Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2023, Cilt: 52 Sayı: 3, 560 - 571, 30.05.2023
https://doi.org/10.15672/hujms.1096357

Öz

Kaynakça

  • [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

Yıl 2023, Cilt: 52 Sayı: 3, 560 - 571, 30.05.2023
https://doi.org/10.15672/hujms.1096357

Öz

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.

Kaynakça

  • [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.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

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

Yayımlanma Tarihi 30 Mayıs 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 52 Sayı: 3

Kaynak Göster

APA Bagul, Y., Chesneau, C., Kostic, M., Lutovac, T., vd. (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. Mayıs 2023;52(3):560-571. doi:10.15672/hujms.1096357
Chicago Bagul, Yogesh, Christophe Chesneau, Marko Kostic, Tatjana Lutovac, Branko Malesevic, ve Marija Rašajski. “Convexity and Double-Sided Taylor’s Approximations”. Hacettepe Journal of Mathematics and Statistics 52, sy. 3 (Mayıs 2023): 560-71. https://doi.org/10.15672/hujms.1096357.
EndNote Bagul Y, Chesneau C, Kostic M, Lutovac T, Malesevic B, Rašajski M (01 Mayıs 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, ve M. Rašajski, “Convexity and double-sided Taylor’s approximations”, Hacettepe Journal of Mathematics and Statistics, c. 52, sy. 3, ss. 560–571, 2023, doi: 10.15672/hujms.1096357.
ISNAD Bagul, Yogesh vd. “Convexity and Double-Sided Taylor’s Approximations”. Hacettepe Journal of Mathematics and Statistics 52/3 (Mayıs 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 vd. “Convexity and Double-Sided Taylor’s Approximations”. Hacettepe Journal of Mathematics and Statistics, c. 52, sy. 3, 2023, ss. 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.