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Year 2024, Volume: 13 Issue: 2, 49 - 60, 28.06.2024
https://doi.org/10.46810/tdfd.1424844

Abstract

References

  • Hardy GH, Littlewood JE, Pólya G. Inequalities. Cambridge, England: Cambridge University Press, 1952.
  • Mitrinović DS. Analytic Inequalities. Berlin, New York, Heidelberg: Springer-Verlag, 1970.
  • Pečarić JE. Convex functions: inequalities. Serbocroatian, Beograd: 1987.
  • Niculescu CP, Persson LE. Convex functions and their applications. United States of America: Springer, 2006.
  • Hadamard, J. Étude sur les propriétés des fonctions entiéres en particulier d’une fonction considéréé par Riemann. J. Math. Pures. Appl. 1893, 58, 171-215.
  • Oldham KB, Spanier J. The fractional calculus. New York: Academic Press, 1974.
  • Podlubny, I. Fractional differential equations: an introduction to fractional derivatives, fractional differential equations to methods of their applications. Academic Press, 1998.
  • Pečarić JE, Prochan F, Tong, Y. Convex functions, partial orderings and statical applications, Academic Press, New York, USA, 1992.
  • Polyak BT. Existence theorems and convergence of minimizing sequences in extremum problems with restictions, Soviet Math. Dokl. 7, 1966, 72–75.
  • Sarikaya MZ, Set E, Yaldiz H, Basak N. Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities. Mathematical and Computer Modelling, 2013; vol. 57, 2403–2407.
  • Set E, Akdemir AO, Özdemir ME. Simpson type integral inequalities for convex functions via Riemann-Liouville integrals. Filomat 2017;31(14):4415–20.
  • Sarikaya MZ, Yildirim H. On Hermite-Hadamard type inequalities for Riemann-Liouville fractional integrals. Miskolc Math. Notes 2017, 17, 1049–1059.
  • Akdemir AO, Aslan S, Dokuyucu MA, Çelik E . Exponentially Convex Functions on the Coordinates and Novel Estimations via Riemann-Liouville Fractional Operator. Journal of Function Spaces, 2023.
  • Abdeljawad T, Baleanu D. On fractional derivatives with exponential kernel and their discrete versions. Rep Math Phys 2017;80(1):11–27.
  • Ardic MA, Akdemir AO, Önalan HK. Integral inequalities for differentiable s-convex functions in the second sense via Atangana-Baleanu fractional integral operators. Filomat 2023, 37, 6229–6244.
  • Kızıl Ş, Ardıç MA. Inequalities for strongly convex functions via Atangana-Baleanu Integral Operators. Turkish J Sci. 2021, 6, 96–109.
  • Ahmad, H, Tariq, M, Sahoo, SK, Askar S, Abouelregal AE, Khedher KM. Refinements of Ostrowski Type Integral Inequalities Involving Atangana-Baleanu Fractional Integral Operator. Symmetry 2021; 13, (11) 2059.
  • Çelik B, Özdemir ME, Akdemir AO, Set E. Integral inequalities for some convexity classes via Atangana-Baleanu Integral Operators. Turkish Journal of Inequalities, 5(2) (2021), 82-92.
  • Karaoğlan A, Çelik B, Set E, Akdemir AO. On New Inequalities Involving AB-fractional Integrals for Some Convexity Classes. Fundamentals of Contemporary Mathematical Sciences, 2(2) (2021), 127-145.
  • Abdeljawad T, Baleanu D. Integration by parts and its applications of a new nonlocal fractional derivative with Mittag-Leffler nonsingular kernel. J Nonlin- ear Sci Appl 2017;10:1098–107.
  • Atangana A, Baleanu D. New fractional derivatives with non-local and non-sin-gular kernel, theory and application to heat transfer model. Therm Sci 2016;20(2):763–9.
  • Set E, Butt SI, Akdemir AO, Karaoglan A, Abdeljawad T. New integral inequalities for differentiable convex functions via Atangana–Baleanu fractional integral operators. Chaos Solitons Fractals 2021;143:110554.
  • Aslan S, Akdemir AO. New estimations for quasi-convex functions and ((h, m))-convex functions with the help of Caputo-Fabrizio fractional integral operators. Electronic Journal of Applied Mathematics 2023; 1(3), 38-46.
  • Akdemir AO, Aslan S, Ekinci A. Novel approaches for s-convex functions via Caputo-Fabrizio fractional integrals. Proceeding of IAM, 2022; 11(1), 3-16.

Inequalities for strongly s-convex functions via Atangana-Baleanu fractional integral operators

Year 2024, Volume: 13 Issue: 2, 49 - 60, 28.06.2024
https://doi.org/10.46810/tdfd.1424844

Abstract

It is more convenient to use fractional derivatives and integrals to express and represent rapid changes than to use integer derivatives and integrals. For this reason, fractional analysis has been found worthy of study in many fields. In recent years, fractional derivatives and integrals have been discussed together with inequality theory and the studies have attracted attention. In this article, we discuss new Hermite-Hadamard type approximations for strongly convex functions with the help of Atangana-Baleanu fractional integral operators. Additionally, new upper bounds have been obtained using various auxiliary inequalities with the help of twice differentiable strongly convex functions.

References

  • Hardy GH, Littlewood JE, Pólya G. Inequalities. Cambridge, England: Cambridge University Press, 1952.
  • Mitrinović DS. Analytic Inequalities. Berlin, New York, Heidelberg: Springer-Verlag, 1970.
  • Pečarić JE. Convex functions: inequalities. Serbocroatian, Beograd: 1987.
  • Niculescu CP, Persson LE. Convex functions and their applications. United States of America: Springer, 2006.
  • Hadamard, J. Étude sur les propriétés des fonctions entiéres en particulier d’une fonction considéréé par Riemann. J. Math. Pures. Appl. 1893, 58, 171-215.
  • Oldham KB, Spanier J. The fractional calculus. New York: Academic Press, 1974.
  • Podlubny, I. Fractional differential equations: an introduction to fractional derivatives, fractional differential equations to methods of their applications. Academic Press, 1998.
  • Pečarić JE, Prochan F, Tong, Y. Convex functions, partial orderings and statical applications, Academic Press, New York, USA, 1992.
  • Polyak BT. Existence theorems and convergence of minimizing sequences in extremum problems with restictions, Soviet Math. Dokl. 7, 1966, 72–75.
  • Sarikaya MZ, Set E, Yaldiz H, Basak N. Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities. Mathematical and Computer Modelling, 2013; vol. 57, 2403–2407.
  • Set E, Akdemir AO, Özdemir ME. Simpson type integral inequalities for convex functions via Riemann-Liouville integrals. Filomat 2017;31(14):4415–20.
  • Sarikaya MZ, Yildirim H. On Hermite-Hadamard type inequalities for Riemann-Liouville fractional integrals. Miskolc Math. Notes 2017, 17, 1049–1059.
  • Akdemir AO, Aslan S, Dokuyucu MA, Çelik E . Exponentially Convex Functions on the Coordinates and Novel Estimations via Riemann-Liouville Fractional Operator. Journal of Function Spaces, 2023.
  • Abdeljawad T, Baleanu D. On fractional derivatives with exponential kernel and their discrete versions. Rep Math Phys 2017;80(1):11–27.
  • Ardic MA, Akdemir AO, Önalan HK. Integral inequalities for differentiable s-convex functions in the second sense via Atangana-Baleanu fractional integral operators. Filomat 2023, 37, 6229–6244.
  • Kızıl Ş, Ardıç MA. Inequalities for strongly convex functions via Atangana-Baleanu Integral Operators. Turkish J Sci. 2021, 6, 96–109.
  • Ahmad, H, Tariq, M, Sahoo, SK, Askar S, Abouelregal AE, Khedher KM. Refinements of Ostrowski Type Integral Inequalities Involving Atangana-Baleanu Fractional Integral Operator. Symmetry 2021; 13, (11) 2059.
  • Çelik B, Özdemir ME, Akdemir AO, Set E. Integral inequalities for some convexity classes via Atangana-Baleanu Integral Operators. Turkish Journal of Inequalities, 5(2) (2021), 82-92.
  • Karaoğlan A, Çelik B, Set E, Akdemir AO. On New Inequalities Involving AB-fractional Integrals for Some Convexity Classes. Fundamentals of Contemporary Mathematical Sciences, 2(2) (2021), 127-145.
  • Abdeljawad T, Baleanu D. Integration by parts and its applications of a new nonlocal fractional derivative with Mittag-Leffler nonsingular kernel. J Nonlin- ear Sci Appl 2017;10:1098–107.
  • Atangana A, Baleanu D. New fractional derivatives with non-local and non-sin-gular kernel, theory and application to heat transfer model. Therm Sci 2016;20(2):763–9.
  • Set E, Butt SI, Akdemir AO, Karaoglan A, Abdeljawad T. New integral inequalities for differentiable convex functions via Atangana–Baleanu fractional integral operators. Chaos Solitons Fractals 2021;143:110554.
  • Aslan S, Akdemir AO. New estimations for quasi-convex functions and ((h, m))-convex functions with the help of Caputo-Fabrizio fractional integral operators. Electronic Journal of Applied Mathematics 2023; 1(3), 38-46.
  • Akdemir AO, Aslan S, Ekinci A. Novel approaches for s-convex functions via Caputo-Fabrizio fractional integrals. Proceeding of IAM, 2022; 11(1), 3-16.
There are 24 citations in total.

Details

Primary Language English
Subjects Mathematical Physics (Other)
Journal Section Articles
Authors

Ebru Yüksel 0000-0001-7081-5924

Early Pub Date June 28, 2024
Publication Date June 28, 2024
Submission Date January 24, 2024
Acceptance Date May 20, 2024
Published in Issue Year 2024 Volume: 13 Issue: 2

Cite

APA Yüksel, E. (2024). Inequalities for strongly s-convex functions via Atangana-Baleanu fractional integral operators. Türk Doğa Ve Fen Dergisi, 13(2), 49-60. https://doi.org/10.46810/tdfd.1424844
AMA Yüksel E. Inequalities for strongly s-convex functions via Atangana-Baleanu fractional integral operators. TJNS. June 2024;13(2):49-60. doi:10.46810/tdfd.1424844
Chicago Yüksel, Ebru. “Inequalities for Strongly S-Convex Functions via Atangana-Baleanu Fractional Integral Operators”. Türk Doğa Ve Fen Dergisi 13, no. 2 (June 2024): 49-60. https://doi.org/10.46810/tdfd.1424844.
EndNote Yüksel E (June 1, 2024) Inequalities for strongly s-convex functions via Atangana-Baleanu fractional integral operators. Türk Doğa ve Fen Dergisi 13 2 49–60.
IEEE E. Yüksel, “Inequalities for strongly s-convex functions via Atangana-Baleanu fractional integral operators”, TJNS, vol. 13, no. 2, pp. 49–60, 2024, doi: 10.46810/tdfd.1424844.
ISNAD Yüksel, Ebru. “Inequalities for Strongly S-Convex Functions via Atangana-Baleanu Fractional Integral Operators”. Türk Doğa ve Fen Dergisi 13/2 (June 2024), 49-60. https://doi.org/10.46810/tdfd.1424844.
JAMA Yüksel E. Inequalities for strongly s-convex functions via Atangana-Baleanu fractional integral operators. TJNS. 2024;13:49–60.
MLA Yüksel, Ebru. “Inequalities for Strongly S-Convex Functions via Atangana-Baleanu Fractional Integral Operators”. Türk Doğa Ve Fen Dergisi, vol. 13, no. 2, 2024, pp. 49-60, doi:10.46810/tdfd.1424844.
Vancouver Yüksel E. Inequalities for strongly s-convex functions via Atangana-Baleanu fractional integral operators. TJNS. 2024;13(2):49-60.

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