본문 바로가기
KERD
논문KCI 등재

Riemann-Liouville fractional versions of Hadamard inequality for strongly $(\alpha,m)$-convex functions

Laxmi Rathour|Lakshmi Narayan Mishra|Ghulam Farid|Saira Bano Akbar
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2021.12|한국수학논문집 (Korean Journal of Mathematics)|제29권 제4호|pp. 687-704

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

Hadamard inequalityConvex functionm)$-convex functionStrongly $({alpha}Riemann-Liouville fractional integrals
주제분류수학

초록

The refinement of an inequality provides better convergence of one quantity towards the other one. We have established the refinements of Hadamard inequalities for Riemann-Liouville fractional integrals via strongly $({\alpha},m)$-convex functions. In particular, we obtain two refinements of the classical Hadamard inequality. By using some known integral identities we also give refinements of error bounds of some fractional Hadamard inequalities.

Abstract

The refinement of an inequality provides better convergence of one quantity towards the other one. We have established the refinements of Hadamard inequalities for Riemann-Liouville fractional integrals via strongly $({\alpha},m)$-convex functions. In particular, we obtain two refinements of the classical Hadamard inequality. By using some known integral identities we also give refinements of error bounds of some fractional Hadamard inequalities.

참고문헌 (29)

  1. S. S. Dragomir, "Two inequalities for di erentiable mappings and applications to special means of real numbers and to trapezoidal formula", Appl. Math. Lett, 11(5), pp.91~95 (1998)
  2. Selected topics on Hermite-Hadamard inequalities and appli-cations, RGMIA Monographs, "S. S. Dragomir", Victoria University, ~ (2000)
  3. G. Farid, "On Hadamard type inequalities for m-convex functions via fractional integrals", J. Inequal. Spec. Funct, 7(4), pp.150~167 (2016)
  4. G. Farid, "On Hadamard-type inequalities for m-convex functions via Riemann-Liouville fractional integrals", Studia Univ. Babes-Bolyai, Math, 62(2), pp.141~150 (2017)
  5. Y. Dong, "Study of fractional integral operators containing Mittag-Le er functions via strongly(;m)-convex functions", Math. Prob. Eng, 2021, pp.13~ (2021)
  6. G. Farid, "Hadamard and Fej er-Hadamard type integral inequal-ities for harmonically convex functions via an extended generalized Mittag-Le er function", J. Math. Comput. Sci, 8(5), pp.630~643 (2018)
  7. _I. _ I scan, "Hermite-Hadamard-Fej er type inequalities for convex functions via fractional integrals", Stud. Univ. Babe s-Bolyai Math, 60(3), pp.355~366 (2015)
  8. Y.C.Kwun, "Rieman-Liouville fractional version of Hadamard inequality for strongly m-convex functions", ~
  9. S. M. Kang, "(h;m)-convex functions and associated frac-tional Hadamard and Fej er-Hadamard inequalities via an extended generalized Mittag-Le er function", J. Inequal. Appl, 2019, pp.78~ (2019)
  10. A. A. Kilbas, "Theory and applications of fractional di erential equa-tions, North-Holland Mathematics Studies", pp.10~204 (2006), Elsevier
  11. U. S. Kirmaci, "Inequalities for di erentiable mappings and applications to special means of real numbers to midpoint formula", Appl. Math. Comput, 147(5), pp.137~146 (2004)
  12. T. Lara, "On strongly m-convex functions", Mathematica Aeterna, 5(3), pp.521~535 (2015)
  13. S.Mehmood, "Fractional Hadamard and Fej er-Hadamard inequalities for exponen-tially m-convex function", Stud. Univ. Babe s-Bolyai Math., to appear., ~
  14. S. Mehmood, "New Hadamard and Fej er-Hadamard fractional inequalities for exponentially m-convex function", Eng. Appl. Sci. Lett, 3(1), pp.45~55 (2020)
  15. S. Mehmood, "New fractional Hadamard and Fej er-Hadamard inequalities associated with exponentially(h 􀀀 m)-convex function", Eng. Appl. Sci. Lett, 3(2), pp.9~18 (2020)
  16. E.Mittal, "Fractional integral and integral transform for-mulae using generalized Appell hypergeometric function", Nonlinear Science Letters A, 8(2), pp.221~227 (2017)
  17. V. N. Mishra, "Marichev-Saigo-Maeda Fractional Calculus Opera-tors, Srivastava Polynomials and Generalized Mittag-Le er Function", Cogent Math, 4, pp.1~11 (2017)
  18. V.G.Mihesan, "A generalization of the convexity", Seminar on Functional Equations, Approx. and Convex (1993)
  19. J. Mako, "On strongly convex functions", Carpathian J. Math, 32(1), pp.87~95 (2016)
  20. A. F. Nikiforov, "Special Functions of Mathematical Physics", Springer Basel AG (1988)
  21. K. Nikodem, "Characterizations of inner product spaces by strongly convex functions", Banach J. Math. Anal, 5(1), pp.83~87 (2011)
  22. C.P.Niculescu, "Old and new on the Hermite-Hadamard inequality", Real Anal. Exch, 29(2), pp.663~685 (2004)
  23. B. T. Polyak, "Existence theorems and convergence of minimizing sequences in extremum problems with restrictions", Soviet Mathematics Doklady, 7, pp.72~75 (1966)
  24. A. W. Roberts, "Convex Functions" (1973), Academic Press
  25. Z. Retkes, "An extension of the Hermite-Hadamard Inequality", Acta Sci. Math.(Szeged),, 74(1), pp.95~106 (2008)
  26. M. Z. Sarikaya, "Hermite-Hadamard's inequalities for fractional in-tegrals and related fractional inequalities", Math. comput. model, 57(9), pp.2403~2407 (2013)
  27. M. Z. Sarikaya, "On Hermite-Hadamard type inequalities for Riemann-Liouville fractional integrals", Miskolc Math. Notes, 17(2), pp.1049~1059 (2017)
  28. G.Toader, "Some generalizations of the convexity", Proceedings of the Colloquium on Approxima-tion and Optimization, Univ. Cluj-Napoca, pp.329~338 (1985)
  29. J.P.Vial, "Strong convexity of sets and functions", J. Math. Econ, 9(1-2), pp.187~205 (1982)

관련 논문AI추천

Fractional versions of Hadamard inequalities for strongly $(s,m)$-convex functions via Caputo fractional derivativesGhulam Farid, Lakshmi Narayan Mishra, Laxmi Rathour, Sidra Bibi, Vishnu Narayan Mishra강원경기수학회 · 한국수학논문집2023 · 제31권 제1호$k-$fractional integral inequalities for $(h-m)-$convex functions via Caputo $k-$fractional derivativesAtiq Ur Rehman, Ghulam Farid, Lakshmi Narayan Mishra, Qurat Ul Ain강원경기수학회 · 한국수학논문집2019 · 제27권 제2호FRACTIONAL HERMITE-HADAMARD TYPE INEQUALITIES FOR n-TIMES r-CONVEX FUNCTIONSBADREDDINE MEFTAH, MERIEM MERAD, NAWEL OUANAS장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2018 · 제21권 제2호On some new fractional Hermite-Hadamard type inequalities for convex and co-ordinated convex functionsHuseyin Budak, Muhammad Aamir Ali, Sadia Sakhi강원경기수학회 · 한국수학논문집2020 · 제28권 제4호Generalized Fractional Hermite Hadamard Type Inequalities for (s, m)-Convex Functions in the 1st and 2nd KindsAsif R. Khan, Muhammad Bilal한국수학교육학회 · 이론수학과 교직수학2025 · 제32권 제4호Fractional integral inequalities of Hermite-Hadamard type for m-HH convex functions with applicationsHui Zhou, Imdat Iscan, Wen Wang장전수학회 · Advanced Studies in Contemporary Mathematics2016 · 제26권 제3호

이 간행물의 다른 논문 (15건)

Organic relationship between laws based on judicial precedents using topological data analysis김성훈, 정재헌pp. 649-664New Banach spaces defined by the domain of Riesz-Fibonacci matrixPinar Zengin Alp, Emrah Evren Karapp. 665-677A new algorithm for variational inclusion problemSalahuddin, Aadil Hussain Dar, Md. Kalimuddin Ahmadpp. 679-685η-RICCI SOLITONS ON PARA-KENMOTSU MANIFOLDS WITH SOME CURVATURE CONDITIONSAshis Mondalpp. 705-714Some remarks on the growth of composite $p$-adic entire functionTanmay Biswas, Chinmay Biswaspp. 715-723
원문 보기