Research Article

Conformable Fractional Milne-Type Inequalities Through Twice-Differentiable Convex Functions

Volume: 8 Number: 1 March 31, 2025
EN

Conformable Fractional Milne-Type Inequalities Through Twice-Differentiable Convex Functions

Abstract

In this article, we present a new integral identity based on conformable fractional integral operators with the help of twice-differentiable functions. Then, using this newly derived identity, we propose several Milne-type inequalities for twice-differentiable convex functions by means of conformable fractional integral operators and offer an example with an associated graph. Also, we note that the obtained results improve and expand some of the previous discoveries in the field of integral inequalities. Moreover, along with expanding on previous results, our results suggest effective approaches and methods for dealing with a variety of mathematical and scientific issues.

Keywords

References

  1. [1] S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, Cambridge, UK, (2004). $\href{https://web.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf}{\mbox{[Web]}} $
  2. [2] M.J. Osborne and A. Rubinstein, A Course in Game Theory, MIT Press, Cambridge, MA, USA, (1994). $ \href{https://sites.math.rutgers.edu/~zeilberg/EM20/OsborneRubinsteinMasterpiece.pdf}{\mbox{[Web]}} $
  3. [3] R.T. Rockafellar and R.J.B.Wets, Variational Analysis, Springer Science & Business Media, Berlin/Heidelberg, Germany, 317(2009). $ \href{https://sites.math.washington.edu/~rtr/papers/rtr169-VarAnalysis-RockWets.pdf}{\mbox{[Web]}} $
  4. [4] J. Hadamard, Etude sur les proprietes des fonctions entieres et en particulier d’une fonction considree par Riemann, J. Math. Pures. et Appl., 58(1893), 171-215.
  5. [5] H. Budak, T. Tunç and M.Z. Sarıkaya, Fractional Hermite-Hadamard-type inequalities for interval-valued functions, Proc. Amer. Math. Soc., 148(2) (2020), 705-718. $ \href{https://doi.org/10.1186/s13660-019-2217-1}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85073568146&origin=resultslist&sort=plf-f&src=s&sid=e090bc4fc46035bb400731a9601b8139&sot=a&sdt=b&s=TITLE%28%22Fractional+Hermite-Hadamard-type+inequalities+for+interval-valued+functions%22%29&sl=41&sessionSearchId=e090bc4fc46035bb400731a9601b8139&relpos=1}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000515135200024}{\mbox{[Web of Science]}} $
  6. [6] S.S. Dragomir and R.P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett., 11(5) (1998), 91-95. $\href{https://doi.org/10.1016/S0893-9659(98)00086-X}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-0002448458&origin=resultslist&sort=plf-f&src=s&sid=e090bc4fc46035bb400731a9601b8139&sot=a&sdt=b&s=TITLE%28%22Two+inequalities+for+differentiable+mappings+and+applications+to+special+means+of+real+numbers+and+to+trapezoidal+formula%22%29&sl=41&sessionSearchId=e090bc4fc46035bb400731a9601b8139}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000075622100017}{\mbox{[Web of Science]}} $
  7. [7] U.S. Kırmacı, Inequalities for differentiable mappings and applications to special means of real numbers to midpoint formula, Appl. Math. Comput., 147(5) (2004), 137-146. $ \href{https://doi.org/10.1016/S0096-3003(02)00657-4}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-0141525042&origin=resultslist&sort=plf-f&src=s&sid=e090bc4fc46035bb400731a9601b8139&sot=a&sdt=b&s=TITLE%28%22Inequalities+for+differentiable+mappings+and+applications+to+special+means+of+real+numbers+and+to+midpoint+formula%22%29&sl=41&sessionSearchId=e090bc4fc46035bb400731a9601b8139&relpos=1}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000185952900012}{\mbox{[Web of Science]}} $
  8. [8] M. Alomari and Z. Liu, New error estimations for the Milne’s quadrature formula in terms of at most first derivatives, Konuralp J. Math., 1(1) (2013), 17-23. $ \href{https://dergipark.org.tr/en/pub/konuralpjournalmath/issue/27676/291702}{\mbox{[Web]}} $

Details

Primary Language

English

Subjects

Approximation Theory and Asymptotic Methods

Journal Section

Research Article

Early Pub Date

March 28, 2025

Publication Date

March 31, 2025

Submission Date

January 1, 2025

Acceptance Date

March 28, 2025

Published in Issue

Year 2025 Volume: 8 Number: 1

APA
Demir, İ., & Üneş, E. (2025). Conformable Fractional Milne-Type Inequalities Through Twice-Differentiable Convex Functions. Fundamental Journal of Mathematics and Applications, 8(1), 31-42. https://doi.org/10.33401/fujma.1610936
AMA
1.Demir İ, Üneş E. Conformable Fractional Milne-Type Inequalities Through Twice-Differentiable Convex Functions. Fundam. J. Math. Appl. 2025;8(1):31-42. doi:10.33401/fujma.1610936
Chicago
Demir, İzzettin, and Esra Üneş. 2025. “Conformable Fractional Milne-Type Inequalities Through Twice-Differentiable Convex Functions”. Fundamental Journal of Mathematics and Applications 8 (1): 31-42. https://doi.org/10.33401/fujma.1610936.
EndNote
Demir İ, Üneş E (March 1, 2025) Conformable Fractional Milne-Type Inequalities Through Twice-Differentiable Convex Functions. Fundamental Journal of Mathematics and Applications 8 1 31–42.
IEEE
[1]İ. Demir and E. Üneş, “Conformable Fractional Milne-Type Inequalities Through Twice-Differentiable Convex Functions”, Fundam. J. Math. Appl., vol. 8, no. 1, pp. 31–42, Mar. 2025, doi: 10.33401/fujma.1610936.
ISNAD
Demir, İzzettin - Üneş, Esra. “Conformable Fractional Milne-Type Inequalities Through Twice-Differentiable Convex Functions”. Fundamental Journal of Mathematics and Applications 8/1 (March 1, 2025): 31-42. https://doi.org/10.33401/fujma.1610936.
JAMA
1.Demir İ, Üneş E. Conformable Fractional Milne-Type Inequalities Through Twice-Differentiable Convex Functions. Fundam. J. Math. Appl. 2025;8:31–42.
MLA
Demir, İzzettin, and Esra Üneş. “Conformable Fractional Milne-Type Inequalities Through Twice-Differentiable Convex Functions”. Fundamental Journal of Mathematics and Applications, vol. 8, no. 1, Mar. 2025, pp. 31-42, doi:10.33401/fujma.1610936.
Vancouver
1.İzzettin Demir, Esra Üneş. Conformable Fractional Milne-Type Inequalities Through Twice-Differentiable Convex Functions. Fundam. J. Math. Appl. 2025 Mar. 1;8(1):31-42. doi:10.33401/fujma.1610936

Cited By

download?token=eyJhdXRoX3JvbGVzIjpbXSwiZW5kcG9pbnQiOiJqb3VybmFsIiwib3JpZ2luYWxuYW1lIjoiQWJzdHJhY3QgR3JhbmQgT3BlbmluZyBBbm5vdW5jZW1lbnQgRnJlZSBJbnN0YWdyYW0gUG9zdCAoMSkucG5nIiwicGF0aCI6IjdjNmYvZWY3NC85ZDMwLzY5Y2U0NjNiMTI0YWUxLjI4OTYzMDEwLnBuZyIsImV4cCI6MTc3NTEyOTY3NSwibm9uY2UiOiJjY2JlNDg0NTg1ZjM5NDhiNjc5OTBiMTQyZGQ1NGJkZiJ9.32mL-W4AxKl9vkmOiZKzTdBUXRMtp2xLb0bNUYSQ61w       download?token=eyJhdXRoX3JvbGVzIjpbXSwiZW5kcG9pbnQiOiJqb3VybmFsIiwib3JpZ2luYWxuYW1lIjoiQWJzdHJhY3QgR3JhbmQgT3BlbmluZyBBbm5vdW5jZW1lbnQgRnJlZSBJbnN0YWdyYW0gUG9zdCAoMSkucG5nIiwicGF0aCI6ImI1ODYvMjQ0My9jMWViLzY5ZDYyYjAwODY1YzUwLjg2OTE5ODk1LnBuZyIsImV4cCI6MTc3NTY0Njk5Miwibm9uY2UiOiIwY2Y4NDNkN2IzYTBmOWZjNmM3YjJjOTM5MDFlODcwZiJ9.CF8E27Ea4s80p4hO_2OZg23PRrjTZehq_uGq5OpcHg8

35258

Creative Commons License

The published articles in Fundamental Journal of Mathematics and Applications are licensed under a

Creative Commons Attribution-NonCommercial 4.0 International License


28893   28892   28894   28895   28896   28897