Novel inequalities for subadditive functions via tempered fractional integrals and their numerical investigations

Artion Kashuri; Soubhagya Kumar Sahoo; Pshtiwan Othman Mohammed; Eman Al-Sarairah; Nejmeddine Chorfi; Artion Kashuri; Soubhagya Kumar Sahoo; Pshtiwan Othman Mohammed; Eman Al-Sarairah; Nejmeddine Chorfi

doi:10.3934/math.2024643

AIMS Mathematics

2024, Volume 9, Issue 5: 13195-13210. doi: 10.3934/math.2024643

Previous Article Next Article

Research article Special Issues

Novel inequalities for subadditive functions via tempered fractional integrals and their numerical investigations

1.
Department of Mathematical Engineering, Polytechnic University of Tirana, Tirana 1001, Albania
2.
Department of Mathematics, ITER, Siksha O Anusandhan University, Bhubaneswar 751030, India
3.
Department of Mathematics, College of Education, University of Sulaimani, Sulaymaniyah 46001, Iraq
4.
Research and Development Center, University of Sulaimani, Sulaymaniyah 46001, Iraq
5.
Department of Mathematics, Khalifa University, P.O. Box 127788, Abu Dhabi, United Arab Emirates
6.
Department of Mathematics, Al-Hussein Bin Talal University, P.O. Box 20, Ma'an 71111, Jordan
7.
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received: 29 January 2024 Revised: 25 March 2024 Accepted: 03 April 2024 Published: 09 April 2024
MSC : 26A33, 26A51, 26D07, 26D10, 26D15

In this paper, we proposed some new integral inequalities for subadditive functions and the product of subadditive functions. Additionally, a novel integral identity was established and a number of inequalities of the Hermite-Hadamard type for subadditive functions pertinent to tempered fractional integrals were proved. Finally, to support the major results, we provided several examples of subadditive functions and corresponding graphs for the newly proposed inequalities.
- Hermite-Hadamard inequality,
- subadditivity,
- tempered fractional integral operators,
- Hölder's inequality,
- power-mean inequality,
- estimations
Citation: Artion Kashuri, Soubhagya Kumar Sahoo, Pshtiwan Othman Mohammed, Eman Al-Sarairah, Nejmeddine Chorfi. Novel inequalities for subadditive functions via tempered fractional integrals and their numerical investigations[J]. AIMS Mathematics, 2024, 9(5): 13195-13210. doi: 10.3934/math.2024643

Related Papers:

Abstract

In this paper, we proposed some new integral inequalities for subadditive functions and the product of subadditive functions. Additionally, a novel integral identity was established and a number of inequalities of the Hermite-Hadamard type for subadditive functions pertinent to tempered fractional integrals were proved. Finally, to support the major results, we provided several examples of subadditive functions and corresponding graphs for the newly proposed inequalities.

References

[1]	E. Hille, R. S. Phillips, Functional analysis and semigroups, American Mathematical Society, 1996.
[2]	R. A. Rosenbaum, Sub-additive functions, Duke Math. J., 17 (1950), 227–247. https://doi.org/10.1215/S0012-7094-50-01721-2 doi: 10.1215/S0012-7094-50-01721-2
[3]	F. M. Dannan, Submultiplicative and subadditive functions and integral inequalities of Bellman-Bihari type, J. Math. Anal. Appl., 120 (1986), 631–646. https://doi.org/10.1016/0022-247X(86)90185-X doi: 10.1016/0022-247X(86)90185-X
[4]	R. G. Laatsch, Subadditive functions of one real variable, Oklahoma State University, 1962.
[5]	J. Matkowski, On subadditive functions and $\Psi$-additive mappings, Open Math., 1 (2003), 435–440.
[6]	S. K. Sahoo, E. Al-Sarairah, P. O. Mohammed, M. Tariq, K. Nonlaopon, Modified inequalities on center-radius order interval-valued functions pertaining to Riemann-Liouville fractional integrals, Axioms, 11 (2022), 1–18. https://doi.org/10.3390/axioms11120732 doi: 10.3390/axioms11120732
[7]	J. Matkowski, T. Swiatkowski, On subadditive functions, Proc. Amer. Math. Soc., 119 (1993), 187–197.
[8]	M. A. Ali, M. Z. Sarikaya, H. Budak, Fractional Hermite-Hadamard type inequalities for subadditive functions, Filomat, 36 (2022), 3715–3729. https://doi.org/10.2298/FIL2211715A doi: 10.2298/FIL2211715A
[9]	H. Kadakal, Hermite-Hadamard type inequalities for subadditive functions, AIMS Math., 5 (2020), 930–939. https://doi.org/10.3934/math.2020064 doi: 10.3934/math.2020064
[10]	M. Kadakal, İ. İşcan, Exponential type convexity and some related inequalities, J. Inequal. Appl., 2020 (2020), 1–9. https://doi.org/10.1186/s13660-020-02349-1 doi: 10.1186/s13660-020-02349-1
[11]	M. Alomari, M. Darus, U. S. Kirmaci, Refinements of Hadamard-type inequalities for quasi-convex functions with applications to trapezoidal formula and to special means, Comput. Math. Appl., 59 (2010), 225–232. https://doi.org/10.1016/j.camwa.2009.08.002 doi: 10.1016/j.camwa.2009.08.002
[12]	X. M. Zhang, Y. M. Chu, X. H. Zhang, The Hermite-Hadamard type inequality of $GA$-convex functions and its applications, J. Inequal. Appl., 2010 (2010), 1–11. https://doi.org/10.1155/2010/507560 doi: 10.1155/2010/507560
[13]	S. S. Dragomir, J. Pećarič, L. E. Persson, Some inequalities of Hadamard type, Soochow J. Math., 21 (1995), 335–341.
[14]	H. M. Srivastava, S. K. Sahoo, P. O. Mohammed, A. Kashuri, N. Chorfi, Results on Minkowski-type inequalities for weighted fractional integral operators, Symmetry, 15 (2023), 1–26. https://doi.org/10.3390/sym15081522 doi: 10.3390/sym15081522
[15]	B. Y. Xi, F. Qi, Some Hermite-Hadamard type inequalities for differentiable convex functions and applications, Hacet. J. Math. Stat., 42 (2013), 243–257.
[16]	S. Mehmood, P. O. Mohammed, A. Kashuri, N. Chorfi, S. A. Mahmood, M. A. Yousif, Some new fractional inequalities defined using cr-Log-h-convex functions and applications, Symmetry, 16 (2024), 1–12. https://doi.org/10.3390/sym16040407 doi: 10.3390/sym16040407
[17]	P. O. Mohammed, T. Abdeljawad, S. D. Zeng, A. Kashuri, Fractional Hermite-Hadamard integral inequalities for a new class of convex functions, Symmetry, 12 (2020), 1–12. https://doi.org/10.3390/sym12091485 doi: 10.3390/sym12091485
[18]	L. L. Zhang, Y. Peng, T. S. Du, On multiplicative Hermite-Hadamard- and Newton-type inequalities for multiplicatively $(P, m)$-convex functions, J. Math. Anal. Appl., 534 (2024), 128117. https://doi.org/10.1016/j.jmaa.2024.128117 doi: 10.1016/j.jmaa.2024.128117
[19]	M. Z. Sarikaya, M. A. Ali, Hermite-Hadamard type inequalities and related inequalities for subadditive functions, Miskolc Math. Notes, 22 (2021), 929–937. https://doi.org/10.18514/MMN.2021.3154 doi: 10.18514/MMN.2021.3154
[20]	P. O. Mohammed, M. Z. Sarikaya, D. Baleanu, On the generalized Hermite-Hadamard inequalities via the tempered fractional integrals, Symmetry, 12 (2020), 1–17. https://doi.org/10.3390/sym12040595 doi: 10.3390/sym12040595
[21]	Y. Cao, J. F. Cao, P. Z. Tan, T. S. Du, Some parameterized inequalities arising from the tempered fractional integrals involving the $(\mu, \eta)$-incomplete gamma functions, J. Math. Inequal., 16 (2022), 1091–1121. https://doi.org/10.7153/jmi-2022-16-73 doi: 10.7153/jmi-2022-16-73

Reader Comments

Your name:*

Email:*
© 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)