본문 바로가기
KERD
논문KCI 등재

Note on Newton-type inequalities involving tempered fractional integrals

0

조회

0

다운로드

0

인용

0

참고문헌

키워드

주제분류수학

초록

We propose a new method of investigation of an integral equality associated with tempered fractional integrals. In addition to this, several Newton-type inequalities are considered for differentiable convex functions by taking the modulus of the newly established identity. Moreover, we establish some Newton-type inequalities with the help of H\"{o}lder and power-mean inequality. Furthermore, several new results are presented by using special choices of obtained inequalities.

Abstract

We propose a new method of investigation of an integral equality associated with tempered fractional integrals. In addition to this, several Newton-type inequalities are considered for differentiable convex functions by taking the modulus of the newly established identity. Moreover, we establish some Newton-type inequalities with the help of H\"{o}lder and power-mean inequality. Furthermore, several new results are presented by using special choices of obtained inequalities.

참고문헌 (25)

  1. Ali, M.A, "A new extension of quantum Simpson's and quantum Newton's type inequalities for quantum dierentiable convex functions", Math. Methods Appl. Sci, 45(4), pp.1845~1863 (2022)[DOI]
  2. Buschman, R.G., "Decomposition of an integral operator by use of Mikusinski calculus", SIAM J. Math. Anal, 3, pp.83~85 (1972)[DOI]
  3. Erden, S.;, "Some Newton's like inequalities with applica-tions", Rev. R. Acad. Cienc. Exactas Fꠕs. Nat. Ser. A Mat. RACSAM, 114(4), pp.195~ (2020)[DOI]
  4. Erden, S, "On error estimations of Simpson's second type quadrature formula", Math. Methods Appl. Sci, 2020, pp.1~13 (2020)[DOI]
  5. Hezenci, F, "A new version of Newton's inequalities for Riemann-Liouville fractional integrals", Rocky Mountain J. Math, 53(1), pp.49~64 (2023)[DOI]
  6. Gao, S, "On new inequalities of Newton's type for functions whose second derivatives absolute values are convex", Int. J. Pure Appl. Math, 74(1), pp.33~41 (2012)
  7. Goren o R, "Fractional calculus: Integral and dierential equations of fractional order" (1997), Springer Verlag
  8. Iftikhar, S, "Simpson's second-type inequalities for coordinated convex functions and applications for cubature formulas", Fractal Fract, 6(1), pp.33~ (2022)[DOI]
  9. Iftikhar, S, "Local fractional Newton's inequalities involving generalized harmonic convex functions", Dierence Equ, 2020(1), pp.185~ (2020)[DOI]
  10. Iftikhar, S, "Newton's-type integral inequalities via local fractional inte-grals", Fractals, 28(3), pp.2050037~ (2020)[DOI]
  11. Kilbas, A.A, "Theory and Applications of Fractional Dierential Equations" (2006), Elsevier Sci. B.V
  12. Li, C, "Well-posedness and numerical algorithm for the tempered fractional ordinary dierential equations", Discrete Contin. Dyn. Syst. Ser. B, 24, pp.1989~2015 (2019)[DOI]
  13. Luangboon, W., "Simpson-and Newton-type inequal-ities for convex functions via (p; q)-calculus", Mathematics, 9(12), pp.1338~ (2021)[DOI]
  14. Meerschaert, M.M, "Tempered fractional calculus", J. Comput. Phys, 293, pp.14~28 (2015)[DOI]
  15. Meerschaert, M.M, "Stochastic Models for Fractional Calculus" (2012), Walter de Gruyter and Co
  16. Mohammed, P.O, "On the generalized Hermite-Hadamard inequal-ities via the tempered fractional integrals", Symmetry, 12(4), pp.595~ (2020)[DOI]
  17. Noor, M.A, "Some Newton's type inequalities for geometrically relative convex functions", Malays. J. Math. Sci, 9(3), pp.491~502 (2015)
  18. Noor, M. A, "Some Newton's type inequalities for harmonic convex functions", J. Adv. Math. Stud, 9(1), pp.07~16 (2016)
  19. Noor,M.A, "Newton inequalities for p-harmonic convex functions", Honam Math. J, 40(2), pp.239~250 (2018)[DOI]
  20. Pecaric J.E, "Convex Functions, Partial Orderings and Statistical Ap-plications" (1992), Academic Press
  21. Samko, S, "Fractional Integrals and Derivatives: Theory and Applica-tions" (1993), Gordon and Breach
  22. Sarikaya, M.Z, "Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities", Math. Comput. Model, 57, pp.2403~2407 (2013)[DOI]
  23. Sarikaya, M.Z, "On Hermite-Hadamard type inequalities for Riemann-Liouville fractional integrals", Miskolc Math. Notes, 17, pp.1049~1059 (2017)[DOI]
  24. Sitthiwirattham, T, "Riemann-Liouville fractional New-ton's type inequalities for dierentiable convex functions", Fractal Fract, 6(3), pp.175~ (2022)[DOI]
  25. Srivastava, H.M, "Convolution Integral Equations with Special Function Ker-nels" (1977), John Wiley & Sons

관련 논문AI추천

이 간행물의 다른 논문 (10건)