Research Article

Generalizations of Different Type Inequalities for $s$-Convex, Quasi-Convex and $P$-Function

Volume: 10 Number: 2 October 31, 2022
EN

Generalizations of Different Type Inequalities for $s$-Convex, Quasi-Convex and $P$-Function

Abstract

The main purpose of this article is to present the Bullen, Midpoint, Trapezoid and Simpson type inequalities, respectively, for different classes of convexity, with the help of identities existing in the literature.

Keywords

References

  1. [1] M. Alomari, M. Darus, S.S. Dragomir, New inequalities of Simpson’s type for s-convex functions with applications, RGMIA Res. Rep. Coll., 12(4) (2009).
  2. [2] M.A. Ali, H. Kara, J. Tariboon, S. Asawasamrit, H. Budak, F. Hezenci, Some new Simpson’s formula type inequalities for twice differentiable convex functions via generalized fractional operators, Symmetry, 13(12) (2021), Art. 2249.
  3. [3] W.W. Breckner, Stetigkeitsaussagen fr eine Klasse verallgemeinerter konvexer funktionen in topologischen linearen Raumen, Pupl. Inst. Math., 23 (1978), 1320.
  4. [4] P.S. Bullen, Error estimates for some elementary quadrature rules, Publikacije Elektrotehnickog fakulteta. Serija Matematika i fizika (602/633) (1978), 97–103.
  5. [5] S.S. Dragomir, J. Peˇcari´c and L.E. Person, Some inequalities of Hadamard Type, Soochow J. Math., 21(3) (1995), 335-341.
  6. [6] S.S. Dragomir, S. Fitzpatrick, The Hadamard’s inequality for s-convex functions in the second sense, Demonstratio Math., 32(4) (1999), 687–696.
  7. [7] T. Du, Y. Li, Z. Yang, A generalization of Simpson’s inequality via differentiable mapping using extended (s, m)-convex functions, Appl. Math. Comput., 293 (2017), 358–369.
  8. [8] T. Du, C. Luo, Z. Cao, On the Bullen-type inequalities via generalized fractional integrals and their applications, Fractals 29(7) (2021), Article ID 2150188, 20 pages.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Publication Date

October 31, 2022

Submission Date

August 2, 2022

Acceptance Date

September 16, 2022

Published in Issue

Year 2022 Volume: 10 Number: 2

APA
Sarıkaya, M. Z., Çelik, B., Set, E., & Azaklı, H. (2022). Generalizations of Different Type Inequalities for $s$-Convex, Quasi-Convex and $P$-Function. Konuralp Journal of Mathematics, 10(2), 341-354. https://izlik.org/JA28SG76GH
AMA
1.Sarıkaya MZ, Çelik B, Set E, Azaklı H. Generalizations of Different Type Inequalities for $s$-Convex, Quasi-Convex and $P$-Function. Konuralp J. Math. 2022;10(2):341-354. https://izlik.org/JA28SG76GH
Chicago
Sarıkaya, Mehmet Zeki, Barış Çelik, Erhan Set, and Hanife Azaklı. 2022. “Generalizations of Different Type Inequalities for $s$-Convex, Quasi-Convex and $P$-Function”. Konuralp Journal of Mathematics 10 (2): 341-54. https://izlik.org/JA28SG76GH.
EndNote
Sarıkaya MZ, Çelik B, Set E, Azaklı H (October 1, 2022) Generalizations of Different Type Inequalities for $s$-Convex, Quasi-Convex and $P$-Function. Konuralp Journal of Mathematics 10 2 341–354.
IEEE
[1]M. Z. Sarıkaya, B. Çelik, E. Set, and H. Azaklı, “Generalizations of Different Type Inequalities for $s$-Convex, Quasi-Convex and $P$-Function”, Konuralp J. Math., vol. 10, no. 2, pp. 341–354, Oct. 2022, [Online]. Available: https://izlik.org/JA28SG76GH
ISNAD
Sarıkaya, Mehmet Zeki - Çelik, Barış - Set, Erhan - Azaklı, Hanife. “Generalizations of Different Type Inequalities for $s$-Convex, Quasi-Convex and $P$-Function”. Konuralp Journal of Mathematics 10/2 (October 1, 2022): 341-354. https://izlik.org/JA28SG76GH.
JAMA
1.Sarıkaya MZ, Çelik B, Set E, Azaklı H. Generalizations of Different Type Inequalities for $s$-Convex, Quasi-Convex and $P$-Function. Konuralp J. Math. 2022;10:341–354.
MLA
Sarıkaya, Mehmet Zeki, et al. “Generalizations of Different Type Inequalities for $s$-Convex, Quasi-Convex and $P$-Function”. Konuralp Journal of Mathematics, vol. 10, no. 2, Oct. 2022, pp. 341-54, https://izlik.org/JA28SG76GH.
Vancouver
1.Mehmet Zeki Sarıkaya, Barış Çelik, Erhan Set, Hanife Azaklı. Generalizations of Different Type Inequalities for $s$-Convex, Quasi-Convex and $P$-Function. Konuralp J. Math. [Internet]. 2022 Oct. 1;10(2):341-54. Available from: https://izlik.org/JA28SG76GH
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