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Year 2020, Volume: 6 Issue: 2, 9 - 14, 16.12.2020

Muhamet Emin Özdemir Alper Ekinci

Abstract

References

  • W. Orlicz, A note on modular spaces, I, Bull. Acad. Polon. Sci. Math. Astronom. Phys., 9(1961), 157-162.
  • S.S. Dragomir, S. Fitzpatrick, The Hadamard’s inequality for s􀀀convex functions in the second sense, Demonstratio Math., 32 (4) (1999), 687–696.
  • S. S. Dragomir and C. E. M. Pearce, Selected Topics on Hermite-Hadamard Inequalities, RGMIA Monographs http://rgmia.vu.edu.au/monographs/hermite hadamard.html, Victoria University, 2000.
  • M. Avcı, H. Kavurmacı and M.E. Özdemir, New inequalities of Hermite-Hadamard type via s- convex functions in the second sense with applications, Applied Mathematics and Computation, (217), 5171-5176, (2011)
  • M.E. Özdemir, M. Avcı and H. Kavurmacı, Hermite-Hadamard type inequalities via (alpha,m)-convexity, Computers and Mathematics With Applications, 61(9), 2614-2620 (2011)
  • M.E. Özdemir, M. Avcı and E. Set, On Some Inequalities of Hermite-Hadamard Type via m-Convexity, Applied Mathematics Letters, 23, 1065-1070 (2010)
  • H. Hudzik and L. Maligranda, Some remarks on s-convex functions, Aequationes Math., 48(1994), 100-111.

On (α,β)-Convex Functions

Year 2020, Volume: 6 Issue: 2, 9 - 14, 16.12.2020

Muhamet Emin Özdemir Alper Ekinci

Abstract

In this paper, we introduce a new class called (α,β )-convex of Fαβ and give some basic properties for this class like positivity and (α,β ) convexity of compound function. (α,β )-convex functions are more general form of s-convex and ordinary convex functions. After basic and useful properties of this class we give Hermite-Hadamard inequality for this class then we give inequalities involving mappings H and F. Also we give an ineqauality for (α,β)-convex functions including a third mapping Ff which defined with double integral.

Keywords

convex functions Hadamard Inequality s-convex functions

References

  • W. Orlicz, A note on modular spaces, I, Bull. Acad. Polon. Sci. Math. Astronom. Phys., 9(1961), 157-162.
  • S.S. Dragomir, S. Fitzpatrick, The Hadamard’s inequality for s􀀀convex functions in the second sense, Demonstratio Math., 32 (4) (1999), 687–696.
  • S. S. Dragomir and C. E. M. Pearce, Selected Topics on Hermite-Hadamard Inequalities, RGMIA Monographs http://rgmia.vu.edu.au/monographs/hermite hadamard.html, Victoria University, 2000.
  • M. Avcı, H. Kavurmacı and M.E. Özdemir, New inequalities of Hermite-Hadamard type via s- convex functions in the second sense with applications, Applied Mathematics and Computation, (217), 5171-5176, (2011)
  • M.E. Özdemir, M. Avcı and H. Kavurmacı, Hermite-Hadamard type inequalities via (alpha,m)-convexity, Computers and Mathematics With Applications, 61(9), 2614-2620 (2011)
  • M.E. Özdemir, M. Avcı and E. Set, On Some Inequalities of Hermite-Hadamard Type via m-Convexity, Applied Mathematics Letters, 23, 1065-1070 (2010)
  • H. Hudzik and L. Maligranda, Some remarks on s-convex functions, Aequationes Math., 48(1994), 100-111.
There are 7 citations in total.

Details

Primary Language English
Journal Section makaleler
Authors

Muhamet Emin Özdemir

Alper Ekinci

Publication Date December 16, 2020
Published in Issue Year 2020 Volume: 6 Issue: 2

Cite

APA Özdemir, M. E., & Ekinci, A. (2020). On (α,β)-Convex Functions. Eastern Anatolian Journal of Science, 6(2), 9-14.
AMA Özdemir ME, Ekinci A. On (α,β)-Convex Functions. Eastern Anatolian Journal of Science. December 2020;6(2):9-14.
Chicago Özdemir, Muhamet Emin, and Alper Ekinci. “On (α,β)-Convex Functions”. Eastern Anatolian Journal of Science 6, no. 2 (December 2020): 9-14.
EndNote Özdemir ME, Ekinci A (December 1, 2020) On (α,β)-Convex Functions. Eastern Anatolian Journal of Science 6 2 9–14.
IEEE M. E. Özdemir and A. Ekinci, “On (α,β)-Convex Functions”, Eastern Anatolian Journal of Science, vol. 6, no. 2, pp. 9–14, 2020.
ISNAD Özdemir, Muhamet Emin - Ekinci, Alper. “On (α,β)-Convex Functions”. Eastern Anatolian Journal of Science 6/2 (December 2020), 9-14.
JAMA Özdemir ME, Ekinci A. On (α,β)-Convex Functions. Eastern Anatolian Journal of Science. 2020;6:9–14.
MLA Özdemir, Muhamet Emin and Alper Ekinci. “On (α,β)-Convex Functions”. Eastern Anatolian Journal of Science, vol. 6, no. 2, 2020, pp. 9-14.
Vancouver Özdemir ME, Ekinci A. On (α,β)-Convex Functions. Eastern Anatolian Journal of Science. 2020;6(2):9-14.