[1] W. Afzal; M. Abbas; J.E. Macias-Dıaz; S. Treant, a. Some H-Godunova–Levin Function Inequalities Using Center Radius (Cr) Order Relation. Fractal Fract. 2022, 6, 518. https://doi.org/10.3390/fractalfract6090518
[2] W.Afzal.;A.A.Lupas;K.Shabbir.Hermite–Hadamard and Jensen-Type Inequalities for Harmonical (h1, h2)-Godunova–Levin Interval-Valued Functions. Mathematics 2022, 10, 2970.https://doi.org/10.3390/math10162970
[3] W.Afzal.,K. Shabbir, S.Treanta,K.Nonlaopon. Jensen and Hermite-Hadamard type inclusions for harmonical h-Godunova-Levin functions[J].Aims Mathematics, 2023, 8(2): 3303-3321.doi: 10.3934/math.2023170
[4] W.Afzal.,K.Shabbir,T.Botmart.Generalized version of Jensen and Hermite-Hadamard inequalities for interval-valued (h1,h2)-Godunova-Levin functions[J].AIMSMathematics, 2022,7(10): 19372-19387.doi: 10.3934/math.20221064
[5] W.Afzal,W.Nazeer,T.Botmart,S.Treanta. Some properties and inequalities for generalized class of harmonical Godunova-Levin function via center radius order relation[J]. AIMS Mathematics,2023,8(1): 1696-1712.doi: 10.3934/math.2023087
[6] H. Araki and F. Hansen, Jensen´s operator inequality for functions of several variables, Proc. Amer. Math. Soc. 128 (2000), No. 7, 20
[7] S.I Butt; M. Tariq; A. Aslam; H. Ahmad; T.A. Nofal. Hermite–Hadamard type inequalities via generalized harmonic exponential convexity and applications. J. Funct. Spaces 2021, 2021, 5533491.
[8] S.I Butt, I. Javed, P. Agarwal et al. Newton–Simpson-type inequalities via majorization. J Inequal Appl 2023, 16 (2023). https://doi.org/10.1186/s13660-023-02918-0
[9] A. Chandola , R. Agarwal , M. R. Pandey.Some New Hermite–Hadamard, Hermite–Hadamard Fejer and Weighted Hardy Type Inequalities Involving (k-p) Riemann Liouville Fractional Integral Operator, Appl. Math. Inf. Sci. 16, No. 2, 287–297 (2022).
[10] H. Chen, U.N. Katugampola. Hermite–Hadamard and Hermite–Hadamard–Fejer type inequalities for generalized fractional integrals. J. Math. Anal. Appl. 2017, 446, 1274–1291
[12] S.S. Dragomir, The Hermite-Hadamard type Inequalities for Operator Convex Functions, Applied Mathematics and Computation Volume 218, Issue 3, 1 October 2011, Pages 766-772
[13] S.S Dragomir, Tensorial Norm Inequalities For Taylor’s Expansions Of Functions Of Selfadjoint Operators In Hilbert Spaces , ResearchGate, November 2022.
[14] S.S Dragomir, An Ostrowski Type Tensorial Norm Inequality For Continuous Functions Of Selfadjoint Operators In Hilbert Spaces, Researchgate, November 2022.
[15] S.S. Dragomir, C.E.M. Pearce, Selected topics on Hermite-Hadamard inequalities and applications, in: RGMIA Monographs, Victoria University, 2000.
[16] S.S. Dragomir. A Trapezoid Type Tensorial Norm Inequality for Continuous Functions of Selfadjoint Operators in Hilbert Spaces. Istanbul Journal of Mathematics. 2023;1(2):48-56. https://doi.org/10.26650/ijmath.2023.00006
[17] S.S. Dragomir. Gradient Inequalities for an Integral Transform of Positive Operators in Hilbert Spaces, Annales Mathematicae Silesianae Volume 37 (2023): Issue 2 (September 2023), https://doi.org/10.2478/amsil-2023-0008
[18] H. Guo, What Are Tensors Exactly?, World Scientific, June 2021, https://doi.org/10.1142/12388
[19] F. Hezenci, H. Budak, H. Kara. New version of fractional Simpson type inequalities for twice differentiable functions. Adv. Differ. Equ. 2021, 460 (2021). https://doi.org/10.1186/s13662 021-03615-2
[20] A. Koranyi. On some classes of analytic functions of several variables. Trans. Amer. Math. Soc., 101 (1961), 520-554.
[21] D. S. Mitrinovi´c ,Analytic Inequalities, Springer-Verlag, Berlin, 1970.
[22] J., Nasir, S., Qaisar, S. I., Butt, A. K., Khan, R. S., Mabela, Some Simpson’s Riemann–Liouville Fractional Integral Inequalities with Applications to Special Functions, Journal of Function Spaces, 2022, 2113742, 12 pages, 2022. https://doi.org/10.1155/2022/2113742
[23] J. Peˇcari´c , F. Proschan , Y. Tong , Convex Functions, Partial Orderings, and Statistical Applications, Academic Press, INC, United States of America, 1992.
[24] T. Rasheed, S. I. Butt, G. Peˇcari´c, and ¯D. Peˇcari´ c, New bounds of Popoviciu’s difference via weighted Hadamard type inequalities with applications in information theory, Math. Meth. Appl. Sci. 47 (2024), 5750–5763, DOI 10.1002/mma.9889.
[25] T. Rasheed, S.I. Butt, ¯D. Peˇcari´c, J. Peˇcari´c, Generalized cyclic Jensen and information inequalities, Chaos, Solitons & Fractals, Volume 163, 2022, 112602, ISSN 0960-0779, https://doi.org/10.1016/j.chaos.2022.112602.
[26] M.Z. Sarikaya, E. Set, M.E. Ozdemir, On new inequalities of Simpson’s type for convex functions, RGMIA Res. Rep. Coll. 13 (2) (2010) Article2.
[27] M. Z. Sarıkaya and S. Bardak, “Generalized Simpson Type Integral Inequalities”, Konuralp J. Math., vol. 7, no. 1, pp. 186–191, 2019.
[28] V. Stojiljkovic, Simpson Type Tensorial Norm Inequalities for Continuous Functions of ´ Selfadjoint Operators in Hilbert Spaces, Creat. Math. Inform., 33 (2024), 105–117. https://doi.org/10.37193/CMI.2024.01.10
[29] V. Stojiljkovi´ c; R. Ramaswamy; O.A.A. Abdelnaby; S. Radenovi´c. Some Refine ments of the Tensorial Inequalities in Hilbert Spaces. Symmetry 2023, 15, 925. https://doi.org/10.3390/sym15040925
[30] V. Stojiljkovi´c.; Hermite–Hadamard–type fractional–integral inequalities for (p,h) convex fuzzy-interval-valued mappings, Electron. J. Math. 5 (2023) 18–28, DOI: 10.47443/ejm.2023.004
[31] V. Stojiljkovi´ c. (2023). ’Twice Differentiable Ostrowski Type Tensorial Norm Inequal ity for Continuous Functions of Selfadjoint Operators in Hilbert Spaces’ , Electronic Journal of Mathematical Analysis and Applications, 11(2), pp. 1-15. doi: 10.21608/ej maa.2023.199881.1014
[32] V. Stojiljkovi´c. Twice Differentiable Ostrowski Type Tensorial Norm Inequality for Contin uous Functions of Selfadjoint Operators in Hilbert Spaces. European Journal of Pure and Applied Mathematics, 16(3), (2023), 1421–1433.
[33] V. Stojiljkovi´ c., & S.S. Dragomir. (2023). Differentiable Ostrowski type tensorial norm in equality for continuous functions of selfadjoint operators in Hilbert spaces. Gulf Journal of Mathematics, 15(2), 40-55. https://doi.org/10.56947/gjom.v15i2.1247
[34] V. Stojiljkovi´c; N. Mirkov; S. Radenovi´c. Variations in the Tensorial Trapezoid Type Inequal ities for Convex Functions of Self-Adjoint Operators in Hilbert Spaces. Symmetry 2024, 16, 121. https://doi.org/10.3390/sym16010121
Generalized Tensorial Simpson type Inequalities for Convex functions of Selfadjoint Operators in Hilbert Space
Year 2024,
Volume: 6 Issue: 2, 78 - 89, 08.11.2024
Several generalized Simpson tensorial type inequalities for self adjoint operators have been obtained with variation depending on the conditions imposed on the function f.
[1] W. Afzal; M. Abbas; J.E. Macias-Dıaz; S. Treant, a. Some H-Godunova–Levin Function Inequalities Using Center Radius (Cr) Order Relation. Fractal Fract. 2022, 6, 518. https://doi.org/10.3390/fractalfract6090518
[2] W.Afzal.;A.A.Lupas;K.Shabbir.Hermite–Hadamard and Jensen-Type Inequalities for Harmonical (h1, h2)-Godunova–Levin Interval-Valued Functions. Mathematics 2022, 10, 2970.https://doi.org/10.3390/math10162970
[3] W.Afzal.,K. Shabbir, S.Treanta,K.Nonlaopon. Jensen and Hermite-Hadamard type inclusions for harmonical h-Godunova-Levin functions[J].Aims Mathematics, 2023, 8(2): 3303-3321.doi: 10.3934/math.2023170
[4] W.Afzal.,K.Shabbir,T.Botmart.Generalized version of Jensen and Hermite-Hadamard inequalities for interval-valued (h1,h2)-Godunova-Levin functions[J].AIMSMathematics, 2022,7(10): 19372-19387.doi: 10.3934/math.20221064
[5] W.Afzal,W.Nazeer,T.Botmart,S.Treanta. Some properties and inequalities for generalized class of harmonical Godunova-Levin function via center radius order relation[J]. AIMS Mathematics,2023,8(1): 1696-1712.doi: 10.3934/math.2023087
[6] H. Araki and F. Hansen, Jensen´s operator inequality for functions of several variables, Proc. Amer. Math. Soc. 128 (2000), No. 7, 20
[7] S.I Butt; M. Tariq; A. Aslam; H. Ahmad; T.A. Nofal. Hermite–Hadamard type inequalities via generalized harmonic exponential convexity and applications. J. Funct. Spaces 2021, 2021, 5533491.
[8] S.I Butt, I. Javed, P. Agarwal et al. Newton–Simpson-type inequalities via majorization. J Inequal Appl 2023, 16 (2023). https://doi.org/10.1186/s13660-023-02918-0
[9] A. Chandola , R. Agarwal , M. R. Pandey.Some New Hermite–Hadamard, Hermite–Hadamard Fejer and Weighted Hardy Type Inequalities Involving (k-p) Riemann Liouville Fractional Integral Operator, Appl. Math. Inf. Sci. 16, No. 2, 287–297 (2022).
[10] H. Chen, U.N. Katugampola. Hermite–Hadamard and Hermite–Hadamard–Fejer type inequalities for generalized fractional integrals. J. Math. Anal. Appl. 2017, 446, 1274–1291
[12] S.S. Dragomir, The Hermite-Hadamard type Inequalities for Operator Convex Functions, Applied Mathematics and Computation Volume 218, Issue 3, 1 October 2011, Pages 766-772
[13] S.S Dragomir, Tensorial Norm Inequalities For Taylor’s Expansions Of Functions Of Selfadjoint Operators In Hilbert Spaces , ResearchGate, November 2022.
[14] S.S Dragomir, An Ostrowski Type Tensorial Norm Inequality For Continuous Functions Of Selfadjoint Operators In Hilbert Spaces, Researchgate, November 2022.
[15] S.S. Dragomir, C.E.M. Pearce, Selected topics on Hermite-Hadamard inequalities and applications, in: RGMIA Monographs, Victoria University, 2000.
[16] S.S. Dragomir. A Trapezoid Type Tensorial Norm Inequality for Continuous Functions of Selfadjoint Operators in Hilbert Spaces. Istanbul Journal of Mathematics. 2023;1(2):48-56. https://doi.org/10.26650/ijmath.2023.00006
[17] S.S. Dragomir. Gradient Inequalities for an Integral Transform of Positive Operators in Hilbert Spaces, Annales Mathematicae Silesianae Volume 37 (2023): Issue 2 (September 2023), https://doi.org/10.2478/amsil-2023-0008
[18] H. Guo, What Are Tensors Exactly?, World Scientific, June 2021, https://doi.org/10.1142/12388
[19] F. Hezenci, H. Budak, H. Kara. New version of fractional Simpson type inequalities for twice differentiable functions. Adv. Differ. Equ. 2021, 460 (2021). https://doi.org/10.1186/s13662 021-03615-2
[20] A. Koranyi. On some classes of analytic functions of several variables. Trans. Amer. Math. Soc., 101 (1961), 520-554.
[21] D. S. Mitrinovi´c ,Analytic Inequalities, Springer-Verlag, Berlin, 1970.
[22] J., Nasir, S., Qaisar, S. I., Butt, A. K., Khan, R. S., Mabela, Some Simpson’s Riemann–Liouville Fractional Integral Inequalities with Applications to Special Functions, Journal of Function Spaces, 2022, 2113742, 12 pages, 2022. https://doi.org/10.1155/2022/2113742
[23] J. Peˇcari´c , F. Proschan , Y. Tong , Convex Functions, Partial Orderings, and Statistical Applications, Academic Press, INC, United States of America, 1992.
[24] T. Rasheed, S. I. Butt, G. Peˇcari´c, and ¯D. Peˇcari´ c, New bounds of Popoviciu’s difference via weighted Hadamard type inequalities with applications in information theory, Math. Meth. Appl. Sci. 47 (2024), 5750–5763, DOI 10.1002/mma.9889.
[25] T. Rasheed, S.I. Butt, ¯D. Peˇcari´c, J. Peˇcari´c, Generalized cyclic Jensen and information inequalities, Chaos, Solitons & Fractals, Volume 163, 2022, 112602, ISSN 0960-0779, https://doi.org/10.1016/j.chaos.2022.112602.
[26] M.Z. Sarikaya, E. Set, M.E. Ozdemir, On new inequalities of Simpson’s type for convex functions, RGMIA Res. Rep. Coll. 13 (2) (2010) Article2.
[27] M. Z. Sarıkaya and S. Bardak, “Generalized Simpson Type Integral Inequalities”, Konuralp J. Math., vol. 7, no. 1, pp. 186–191, 2019.
[28] V. Stojiljkovic, Simpson Type Tensorial Norm Inequalities for Continuous Functions of ´ Selfadjoint Operators in Hilbert Spaces, Creat. Math. Inform., 33 (2024), 105–117. https://doi.org/10.37193/CMI.2024.01.10
[29] V. Stojiljkovi´ c; R. Ramaswamy; O.A.A. Abdelnaby; S. Radenovi´c. Some Refine ments of the Tensorial Inequalities in Hilbert Spaces. Symmetry 2023, 15, 925. https://doi.org/10.3390/sym15040925
[30] V. Stojiljkovi´c.; Hermite–Hadamard–type fractional–integral inequalities for (p,h) convex fuzzy-interval-valued mappings, Electron. J. Math. 5 (2023) 18–28, DOI: 10.47443/ejm.2023.004
[31] V. Stojiljkovi´ c. (2023). ’Twice Differentiable Ostrowski Type Tensorial Norm Inequal ity for Continuous Functions of Selfadjoint Operators in Hilbert Spaces’ , Electronic Journal of Mathematical Analysis and Applications, 11(2), pp. 1-15. doi: 10.21608/ej maa.2023.199881.1014
[32] V. Stojiljkovi´c. Twice Differentiable Ostrowski Type Tensorial Norm Inequality for Contin uous Functions of Selfadjoint Operators in Hilbert Spaces. European Journal of Pure and Applied Mathematics, 16(3), (2023), 1421–1433.
[33] V. Stojiljkovi´ c., & S.S. Dragomir. (2023). Differentiable Ostrowski type tensorial norm in equality for continuous functions of selfadjoint operators in Hilbert spaces. Gulf Journal of Mathematics, 15(2), 40-55. https://doi.org/10.56947/gjom.v15i2.1247
[34] V. Stojiljkovi´c; N. Mirkov; S. Radenovi´c. Variations in the Tensorial Trapezoid Type Inequal ities for Convex Functions of Self-Adjoint Operators in Hilbert Spaces. Symmetry 2024, 16, 121. https://doi.org/10.3390/sym16010121
Stojiljkovic, V. (2024). Generalized Tensorial Simpson type Inequalities for Convex functions of Selfadjoint Operators in Hilbert Space. Maltepe Journal of Mathematics, 6(2), 78-89. https://doi.org/10.47087/mjm.1452521
AMA
Stojiljkovic V. Generalized Tensorial Simpson type Inequalities for Convex functions of Selfadjoint Operators in Hilbert Space. Maltepe Journal of Mathematics. November 2024;6(2):78-89. doi:10.47087/mjm.1452521
Chicago
Stojiljkovic, Vuk. “Generalized Tensorial Simpson Type Inequalities for Convex Functions of Selfadjoint Operators in Hilbert Space”. Maltepe Journal of Mathematics 6, no. 2 (November 2024): 78-89. https://doi.org/10.47087/mjm.1452521.
EndNote
Stojiljkovic V (November 1, 2024) Generalized Tensorial Simpson type Inequalities for Convex functions of Selfadjoint Operators in Hilbert Space. Maltepe Journal of Mathematics 6 2 78–89.
IEEE
V. Stojiljkovic, “Generalized Tensorial Simpson type Inequalities for Convex functions of Selfadjoint Operators in Hilbert Space”, Maltepe Journal of Mathematics, vol. 6, no. 2, pp. 78–89, 2024, doi: 10.47087/mjm.1452521.
ISNAD
Stojiljkovic, Vuk. “Generalized Tensorial Simpson Type Inequalities for Convex Functions of Selfadjoint Operators in Hilbert Space”. Maltepe Journal of Mathematics 6/2 (November 2024), 78-89. https://doi.org/10.47087/mjm.1452521.
JAMA
Stojiljkovic V. Generalized Tensorial Simpson type Inequalities for Convex functions of Selfadjoint Operators in Hilbert Space. Maltepe Journal of Mathematics. 2024;6:78–89.
MLA
Stojiljkovic, Vuk. “Generalized Tensorial Simpson Type Inequalities for Convex Functions of Selfadjoint Operators in Hilbert Space”. Maltepe Journal of Mathematics, vol. 6, no. 2, 2024, pp. 78-89, doi:10.47087/mjm.1452521.
Vancouver
Stojiljkovic V. Generalized Tensorial Simpson type Inequalities for Convex functions of Selfadjoint Operators in Hilbert Space. Maltepe Journal of Mathematics. 2024;6(2):78-89.