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Year 2023, Volume: 52 Issue: 3, 560 - 571, 30.05.2023

Yogesh Bagul Christophe Chesneau Marko Kostic Tatjana Lutovac Branko Malesevic Marija Rašajski

https://doi.org/10.15672/hujms.1096357
Cited By: 1

Abstract

References

  • [1] A.L. Cauchy, Trente-Cinquième Leçon, Résumé des leçons données à l’Ecole royale polytechnique sur le calcul infinitésimal, Imprimerie Royale, Paris, 133–140, 1823. Reprint: OEuvres complètes II(4), Gauthier-Villars, Paris, 5-261.
  • [2] J. Dieudonne (ed.), Oeuvres de Camille Jordan I-IV, Gauthier-Villars, Paris, 1961- 1964.
  • [3] H. Kober, Approximation by integral functions in the complex domain, Trans. Amer. Math. Soc. 56 (1), 7-31, 1944.
  • [4] T. Lutovac, B. Malešević, and M. Rašajski, A new method for proving some inequalities related to several special functions, Results Math. 73:100, 15 pp, 2018.
  • [5] B. Malešević, T. Lutovac M. Rašajski, B. Banjac, Double-Sided Taylor’s Approximations and Their Applications in Theory of Trigonometric Inequalities, in: eds M.Th. Rassias, A. Raigorodskii, Trigonometric Sums and Their Applications, 159– 167, Springer, 2020.
  • [6] B. Malešević, T. Lutovac, M. Rašajski, B. Banjac, Error-Functions in Double-Sided Taylor’s Approximations, Appl. Anal. Discrete Math. 14 (3), 599–613, 2020.
  • [7] B. Malešević, T. Lutovac, M. Rašajski and C. Mortici, Extensions of the natural approach to refinements and generalizations of some trigonometric inequalities, Adv. Difference Equ. 2018:90, 15 pp, 2018.
  • [8] B. Malešević, M. Rašajski, and T. Lutovac, Double-sided Taylor’s approximations and their applications in Theory of analytic inequalities, in: eds. Th. Rassias and D. Andrica, Differential and Integral Inequalities, Optimization and Its Applications 151, 569–582, Springer, 2019.
  • [9] M. Nenezić and L. Zhu, Some improvements of Jordan-Steckin and Becker-Stark inequalities, Appl. Anal. Discrete Math. 12, 244–256, 2018.
  • [10] F. Qi, D.-W. Niu, and B.-N. Guo, Refinements, Generalizations and Applications of Jordan’s inequality and related problems, J. Inequal. Appl. 2009, Article ID: 271923, 52 pp., 2009. Doi: 10.1155/2009/271923
  • [11] M. Rašajski, T. Lutovac, and B. Malešević, Sharpening and generalizations of Shafer- Fink and Wilker type inequalities: a new approach, J. Nonlinear Sci. Appl. 11 (7), 885–893, 2018.
  • [12] M. Rašajski, T. Lutovac, and B. Malešević, About some exponential inequalities related to the sinc function, J. Inequal. Appl. 2018:150, 10 pp, 2018.
  • [13] S.-H. Wu and L. Debnath, Jordan-type inequalities for differentiable functions and their applications, Appl. Math. Lett. 21 (8), 803–809, 2008.
  • [14] S.-H. Wu and L. Debnath, A generalization of L’Hospital-type rules for monotonicity and its application, Appl. Math. Lett. 22 (2), 284–290, 2009.
  • [15] S.-H. Wu and H.M. Srivastva, A further refinement of a Jordan type inequality and its applications, Appl. Math. Comput. 197, 914–923, 2008.
  • [16] S.-H. Wu and H.M. Srivastava, A further refinement of Wilker’s inequality, Integral Transforms Spec. Funct. 19 (10), 757–765, 2008.

Convexity and double-sided Taylor's approximations

Year 2023, Volume: 52 Issue: 3, 560 - 571, 30.05.2023

Yogesh Bagul Christophe Chesneau Marko Kostic Tatjana Lutovac Branko Malesevic Marija Rašajski

https://doi.org/10.15672/hujms.1096357
Cited By: 1

Abstract

Using convexity and double-sided Taylor's approximations of functions, we establish new general results in this field which can be used to refine and/or sharp some analytic inequalities in the existing literature.

Keywords

Convexity double-sided Taylor’s approximation Kober’s inequality

References

  • [1] A.L. Cauchy, Trente-Cinquième Leçon, Résumé des leçons données à l’Ecole royale polytechnique sur le calcul infinitésimal, Imprimerie Royale, Paris, 133–140, 1823. Reprint: OEuvres complètes II(4), Gauthier-Villars, Paris, 5-261.
  • [2] J. Dieudonne (ed.), Oeuvres de Camille Jordan I-IV, Gauthier-Villars, Paris, 1961- 1964.
  • [3] H. Kober, Approximation by integral functions in the complex domain, Trans. Amer. Math. Soc. 56 (1), 7-31, 1944.
  • [4] T. Lutovac, B. Malešević, and M. Rašajski, A new method for proving some inequalities related to several special functions, Results Math. 73:100, 15 pp, 2018.
  • [5] B. Malešević, T. Lutovac M. Rašajski, B. Banjac, Double-Sided Taylor’s Approximations and Their Applications in Theory of Trigonometric Inequalities, in: eds M.Th. Rassias, A. Raigorodskii, Trigonometric Sums and Their Applications, 159– 167, Springer, 2020.
  • [6] B. Malešević, T. Lutovac, M. Rašajski, B. Banjac, Error-Functions in Double-Sided Taylor’s Approximations, Appl. Anal. Discrete Math. 14 (3), 599–613, 2020.
  • [7] B. Malešević, T. Lutovac, M. Rašajski and C. Mortici, Extensions of the natural approach to refinements and generalizations of some trigonometric inequalities, Adv. Difference Equ. 2018:90, 15 pp, 2018.
  • [8] B. Malešević, M. Rašajski, and T. Lutovac, Double-sided Taylor’s approximations and their applications in Theory of analytic inequalities, in: eds. Th. Rassias and D. Andrica, Differential and Integral Inequalities, Optimization and Its Applications 151, 569–582, Springer, 2019.
  • [9] M. Nenezić and L. Zhu, Some improvements of Jordan-Steckin and Becker-Stark inequalities, Appl. Anal. Discrete Math. 12, 244–256, 2018.
  • [10] F. Qi, D.-W. Niu, and B.-N. Guo, Refinements, Generalizations and Applications of Jordan’s inequality and related problems, J. Inequal. Appl. 2009, Article ID: 271923, 52 pp., 2009. Doi: 10.1155/2009/271923
  • [11] M. Rašajski, T. Lutovac, and B. Malešević, Sharpening and generalizations of Shafer- Fink and Wilker type inequalities: a new approach, J. Nonlinear Sci. Appl. 11 (7), 885–893, 2018.
  • [12] M. Rašajski, T. Lutovac, and B. Malešević, About some exponential inequalities related to the sinc function, J. Inequal. Appl. 2018:150, 10 pp, 2018.
  • [13] S.-H. Wu and L. Debnath, Jordan-type inequalities for differentiable functions and their applications, Appl. Math. Lett. 21 (8), 803–809, 2008.
  • [14] S.-H. Wu and L. Debnath, A generalization of L’Hospital-type rules for monotonicity and its application, Appl. Math. Lett. 22 (2), 284–290, 2009.
  • [15] S.-H. Wu and H.M. Srivastva, A further refinement of a Jordan type inequality and its applications, Appl. Math. Comput. 197, 914–923, 2008.
  • [16] S.-H. Wu and H.M. Srivastava, A further refinement of Wilker’s inequality, Integral Transforms Spec. Funct. 19 (10), 757–765, 2008.
There are 16 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Yogesh Bagul 0000-0002-8331-3920

Christophe Chesneau 0000-0002-1522-9292

Marko Kostic 0000-0002-0392-4976

Tatjana Lutovac 0000-0003-2138-6400

Branko Malesevic 0000-0002-4963-4149

Marija Rašajski 0000-0003-1212-0803

Publication Date May 30, 2023
Published in Issue Year 2023 Volume: 52 Issue: 3

Cite

APA Bagul, Y., Chesneau, C., Kostic, M., Lutovac, T., et al. (2023). Convexity and double-sided Taylor’s approximations. Hacettepe Journal of Mathematics and Statistics, 52(3), 560-571. https://doi.org/10.15672/hujms.1096357
AMA Bagul Y, Chesneau C, Kostic M, Lutovac T, Malesevic B, Rašajski M. Convexity and double-sided Taylor’s approximations. Hacettepe Journal of Mathematics and Statistics. May 2023;52(3):560-571. doi:10.15672/hujms.1096357
Chicago Bagul, Yogesh, Christophe Chesneau, Marko Kostic, Tatjana Lutovac, Branko Malesevic, and Marija Rašajski. “Convexity and Double-Sided Taylor’s Approximations”. Hacettepe Journal of Mathematics and Statistics 52, no. 3 (May 2023): 560-71. https://doi.org/10.15672/hujms.1096357.
EndNote Bagul Y, Chesneau C, Kostic M, Lutovac T, Malesevic B, Rašajski M (May 1, 2023) Convexity and double-sided Taylor’s approximations. Hacettepe Journal of Mathematics and Statistics 52 3 560–571.
IEEE Y. Bagul, C. Chesneau, M. Kostic, T. Lutovac, B. Malesevic, and M. Rašajski, “Convexity and double-sided Taylor’s approximations”, Hacettepe Journal of Mathematics and Statistics, vol. 52, no. 3, pp. 560–571, 2023, doi: 10.15672/hujms.1096357.
ISNAD Bagul, Yogesh et al. “Convexity and Double-Sided Taylor’s Approximations”. Hacettepe Journal of Mathematics and Statistics 52/3 (May 2023), 560-571. https://doi.org/10.15672/hujms.1096357.
JAMA Bagul Y, Chesneau C, Kostic M, Lutovac T, Malesevic B, Rašajski M. Convexity and double-sided Taylor’s approximations. Hacettepe Journal of Mathematics and Statistics. 2023;52:560–571.
MLA Bagul, Yogesh et al. “Convexity and Double-Sided Taylor’s Approximations”. Hacettepe Journal of Mathematics and Statistics, vol. 52, no. 3, 2023, pp. 560-71, doi:10.15672/hujms.1096357.
Vancouver Bagul Y, Chesneau C, Kostic M, Lutovac T, Malesevic B, Rašajski M. Convexity and double-sided Taylor’s approximations. Hacettepe Journal of Mathematics and Statistics. 2023;52(3):560-71.

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