Research Article
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Year 2026, Volume: 55 Issue: 2 , 512 - 524 , 29.04.2026
https://doi.org/10.15672/hujms.1464002
https://izlik.org/JA67XY37XT

Abstract

References

  • [1] S. Butt, H. Inam and M. Dokuyucu, New fractal Simpson estimates for twice local differentiable generalized convex mappings, Applied and Computational Mathematics, 23(4), 2024.
  • [2] B. Celik, A. Akdemir, E. Set and S. Aslan, Ostrowski-Mercer type integral inequalities for differentiable convex functions via Atangana-Baleanu fractional integral operators, TWMS Journal of Pure and Applied Mathematics, 15(2), v269–85, 2024.
  • [3] S.S. Dragomir, Inequalities of Hermite-Hadamard type for h-convex functions on linear spaces, Proyecciones (Antofagasta), 34(4), 323–341, 2015.
  • [4] S.S. Dragomir and S. Fitzpatrick, The Hadamard inequalities for s-convex functions in the second sense, Demonstratio Mathematica, 32(4), 687–696, 1999.
  • [5] A.E. Farissi, Simple proof and refinement of Hermite-Hamard inequality, Journal of Mathematical Inequalities, 4(3), 365–369, 2010.
  • [6] L. Fejér, Uber die fourierreihen, II, Math. Naturwiss Anz Ungar Akad Wiss, 24, 369–390, 1906.
  • [7] M. Kadakal, I. Iscan and H. Kadakal. Construction of a new generalization for npolynomial convexity with their certain inequalities, Hacettepe Journal of Mathematics and Statistics, 53(6), 1529–1541, 2024.
  • [8] M. Kunt and I. Iscan, Hermite-Hadamard-Fejér type inequalities for p-convex functions, Arab Journal of Mathematical Sciences, 23(2), 215–230, 2017.
  • [9] F.C. Mitroi, K. Nikodem and S. Wkasowicz, HermiteHadamard inequalities for convex set-valued functions, Demonstratio Mathematica, 46(4), 655–662, 2013.
  • [10] M.A. Noor, M.U. Awan, K.I. Noor and M. Postolache, Some Integral Inequalities for Convex Functions, Filomat, 30(9), 2435–2444, 2016.
  • [11] C. Park, Y.M. Chu, M. Shoaib Saleem, N. Jahangir and N. Rehman, On n-polynomial p-convex functions and some related inequalities, Advances in Difference Equations, 2020(1), 1–12, 2020.
  • [12] E. Set, Inequalities Involving Conformable Fractional Integrals for $\eta$-Convex Functions, Turkish Journal of Science, 8(3), 107–13, 2023.
  • [13] T. Toplu, M. Kadakal and I. Iscan, On n-polynomial convexity and some related inequalities, AIMS Math, 5(2), 1304–1318, 2020.
  • [14] A. Yalçn, E. Gül and A. Akdemir, Hermite-Hadamard type inequalities for Coordinated convex functions with variable-order fractional integrals, Applied and Computational Mathematics, 24(2), 326–43, 2025.
  • [15] E. Zeynep, S. Kemali, G. Tinaztepe and G. Adilov, The Hermite-Hadamard inequalities for p-convex functions, Hacettepe Journal of Mathematics and Statistics, 50(5), 1268–1279, 2021.
  • [16] K. Zhang and J. Wan, p-convex functions and their properties, Pure Appl. Math. 23(1), 130–133, 2007.

Hermite-Hadamard-Fejér type inequalities for generalized $n$-polynomial $p$-convex functions

Year 2026, Volume: 55 Issue: 2 , 512 - 524 , 29.04.2026
https://doi.org/10.15672/hujms.1464002
https://izlik.org/JA67XY37XT

Abstract

Recently, integral inequalities gained great attention for special kinds of functions of convex functions. Through an analysis of this work, we deal with Hermite Hadamard and Hermite Hadamard-F{\'e}jer type inequalities for a special kind of convex function, termed as a generalized $n$-polynomial $p$-convex function and some of the properties of such functions.

References

  • [1] S. Butt, H. Inam and M. Dokuyucu, New fractal Simpson estimates for twice local differentiable generalized convex mappings, Applied and Computational Mathematics, 23(4), 2024.
  • [2] B. Celik, A. Akdemir, E. Set and S. Aslan, Ostrowski-Mercer type integral inequalities for differentiable convex functions via Atangana-Baleanu fractional integral operators, TWMS Journal of Pure and Applied Mathematics, 15(2), v269–85, 2024.
  • [3] S.S. Dragomir, Inequalities of Hermite-Hadamard type for h-convex functions on linear spaces, Proyecciones (Antofagasta), 34(4), 323–341, 2015.
  • [4] S.S. Dragomir and S. Fitzpatrick, The Hadamard inequalities for s-convex functions in the second sense, Demonstratio Mathematica, 32(4), 687–696, 1999.
  • [5] A.E. Farissi, Simple proof and refinement of Hermite-Hamard inequality, Journal of Mathematical Inequalities, 4(3), 365–369, 2010.
  • [6] L. Fejér, Uber die fourierreihen, II, Math. Naturwiss Anz Ungar Akad Wiss, 24, 369–390, 1906.
  • [7] M. Kadakal, I. Iscan and H. Kadakal. Construction of a new generalization for npolynomial convexity with their certain inequalities, Hacettepe Journal of Mathematics and Statistics, 53(6), 1529–1541, 2024.
  • [8] M. Kunt and I. Iscan, Hermite-Hadamard-Fejér type inequalities for p-convex functions, Arab Journal of Mathematical Sciences, 23(2), 215–230, 2017.
  • [9] F.C. Mitroi, K. Nikodem and S. Wkasowicz, HermiteHadamard inequalities for convex set-valued functions, Demonstratio Mathematica, 46(4), 655–662, 2013.
  • [10] M.A. Noor, M.U. Awan, K.I. Noor and M. Postolache, Some Integral Inequalities for Convex Functions, Filomat, 30(9), 2435–2444, 2016.
  • [11] C. Park, Y.M. Chu, M. Shoaib Saleem, N. Jahangir and N. Rehman, On n-polynomial p-convex functions and some related inequalities, Advances in Difference Equations, 2020(1), 1–12, 2020.
  • [12] E. Set, Inequalities Involving Conformable Fractional Integrals for $\eta$-Convex Functions, Turkish Journal of Science, 8(3), 107–13, 2023.
  • [13] T. Toplu, M. Kadakal and I. Iscan, On n-polynomial convexity and some related inequalities, AIMS Math, 5(2), 1304–1318, 2020.
  • [14] A. Yalçn, E. Gül and A. Akdemir, Hermite-Hadamard type inequalities for Coordinated convex functions with variable-order fractional integrals, Applied and Computational Mathematics, 24(2), 326–43, 2025.
  • [15] E. Zeynep, S. Kemali, G. Tinaztepe and G. Adilov, The Hermite-Hadamard inequalities for p-convex functions, Hacettepe Journal of Mathematics and Statistics, 50(5), 1268–1279, 2021.
  • [16] K. Zhang and J. Wan, p-convex functions and their properties, Pure Appl. Math. 23(1), 130–133, 2007.
There are 16 citations in total.

Details

Primary Language English
Subjects Operator Algebras and Functional Analysis
Journal Section Research Article
Authors

Anjum Mustafa Khan Abbasi 0000-0002-6301-398X

Matloob Anwar 0000-0001-5649-9769

Submission Date April 4, 2024
Acceptance Date August 11, 2025
Early Pub Date October 6, 2025
Publication Date April 29, 2026
DOI https://doi.org/10.15672/hujms.1464002
IZ https://izlik.org/JA67XY37XT
Published in Issue Year 2026 Volume: 55 Issue: 2

Cite

APA Abbasi, A. M. K., & Anwar, M. (2026). Hermite-Hadamard-Fejér type inequalities for generalized $n$-polynomial $p$-convex functions. Hacettepe Journal of Mathematics and Statistics, 55(2), 512-524. https://doi.org/10.15672/hujms.1464002
AMA 1.Abbasi AMK, Anwar M. Hermite-Hadamard-Fejér type inequalities for generalized $n$-polynomial $p$-convex functions. Hacettepe Journal of Mathematics and Statistics. 2026;55(2):512-524. doi:10.15672/hujms.1464002
Chicago Abbasi, Anjum Mustafa Khan, and Matloob Anwar. 2026. “Hermite-Hadamard-Fejér Type Inequalities for Generalized $n$-Polynomial $p$-Convex Functions”. Hacettepe Journal of Mathematics and Statistics 55 (2): 512-24. https://doi.org/10.15672/hujms.1464002.
EndNote Abbasi AMK, Anwar M (April 1, 2026) Hermite-Hadamard-Fejér type inequalities for generalized $n$-polynomial $p$-convex functions. Hacettepe Journal of Mathematics and Statistics 55 2 512–524.
IEEE [1]A. M. K. Abbasi and M. Anwar, “Hermite-Hadamard-Fejér type inequalities for generalized $n$-polynomial $p$-convex functions”, Hacettepe Journal of Mathematics and Statistics, vol. 55, no. 2, pp. 512–524, Apr. 2026, doi: 10.15672/hujms.1464002.
ISNAD Abbasi, Anjum Mustafa Khan - Anwar, Matloob. “Hermite-Hadamard-Fejér Type Inequalities for Generalized $n$-Polynomial $p$-Convex Functions”. Hacettepe Journal of Mathematics and Statistics 55/2 (April 1, 2026): 512-524. https://doi.org/10.15672/hujms.1464002.
JAMA 1.Abbasi AMK, Anwar M. Hermite-Hadamard-Fejér type inequalities for generalized $n$-polynomial $p$-convex functions. Hacettepe Journal of Mathematics and Statistics. 2026;55:512–524.
MLA Abbasi, Anjum Mustafa Khan, and Matloob Anwar. “Hermite-Hadamard-Fejér Type Inequalities for Generalized $n$-Polynomial $p$-Convex Functions”. Hacettepe Journal of Mathematics and Statistics, vol. 55, no. 2, Apr. 2026, pp. 512-24, doi:10.15672/hujms.1464002.
Vancouver 1.Anjum Mustafa Khan Abbasi, Matloob Anwar. Hermite-Hadamard-Fejér type inequalities for generalized $n$-polynomial $p$-convex functions. Hacettepe Journal of Mathematics and Statistics. 2026 Apr. 1;55(2):512-24. doi:10.15672/hujms.1464002