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Year 2022, Volume: 10 Issue: 2, 341 - 354, 31.10.2022

Abstract

References

  • [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] 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] W.W. Breckner, Stetigkeitsaussagen fr eine Klasse verallgemeinerter konvexer funktionen in topologischen linearen Raumen, Pupl. Inst. Math., 23 (1978), 1320.
  • [4] P.S. Bullen, Error estimates for some elementary quadrature rules, Publikacije Elektrotehnickog fakulteta. Serija Matematika i fizika (602/633) (1978), 97–103.
  • [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] 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] 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] 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.
  • [9] S. Erden, M.Z. Sarikaya, Generalized Bullen-type inequalities for local fractional integrals and its applications, Palest. J. Math., 9(2) (2020), 945–956.
  • [10] F. Ertugral, M.Z. Sarikaya, Simpson type integral inequalities for generalized fractional integral Revista de la Real Academia de Ciencias Exactas, F´ısicas y Naturales. Serie A. Matematicas 113(4), 3115–3124 (2019).
  • [11] L. Fejer, Uber die fourierreihen, ii, Math. Naturwise. Anz Ungar. Akad., Wiss, 24 (1906), 369–390.
  • [12] J. Hadamard, ´ Etude sur les propri´et´es des fonctions enti´eres en particulier d’une fonction consid´er´e´e par Riemann, J. Math. Pures Appl., 58 (1893), 171–215.
  • [13] F. Hezenci,H. Budak, H. Kara,: New version of Fractional Simpson type inequalities for twice differentiable functions, Adv. Differ. Equ. 2021(460), 1–10 (2021).
  • [14] H. Hudzik, L. Maligranda, Some remarks on s-convex functions, Aequationes Math. 48 (1994), 100-111.
  • [15] D.A. Ion, Some estimates on the Hermite-Hadamard inequality through quasi-convex functions, Annals of University of Craiova, Math. Comp. Sci. Ser., 34 (2007), 82-87.
  • [16] I. Iscan, Hermite-Hadamard and Simpson-like type inequalities for differentiable harmonically convex functions, J. Math. (2014)Article ID 346305, 10 pages.
  • [17] M.Z. Sarikaya, On the some generalization of inequalities associated with Bullen, Simpson, Midpoint and Trapezoid type, ResearchGate, https://www.researchgate.net/publication/358884784.
  • [18] M.Z. Sarikaya, H. Budak, Some integral inequalities for local fractional integrals, Int. J. Anal. Appl., 14(1) (2017), 9–19.
  • [19] E. Set, New inequalities of Ostrowski type for mappings whose derivatives are s-convex in the second sense via fractional integrals, Computers & Mathematics with Applications, 63(7) (2012), 1147-1154.
  • [20] E. Set, A.O. Akdemir, M.E. ¨ Ozdemir, Simpson type integral inequalities for convex functions via Riemann-Liouville integrals, Filomat, 31(14) (2017), 4415-4420.

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

Year 2022, Volume: 10 Issue: 2, 341 - 354, 31.10.2022

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.

References

  • [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] 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] W.W. Breckner, Stetigkeitsaussagen fr eine Klasse verallgemeinerter konvexer funktionen in topologischen linearen Raumen, Pupl. Inst. Math., 23 (1978), 1320.
  • [4] P.S. Bullen, Error estimates for some elementary quadrature rules, Publikacije Elektrotehnickog fakulteta. Serija Matematika i fizika (602/633) (1978), 97–103.
  • [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] 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] 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] 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.
  • [9] S. Erden, M.Z. Sarikaya, Generalized Bullen-type inequalities for local fractional integrals and its applications, Palest. J. Math., 9(2) (2020), 945–956.
  • [10] F. Ertugral, M.Z. Sarikaya, Simpson type integral inequalities for generalized fractional integral Revista de la Real Academia de Ciencias Exactas, F´ısicas y Naturales. Serie A. Matematicas 113(4), 3115–3124 (2019).
  • [11] L. Fejer, Uber die fourierreihen, ii, Math. Naturwise. Anz Ungar. Akad., Wiss, 24 (1906), 369–390.
  • [12] J. Hadamard, ´ Etude sur les propri´et´es des fonctions enti´eres en particulier d’une fonction consid´er´e´e par Riemann, J. Math. Pures Appl., 58 (1893), 171–215.
  • [13] F. Hezenci,H. Budak, H. Kara,: New version of Fractional Simpson type inequalities for twice differentiable functions, Adv. Differ. Equ. 2021(460), 1–10 (2021).
  • [14] H. Hudzik, L. Maligranda, Some remarks on s-convex functions, Aequationes Math. 48 (1994), 100-111.
  • [15] D.A. Ion, Some estimates on the Hermite-Hadamard inequality through quasi-convex functions, Annals of University of Craiova, Math. Comp. Sci. Ser., 34 (2007), 82-87.
  • [16] I. Iscan, Hermite-Hadamard and Simpson-like type inequalities for differentiable harmonically convex functions, J. Math. (2014)Article ID 346305, 10 pages.
  • [17] M.Z. Sarikaya, On the some generalization of inequalities associated with Bullen, Simpson, Midpoint and Trapezoid type, ResearchGate, https://www.researchgate.net/publication/358884784.
  • [18] M.Z. Sarikaya, H. Budak, Some integral inequalities for local fractional integrals, Int. J. Anal. Appl., 14(1) (2017), 9–19.
  • [19] E. Set, New inequalities of Ostrowski type for mappings whose derivatives are s-convex in the second sense via fractional integrals, Computers & Mathematics with Applications, 63(7) (2012), 1147-1154.
  • [20] E. Set, A.O. Akdemir, M.E. ¨ Ozdemir, Simpson type integral inequalities for convex functions via Riemann-Liouville integrals, Filomat, 31(14) (2017), 4415-4420.
There are 20 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Mehmet Zeki Sarıkaya

Barış Çelik 0000-0001-5372-7543

Erhan Set

Hanife Azaklı

Publication Date October 31, 2022
Submission Date August 2, 2022
Acceptance Date September 16, 2022
Published in Issue Year 2022 Volume: 10 Issue: 2

Cite

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.
AMA Sarıkaya MZ, Çelik B, Set E, Azaklı H. Generalizations of Different Type Inequalities for $s$-Convex, Quasi-Convex and $P$-Function. Konuralp J. Math. October 2022;10(2):341-354.
Chicago Sarıkaya, Mehmet Zeki, Barış Çelik, Erhan Set, and Hanife Azaklı. “Generalizations of Different Type Inequalities for $s$-Convex, Quasi-Convex and $P$-Function”. Konuralp Journal of Mathematics 10, no. 2 (October 2022): 341-54.
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 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, 2022.
ISNAD Sarıkaya, Mehmet Zeki et al. “Generalizations of Different Type Inequalities for $s$-Convex, Quasi-Convex and $P$-Function”. Konuralp Journal of Mathematics 10/2 (October 2022), 341-354.
JAMA 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, 2022, pp. 341-54.
Vancouver 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):341-54.
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