Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지
DOI QR코드

DOI QR Code

RIGHT-RADAU-TYPE INEQUALITIES FOR MULTIPLICATIVE DIFFERENTIABLE s-CONVEX FUNCTIONS

  • A. BERKANE (Higher School of Management Sciences) ;
  • B. MEFTAH (Department of Mathematics, University 8 may 1945 Guelma) ;
  • A. LAKHDARI (Laboratory of Energy Systems Technology, Department CPST, National Higher School of Technology and Engineering)
  • Received : 2023.08.31
  • Accepted : 2024.03.07
  • Published : 2024.07.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this study, a new identity is introduced for multiplicative differentiable functions, forming the foundation for a range of 2-point right-Radau-type inequalities applicable to multiplicative s-convex functions. These established results are then showcased through applications that underscore their relevance within the domain of special means.

Keywords

Acknowledgement

The work of the third author was supported by DGRSDT, MESRS of Algeria (PRFU Project A14N01EP230220230001)

References

  1. M.A. Ali, M. Abbas, Z. Zhang, I.B. Sial and R. Arif, On integral inequalities for product and quotient of two multiplicatively convex functions, Asian Res. J. Math. 12 (2019), 1-11. https://doi.org/10.9734/arjom/2019/v12i330084
  2. M.A. Ali, M. Abbas and A.A. Zafer, On some Hermite-Hadamard integral inequalities in multiplicative calculus, J. Ineq. Special Func. 10 (2019), 111-122.
  3. M.A. Ali, Z. Zhang, H. Budak and M.Z. Sarikaya, On Hermite-Hadamard type inequalities for interval-valued multiplicative integrals, Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat. 69 (2020), 1428-1448.
  4. M.A. Ali, H. Budak, M.Z. Sarikaya and Z. Zhang, Ostrowski and Simpson type inequalities for multiplicative integrals, Proyecciones 40 (2021), 743-763. https://doi.org/10.22199/issn.0717-6279-4136
  5. M. B. Almatrafi, W. Saleh, A. Lakhdari, F. Jarad and B. Meftah, On the multiparameterized fractional multiplicative integral inequalities, J. Inequal. Appl. (2024), pp 27.
  6. A.E. Bashirov, E.M. Kurpinar and A. Ozyapici, Multiplicative calculus and its applications. J. Math. Anal. Appl. 337 (2008), 36-48. https://doi.org/10.1016/j.jmaa.2007.03.081
  7. A.E. Bashirov, E. Misirli, Y. Tando'ggdu, On modeling with multiplicative differential equations, Appl. Math. J. Chin. Univ. 26 (2011), 425-438. https://doi.org/10.1007/s11766-011-2767-6
  8. D.C. Benchettah, A. Lakhdari and B. Meftah. Refinement of the general form of the twopoint quadrature formulas via convexity, Journal of Applied Mathematics, Statistics and Informatics 19 (2023), 93-101.
  9. A. Berhail and B. Meftah, Refinement of midpoint and trapezoid type inequalities for multiplicatively convex functions, Sahand Commun. Math. Anal. 21 (2022), 267-278.
  10. H. Boulares, B. Meftah, A. Moumen, R. Shafqat, H. Saber, T. Alraqad and E. Ahmad, Fractional multiplicative Bullen type inequalities for multiplicative differentiable functions, Symmetry 15 (2023), p. 451.
  11. H. Budak and K. Ozcelik, On Hermite-Hadamard type inequalities for multiplicative fractional integrals, Miskolc Math. Notes 21 (2020), 91-99. https://doi.org/10.18514/MMN.2020.3129
  12. S. Chasreechai, M.A. Ali, S. Naowarat, T. Sitthiwirattham and K. Nonlaopon, On some Simpson's and Newton's type of inequalities in multiplicative calculus with applications, AIMS Math. 8 (2023), 3885-3896.
  13. T. Chiheb, N. Boumaza and B. Meftah, Some new Simpson-like type inequalities via preqausiinvexity, Transylv. J. Math. Mech. 12 (2020), 1-10.
  14. S.S. Dragomir, J.E. Pecaric and J. Sandor, A note on the Jensen-Hadamard inequality, Anal. Numer. Theor. Approx. 19 (1990), 29-34.
  15. T. Du, Y. Li and Z. Yang, A generalization of Simpson's inequality via differentiable mapping using extended (s,m)-convex functions, Appl. Math. Comput. 293 (2017), 358-369.
  16. T.S. Du, C.Y. Luo, Z.J. Cao, On the Bullen-type inequalities via generalized fractional integrals and their applications, Fractals 29 (2021), Article ID 2150188, 20 pages.
  17. T.S. Du, T.C. Zhou, On the fractional double integral inclusion relations having exponential kernels via interval-valued co-ordinated convex mappings, Chaos, Solitons & Fractals 156 (2022), Article ID 111846, 19 pages.
  18. L. Florack, H.V. Assen, Multiplicative calculus in biomedical image analysis, J. Math. Imaging Vis. 42 (2012), 64-75. https://doi.org/10.1007/s10851-011-0275-1
  19. A. Frioui, B. Meftah, A. Shokri, A. Lakhdari and H. Mukalazi, Parametrized multiplicative integral inequalities, Adv. Contin. Discrete Models (2024), pp. 18.
  20. H. Fu, Y. Peng and T. Du, Some inequalities for multiplicative tempered fractional integrals involving the λ-incomplete gamma functions, AIMS Math. 6 (2021), 7456-7478. https://doi.org/10.3934/math.2021436
  21. M. Grossman and R. Katz, Non-Newtonian calculus, Lee Press, Pigeon Cove, Mass., 1972.
  22. S. Khan and H. Budak, On midpoint and trapezoid type inequalities for multiplicative integrals, Mathematica 64 (2022), 95-108. https://doi.org/10.24193/mathcluj.2022.1.11
  23. A. Lakhdari and B. Meftah, Some fractional weighted trapezoid type inequalities for preinvex functions, Int. J. Nonlinear Anal. Appl. 13 (2022), 3567-3587.
  24. B. Meftah, Ostrowski's inequality for functions whose first derivatives are s-preinvex in the second sense, Khayyam J. Math. 3 (2017), 61-80.
  25. B. Meftah, Fractional Hermite-Hadamard type integral inequalities for functions whose modulus of derivatives are co-ordinated log-preinvex, Punjab Univ. J. Math. (Lahore) 51 (2019), 21-37.
  26. B. Meftah, Maclaurin type inequalities for multiplicatively convex functions, Proc. Amer. Math. Soc. 151 (2023), 2115-2125.
  27. B. Meftah and A. Lakhdari, Dual Simpson type inequalities for multiplicatively convex functions, Filomat 37 (2023), 7673-7683.
  28. B. Meftah, A. Lakhdari and W. Saleh, 2-point left Radau-type inequalities via s-convexity, Journal of Applied Analysis 29 (2023), 341-346.
  29. B. Meftah, H. Boulares, A. Khan and T. Abdeljawad. Fractional multiplicative Ostrowskitype inequalities for multiplicative differentiable convex functions, Jordan J. Math. Stat. To appear.
  30. B. Meftah, A. Lakhdari, W. Saleh and D.C. Benchettah, Companion of Ostrowski inequality for multiplicatively convex functions, Sahand Commun. Math. Anal. 21 (2024), 289-304.
  31. A. Moumen, H. Boulares, B. Meftah, R. Shafqat, T. Alraqad, E.E. Ali and Z. Khaled, Multiplicatively Simpson Type Inequalities via Fractional Integral, Symmetry 15 (2023), p. 460.
  32. S. Ozcan, Hermite-Hadamard type inequalities for multiplicatively s-convex functions, Cumhuriyet Sci. J. 41 (2020), 245-259. https://doi.org/10.17776/csj.663559
  33. J.E. Pecaric, F. Proschan and Y.L. Tong, Convex functions, partial orderings, and statistical applications, Mathematics in Science and Engineering, 187. Academic Press, Inc., Boston, MA, 1992.
  34. Y. Peng, H. Fu and T.S. Du, Estimations of bounds on the multiplicative fractional integral inequalities having exponential kernels, Commun. Math. Stat., 12 (2022), 187-211. https://doi.org/10.1007/s40304-022-00285-8
  35. Y. Peng and T.S. Du, Fractional Maclaurin-type inequalities for multiplicatively convex functions and multiplicatively P-functions, Filomat 37 (2023), 9497-9509. https://doi.org/10.2298/FIL2328497P
  36. W. Saleh, S. Meftah and A. Lakhdari, Quantum dual Simpson type inequalities for qdifferentiable convex functions, Int. J. Nonlinear Anal. Appl. 14 (2023), 63-76.
  37. E. Set, M. Emin Ozdemir and S.S. Dragomir, On Hadamard-type inequalities involving several kinds of convexity, J. Inequal. Appl. (2010), Art. ID 286845, P. 12.
  38. G. Singh, S. Bhalla, Two step Newton's method with multiplicative calculus to solve the non-linear equations, J. Comput. Anal. Appl. 31 (2023), 171-179.
  39. B.-Y. Xi and F. Qi, Some integral inequalities of Hermite-Hadamard type for slogarithmically convex functions, Acta Mathematica Scientis, English Series 35 (2015), 515-526.
  40. W.S. Zhu, B. Meftah, H. Xu, F. Jarad and A. Lakhdari, On parameterized inequalities for fractional multiplicative integrals, Demonstr. Math. 57 (2024), pp. 17.