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Year 2024, , 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, , 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

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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