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Refinement of Hermite Hadamard Type Inequalities for Convex Functions with Applications

Muhammad Bilal|Asif R. Khan
한국수학교육학회|2024.02|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제31권 제1호|pp. 33-48|DOI 10.7468/jksmeb.2024.31.1.33

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키워드

convex functionsHermite Hadamard type inequalitiesHölder-İşcan integral inequalityimproved power mean integral inequality.
주제분류수학

초록

In this study, we would like to state two refined results related to Hermite Hadamard type inequality for convex functions with two distinct techniques. Hence our obtained results would be better than the results already established for the class of convex functions. Applications to trapezoidal rule and special means are also discussed.

Abstract

In this study, we would like to state two refined results related to Hermite Hadamard type inequality for convex functions with two distinct techniques. Hence our obtained results would be better than the results already established for the class of convex functions. Applications to trapezoidal rule and special means are also discussed.

참고문헌 (15)

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  3. M. I. Bhatti, "Hadamard-type inequalities for s-convex functions I", Punjab. Univ. J. Math, 41, pp.51~60 (2009)
  4. M. Bilal, "New Generalized Hermite Hadamard Inequalities for p-convex functions in the mixed kind", EJPAM, 14(3), pp.863~880 (2021)[DOI]
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  6. M. Bilal, "New Hermite Hadamard Dual Inequality for s-p-convex func-tions in mixed kind", ~
  7. M. Bilal, "New version of generalized Ostrowski-GrÄuss type inequality", Stud. Univ. Babe»s-Bolyai Math, 66(3), pp.441~455 (2021)[DOI]
  8. Ch. Hermite, "Sur deux limites d'une int'egrale definie", Mathesis, 3, pp.82~ (1883)
  9. I. I scan, "New refinements for integral and sum forms of H'older inequality", J. Ineq. &Appl, 2019, pp.304~ (2019)[DOI]
  10. "On improvements of some integral inequalities"[URL]
  11. A. R. Khan, "Hermite Hadamard type fractional inequali-ties for s-convex functions of mixed kind", TMCS, 1, pp.25~37 (2021)
  12. D. S. Mitrinovic, "Classical and new inequalities in analysis" (1993), Kluwer Academic Publishers
  13. M. E. ÄOzdemir, "Hermite Hadamard-type inequalities via (α, m) convexity", Comp. Math. App, 61, pp.2614~2620 (2011)[DOI]
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  15. J. Pe·caric, "Convex functions, Partial Orderings and Statis-tical Applications" (1992), Academic Press

관련 논문AI추천

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