81fa61a1532600f63071f79cd12df452&relpos=0}{[\mbox{Scopus}]}$
  • [3] J.E. Pecaric and P.R. Beesack, On Jessen’s inequality for convex functions (II), J. Math. Anal. Appl., 156 (1991), 231-239. $\href{https://doi.org/10.1016/0022-247X(86)90296-9}{[\mbox{CrossRef}]} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-38249039395&origin=resultslist&sort=plf-f&src=s&sid=81fa61a1532600f63071f79cd12df452&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22On+Jessen%27s+inequality+for+convex+functions%22%29&sl=67&sessionSearchId=81fa61a1532600f63071f79cd12df452&relpos=1}{[\mbox{Scopus}]}$
  • [4] D. Andrica and C. Badea, Gruss’ inequality for positive linear functionals, Periodica Math. Hung., 19 (1998), 155-167. $\href{https://doi.org/10.1007/BF01848061}{[\mbox{CrossRef}]} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-0010162730&origin=resultslist&sort=plf-f&src=s&sid=4cc854a753b93f4c5fe2d4fbfcda623d&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Gr%C3%BCss%27+inequality+for+positive+linear+functionals%22%29&sl=78&sessionSearchId=4cc854a753b93f4c5fe2d4fbfcda623d&relpos=0}{[\mbox{Scopus}]} $
  • [5] S.S. Dragomir, A refinement of Hadamard’s inequality for isotonic linear functionals, Tamkang J. Math., 24(1) (1992), 101-106.
  • [6] S.S. Dragomir, On a reverse of Jessen’s inequality for isotonic linear functionals, J. Ineq. Pure & Appl. Math., 2(3)(2001), Article 36.
  • [7] S.S. Dragomir, On the Jessen’s inequality for isotonic linear functionals, Nonlinear Anal. Forum, 7(2)(2002), 139-151.
  • [8] S.S. Dragomir, On the Lupas-Beesack-Pecaric inequality for isotonic linear functionals, Nonlinear Funct. Anal. & Appl., 7(2)(2002), 285-298.
  • [9] S.S. Dragomir, Bounds for the normalized Jensen functional, Bull. Austral. Math. Soc. 74(3)(2006), 417-478. $\href{https://doi.org/10.1017/S000497270004051X}{[\mbox{CrossRef}]} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-33845754082&origin=resultslist&sort=plf-f&src=s&sid=4cc854a753b93f4c5fe2d4fbfcda623d&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Bounds+for+the+normalized+Jensen+functional%22%29&sl=78&sessionSearchId=4cc854a753b93f4c5fe2d4fbfcda623d&relpos=3}{[\mbox{Scopus}]}$
  • [10] S.S. Dragomir and N.M. Ionescu, On some inequalities for convex-dominated functions, L’Anal. Num. Theor. L’Approx., 19(1) (1990), 21-27.
  • [11] S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000. http://rgmia.vu.edu.au/monographs.html
  • [12] S.S. Dragomir, C.E.M. Pearce and J.E. Peˇcari´c, On Jessen’s and related inequalities for isotonic sublinear functionals, Acta. Sci. Math., 61 (1995), 373-382.
  • [13] F. Kittaneh and Y. Manasrah, Improved Young and Heinz inequalities for matrix, J. Math. Anal. Appl., 361(1) (2010), 262-269 $\href{https://doi.org/10.1016/j.jmaa.2009.08.059}{[\mbox{CrossRef}]} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-70349378865&origin=resultslist&sort=plf-f&src=s&sid=81fa61a1532600f63071f79cd12df452&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Improved+Young+and+Heinz+inequalities+for+matrices%22%29&sl=67&sessionSearchId=81fa61a1532600f63071f79cd12df452&relpos=1}{[\mbox{Scopus}]} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000273063900024}{[\mbox{Web of Science}]}$
  • [14] F. Kittaneh and Y. Manasrah, Reverse Young and Heinz inequalities for matrices, Linear Multilinear Algebra., 59(9) (2011), 1031-1037. $\href{https://doi.org/10.1080/03081087.2010.551661}{[\mbox{CrossRef}]} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-79961134150&origin=resultslist&sort=plf-f&src=s&sid=81fa61a1532600f63071f79cd12df452&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Reverse+Young+and+Heinz+inequalities+for+matrices%22%29&sl=67&sessionSearchId=81fa61a1532600f63071f79cd12df452&relpos=0}{[\mbox{Scopus}]} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000293598100007}{[\mbox{Web of Science}]}$
  • [15] A. Lupas¸, A generalisation of Hadamard’s inequalities for convex functions, Univ. Beograd. Elek. Fak., 577-579 (1976), 115-121.
  • [16] D.I. Cartwright and M.J. Field, A refinement of the arithmetic mean-geometric mean inequality, Proc. Amer. Math. Soc., 71 (1978), 36-38. $$
  • [17] D.K. Callebaut, Generalization of Cauchy-Schwarz inequality, J. Math. Anal. Appl. 12 (1965), 491-494. $\href{https://doi.org/10.1016/0022-247X(65)90016-8}{[\mbox{CrossRef}]} %\href{https://www.scopus.com/record/display.uri?eid=2-s2.0-0001542604&origin=resultslist&sort=plf-f&src=s&sid=4cc854a753b93f4c5fe2d4fbfcda623d&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22On+Jessen%27s+inequality+for+convex+functions%22%29&sl=78&sessionSearchId=4cc854a753b93f4c5fe2d4fbfcda623d&relpos=2}{[\mbox{Scopus}]} %\href{https://www.webofscience.com/wos/woscc/full-record/WOS:000513943500001}{[\mbox{Web of Science}]}$

Some Refinements and Reverses of Callebaut's Inequality for Isotonic Functionals via a Result Due to Cartwright and Field

Year 2024, Volume: 7 Issue: 1, 1 - 11, 31.03.2024

Sever Dragomır

https://doi.org/10.33401/fujma.1362681

Abstract

In this paper we obtain some refinements and reverses of Callebaut's inequality for isotonic functionals via a result of Young's inequality due to Cartwright and Field.

Keywords

Isotonic Functionals Schwarz Callebaut Integral inequalities Discrete inequalities

References

  • [1] P.R. Beesack and J.E. Pecaric, On Jessen’s inequality for convex functions, J. Math. Anal. Appl.110 (1985), 536-552. $\href{https://doi.org/10.1016/0022-247X(85)90315-4}{[\mbox{CrossRef}]} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-0001542604&origin=resultslist&sort=plf-f&src=s&sid=4cc854a753b93f4c5fe2d4fbfcda623d&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22On+Jessen%27s+inequality+for+convex+functions%22%29&sl=78&sessionSearchId=4cc854a753b93f4c5fe2d4fbfcda623d&relpos=2}{[\mbox{Scopus}]} %\href{https://www.webofscience.com/wos/woscc/full-record/WOS:000513943500001}{[\mbox{Web of Science}]}$
  • [2] J.E. Pecaric, On Jessen’s inequality for convex functions (III), J. Math. Anal. Appl., 156 (1991), 231-239. $\href{https://doi.org/10.1016/0022-247X(91)90393-E}{[\mbox{CrossRef}]} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-5644248294&origin=resultslist&sort=plf-f&src=s&sid=81fa61a1532600f63071f79cd12df452&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22On+Jessen%27s+inequality+for+convex+functions%22%29&sl=67&sessionSearchId=81fa61a1532600f63071f79cd12df452&relpos=0}{[\mbox{Scopus}]}$
  • [3] J.E. Pecaric and P.R. Beesack, On Jessen’s inequality for convex functions (II), J. Math. Anal. Appl., 156 (1991), 231-239. $\href{https://doi.org/10.1016/0022-247X(86)90296-9}{[\mbox{CrossRef}]} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-38249039395&origin=resultslist&sort=plf-f&src=s&sid=81fa61a1532600f63071f79cd12df452&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22On+Jessen%27s+inequality+for+convex+functions%22%29&sl=67&sessionSearchId=81fa61a1532600f63071f79cd12df452&relpos=1}{[\mbox{Scopus}]}$
  • [4] D. Andrica and C. Badea, Gruss’ inequality for positive linear functionals, Periodica Math. Hung., 19 (1998), 155-167. $\href{https://doi.org/10.1007/BF01848061}{[\mbox{CrossRef}]} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-0010162730&origin=resultslist&sort=plf-f&src=s&sid=4cc854a753b93f4c5fe2d4fbfcda623d&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Gr%C3%BCss%27+inequality+for+positive+linear+functionals%22%29&sl=78&sessionSearchId=4cc854a753b93f4c5fe2d4fbfcda623d&relpos=0}{[\mbox{Scopus}]} $
  • [5] S.S. Dragomir, A refinement of Hadamard’s inequality for isotonic linear functionals, Tamkang J. Math., 24(1) (1992), 101-106.
  • [6] S.S. Dragomir, On a reverse of Jessen’s inequality for isotonic linear functionals, J. Ineq. Pure & Appl. Math., 2(3)(2001), Article 36.
  • [7] S.S. Dragomir, On the Jessen’s inequality for isotonic linear functionals, Nonlinear Anal. Forum, 7(2)(2002), 139-151.
  • [8] S.S. Dragomir, On the Lupas-Beesack-Pecaric inequality for isotonic linear functionals, Nonlinear Funct. Anal. & Appl., 7(2)(2002), 285-298.
  • [9] S.S. Dragomir, Bounds for the normalized Jensen functional, Bull. Austral. Math. Soc. 74(3)(2006), 417-478. $\href{https://doi.org/10.1017/S000497270004051X}{[\mbox{CrossRef}]} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-33845754082&origin=resultslist&sort=plf-f&src=s&sid=4cc854a753b93f4c5fe2d4fbfcda623d&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Bounds+for+the+normalized+Jensen+functional%22%29&sl=78&sessionSearchId=4cc854a753b93f4c5fe2d4fbfcda623d&relpos=3}{[\mbox{Scopus}]}$
  • [10] S.S. Dragomir and N.M. Ionescu, On some inequalities for convex-dominated functions, L’Anal. Num. Theor. L’Approx., 19(1) (1990), 21-27.
  • [11] S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000. http://rgmia.vu.edu.au/monographs.html
  • [12] S.S. Dragomir, C.E.M. Pearce and J.E. Peˇcari´c, On Jessen’s and related inequalities for isotonic sublinear functionals, Acta. Sci. Math., 61 (1995), 373-382.
  • [13] F. Kittaneh and Y. Manasrah, Improved Young and Heinz inequalities for matrix, J. Math. Anal. Appl., 361(1) (2010), 262-269 $\href{https://doi.org/10.1016/j.jmaa.2009.08.059}{[\mbox{CrossRef}]} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-70349378865&origin=resultslist&sort=plf-f&src=s&sid=81fa61a1532600f63071f79cd12df452&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Improved+Young+and+Heinz+inequalities+for+matrices%22%29&sl=67&sessionSearchId=81fa61a1532600f63071f79cd12df452&relpos=1}{[\mbox{Scopus}]} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000273063900024}{[\mbox{Web of Science}]}$
  • [14] F. Kittaneh and Y. Manasrah, Reverse Young and Heinz inequalities for matrices, Linear Multilinear Algebra., 59(9) (2011), 1031-1037. $\href{https://doi.org/10.1080/03081087.2010.551661}{[\mbox{CrossRef}]} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-79961134150&origin=resultslist&sort=plf-f&src=s&sid=81fa61a1532600f63071f79cd12df452&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Reverse+Young+and+Heinz+inequalities+for+matrices%22%29&sl=67&sessionSearchId=81fa61a1532600f63071f79cd12df452&relpos=0}{[\mbox{Scopus}]} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000293598100007}{[\mbox{Web of Science}]}$
  • [15] A. Lupas¸, A generalisation of Hadamard’s inequalities for convex functions, Univ. Beograd. Elek. Fak., 577-579 (1976), 115-121.
  • [16] D.I. Cartwright and M.J. Field, A refinement of the arithmetic mean-geometric mean inequality, Proc. Amer. Math. Soc., 71 (1978), 36-38. $$
  • [17] D.K. Callebaut, Generalization of Cauchy-Schwarz inequality, J. Math. Anal. Appl. 12 (1965), 491-494. $\href{https://doi.org/10.1016/0022-247X(65)90016-8}{[\mbox{CrossRef}]} %\href{https://www.scopus.com/record/display.uri?eid=2-s2.0-0001542604&origin=resultslist&sort=plf-f&src=s&sid=4cc854a753b93f4c5fe2d4fbfcda623d&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22On+Jessen%27s+inequality+for+convex+functions%22%29&sl=78&sessionSearchId=4cc854a753b93f4c5fe2d4fbfcda623d&relpos=2}{[\mbox{Scopus}]} %\href{https://www.webofscience.com/wos/woscc/full-record/WOS:000513943500001}{[\mbox{Web of Science}]}$
There are 17 citations in total.

Details

Primary Language English
Subjects Pure Mathematics (Other), Approximation Theory and Asymptotic Methods, Applied Mathematics (Other)
Journal Section Articles
Authors

Sever Dragomır 0000-0003-2902-6805

Early Pub Date March 29, 2024
Publication Date March 31, 2024
Submission Date September 19, 2023
Acceptance Date December 27, 2023
Published in Issue Year 2024 Volume: 7 Issue: 1

Cite

APA Dragomır, S. (2024). Some Refinements and Reverses of Callebaut’s Inequality for Isotonic Functionals via a Result Due to Cartwright and Field. Fundamental Journal of Mathematics and Applications, 7(1), 1-11. https://doi.org/10.33401/fujma.1362681
AMA Dragomır S. Some Refinements and Reverses of Callebaut’s Inequality for Isotonic Functionals via a Result Due to Cartwright and Field. Fundam. J. Math. Appl. March 2024;7(1):1-11. doi:10.33401/fujma.1362681
Chicago Dragomır, Sever. “Some Refinements and Reverses of Callebaut’s Inequality for Isotonic Functionals via a Result Due to Cartwright and Field”. Fundamental Journal of Mathematics and Applications 7, no. 1 (March 2024): 1-11. https://doi.org/10.33401/fujma.1362681.
EndNote Dragomır S (March 1, 2024) Some Refinements and Reverses of Callebaut’s Inequality for Isotonic Functionals via a Result Due to Cartwright and Field. Fundamental Journal of Mathematics and Applications 7 1 1–11.
IEEE S. Dragomır, “Some Refinements and Reverses of Callebaut’s Inequality for Isotonic Functionals via a Result Due to Cartwright and Field”, Fundam. J. Math. Appl., vol. 7, no. 1, pp. 1–11, 2024, doi: 10.33401/fujma.1362681.
ISNAD Dragomır, Sever. “Some Refinements and Reverses of Callebaut’s Inequality for Isotonic Functionals via a Result Due to Cartwright and Field”. Fundamental Journal of Mathematics and Applications 7/1 (March 2024), 1-11. https://doi.org/10.33401/fujma.1362681.
JAMA Dragomır S. Some Refinements and Reverses of Callebaut’s Inequality for Isotonic Functionals via a Result Due to Cartwright and Field. Fundam. J. Math. Appl. 2024;7:1–11.
MLA Dragomır, Sever. “Some Refinements and Reverses of Callebaut’s Inequality for Isotonic Functionals via a Result Due to Cartwright and Field”. Fundamental Journal of Mathematics and Applications, vol. 7, no. 1, 2024, pp. 1-11, doi:10.33401/fujma.1362681.
Vancouver Dragomır S. Some Refinements and Reverses of Callebaut’s Inequality for Isotonic Functionals via a Result Due to Cartwright and Field. Fundam. J. Math. Appl. 2024;7(1):1-11.
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