Hermite-Hadamard Type Inequalities for Multiplicatively m-Convex Functions
Hermite-Hadamard Type Inequalities for Multiplicatively m-Convex Functions
Résumé
Convex functions play an important role in finding the inequalities, those help in finding the solutions of different types of equations and equations involving functions. In this article we have considered investigated on the m-convex functions in a normed linear space. We have established some results of Hermite-Hadamard like inequality. The results established will be useful for investigation in different branches of science and engineering for solving different problems.
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Références
References:
Dragomir, S.S. and Pearce, C.E.M: Selected Topics on Hermite-Hadamard Inequalities and Applications RGMIA Monographs.Victoria University, (2000).
2. Precaric, J.L, Proschan, L. and Tong Y.L.: Convex functions, Partial Ordering and Statistical Applications. Academic Press Boston, (1992).
3. Iscan, L: Hermite-Hadamard type inequalities for harmonically convex functions. Hacettepe Journal of Mathematics and Statistics.43(6), 935-942 (2014).
4. Butt, S. l., Yousaf, S, Khan, K. A, Mabela, R.M, and Alshrif, A. M.: Fejer-pachpatte-Mercer type inequalities For harmonically convex functions involving exponential function in kernel. Mathematical Problems in Engineering, 2022,1-19(2022).
5. Butt, S,I., AkdemIr, A.O, Nadeem, M., Mlaiki, N., Iscan, I. and Abdeljawad, I.: (m,n)-Harmonically polynomial convex functions and some Hadamard type inequalities on the co-ordinates. AIMS Mathematics, 6(5), 4677-4691 (2021).
6. Latif, M.A., Du, T.: Hermite-Hadamard type inequalities for harmonically convex functions Using fuzzy integrals Filomat, 36(12),4099-4110(2022)
7. Ozcan, S.: Some integral inequalities for harmonically ( ∝,s)-convex functions .Journal of Function Spaces, 2019,1-8 (2019)
8. Iscan, I.: Ostrowski type inequalities for p-convex functions, New Trends in Mathematical Sciences. 4(3), 140-150 (2016)
9. Fang, Z.B. and Shi, R,: On the (p,h)-convex function and some integral inequalities. Journal of Inequalities and Applications, 2014,45, 1-16 (2014)
10. Bashirov, A.F., Kurpinar, F. and Ozyapici, A.: Multiplicative calculus and applications. Journal of Mathematical Analysis and Applications, 337(1),36-48(2008)
11. Ali, M.A., Abbas, M., Zhang, Z., Siaf, I.B. and Arif, R.: On integral inequalities for product and Quotient of two multiplicatively convex functions, Asian Research Journal in Mathematics,12(3), 1-11(2019)
12. Grossman, M. and Kartz, R.: Non-Newtonian Calculus. Lee. Press, Pigeon Cove.(1972)
13. Bashirov, A.E. and Riza, M.: On Complex Multiplicative differentiation, TWMS Journal of Applied and Engineering Mathematics. 1(1), 75-85 (2011)
14. Daletskil, Y.L. and Teterina, N.I., Multiplicative stochastic integrals, Uspekhi Matematicheskikh Nauk, 27(2:164), 167-168(1972)
15. Karandikar, R. I.: Multiplicative decomposition of non-singular matrix valued continuous Semimartingales. Annals of Probability, 10(1),1088-1091(1982)
16. Ali, M.A. Abbas and M., Zafer, A.A.: On some Hermite-Hadamard Integral Inequalities in Multiplicative Calculus, Journal of Inequalities and Special Functions.10(1),111-122(2019)
17. Ali, M.A., Budak, H., Sarikaya, M.Z. and Zhang, Z.: Ostrowski and Simpson type inequalities for multiplicative Integrals, Proyeciones 40(3),743-763(2021)
18. Kadakal, M: Hermite-Hadamard and Simpson type inequalities for multiplicatively harmonically p-functions, Sigma Journal of Engineering and Natural Sciences. 37(4),1315-1324 (2019)
19. Ozcan, S.: Hermite-Hadamard inequalities for multictively h-convex functions, Konuralp Journal of Mathematics, 8(1),158-164(2020)
20, Ozcan,S.: Some integral inequalities of Hermite-Hadamard type for multiplicatively preinvex Functions. AIMS Mathematics, 5(2), 1505-1518 (2020)
21. Riza, M., Ozyapici, A. and Kurpinal, E.: Multiplicative finite difference methods. Quarterly of Applied Mathematics, 67(4) 745-754, (2009)
22. Sahoo, A.K., Kodomsingh, B., Raut, P.K. and Tripathy, B.C.: Hermite-Hadarmad’s inequalities for normed linear Convex function via fractional type inequalities, Bull. Comput. Appl. Math., Vol.13, No.1, 2025,
23. Sahoo, A.K., Kodomsingh, B. and Tripathy, B.C.: Some normed linear space and integral inequalities of composite convex functions, South East Asian J. of Mathematics and Mathematical Sciences Vol. 20, No. 2 (2024), 133-142.
Dragomir, S.S. and Pearce, C.E.M: Selected Topics on Hermite-Hadamard Inequalities and Applications RGMIA Monographs.Victoria University, (2000).
2. Precaric, J.L, Proschan, L. and Tong Y.L.: Convex functions, Partial Ordering and Statistical Applications. Academic Press Boston, (1992).
3. Iscan, L: Hermite-Hadamard type inequalities for harmonically convex functions. Hacettepe Journal of Mathematics and Statistics.43(6), 935-942 (2014).
4. Butt, S. l., Yousaf, S, Khan, K. A, Mabela, R.M, and Alshrif, A. M.: Fejer-pachpatte-Mercer type inequalities For harmonically convex functions involving exponential function in kernel. Mathematical Problems in Engineering, 2022,1-19(2022).
5. Butt, S,I., AkdemIr, A.O, Nadeem, M., Mlaiki, N., Iscan, I. and Abdeljawad, I.: (m,n)-Harmonically polynomial convex functions and some Hadamard type inequalities on the co-ordinates. AIMS Mathematics, 6(5), 4677-4691 (2021).
6. Latif, M.A., Du, T.: Hermite-Hadamard type inequalities for harmonically convex functions Using fuzzy integrals Filomat, 36(12),4099-4110(2022)
7. Ozcan, S.: Some integral inequalities for harmonically ( ∝,s)-convex functions .Journal of Function Spaces, 2019,1-8 (2019)
8. Iscan, I.: Ostrowski type inequalities for p-convex functions, New Trends in Mathematical Sciences. 4(3), 140-150 (2016)
9. Fang, Z.B. and Shi, R,: On the (p,h)-convex function and some integral inequalities. Journal of Inequalities and Applications, 2014,45, 1-16 (2014)
10. Bashirov, A.F., Kurpinar, F. and Ozyapici, A.: Multiplicative calculus and applications. Journal of Mathematical Analysis and Applications, 337(1),36-48(2008)
11. Ali, M.A., Abbas, M., Zhang, Z., Siaf, I.B. and Arif, R.: On integral inequalities for product and Quotient of two multiplicatively convex functions, Asian Research Journal in Mathematics,12(3), 1-11(2019)
12. Grossman, M. and Kartz, R.: Non-Newtonian Calculus. Lee. Press, Pigeon Cove.(1972)
13. Bashirov, A.E. and Riza, M.: On Complex Multiplicative differentiation, TWMS Journal of Applied and Engineering Mathematics. 1(1), 75-85 (2011)
14. Daletskil, Y.L. and Teterina, N.I., Multiplicative stochastic integrals, Uspekhi Matematicheskikh Nauk, 27(2:164), 167-168(1972)
15. Karandikar, R. I.: Multiplicative decomposition of non-singular matrix valued continuous Semimartingales. Annals of Probability, 10(1),1088-1091(1982)
16. Ali, M.A. Abbas and M., Zafer, A.A.: On some Hermite-Hadamard Integral Inequalities in Multiplicative Calculus, Journal of Inequalities and Special Functions.10(1),111-122(2019)
17. Ali, M.A., Budak, H., Sarikaya, M.Z. and Zhang, Z.: Ostrowski and Simpson type inequalities for multiplicative Integrals, Proyeciones 40(3),743-763(2021)
18. Kadakal, M: Hermite-Hadamard and Simpson type inequalities for multiplicatively harmonically p-functions, Sigma Journal of Engineering and Natural Sciences. 37(4),1315-1324 (2019)
19. Ozcan, S.: Hermite-Hadamard inequalities for multictively h-convex functions, Konuralp Journal of Mathematics, 8(1),158-164(2020)
20, Ozcan,S.: Some integral inequalities of Hermite-Hadamard type for multiplicatively preinvex Functions. AIMS Mathematics, 5(2), 1505-1518 (2020)
21. Riza, M., Ozyapici, A. and Kurpinal, E.: Multiplicative finite difference methods. Quarterly of Applied Mathematics, 67(4) 745-754, (2009)
22. Sahoo, A.K., Kodomsingh, B., Raut, P.K. and Tripathy, B.C.: Hermite-Hadarmad’s inequalities for normed linear Convex function via fractional type inequalities, Bull. Comput. Appl. Math., Vol.13, No.1, 2025,
23. Sahoo, A.K., Kodomsingh, B. and Tripathy, B.C.: Some normed linear space and integral inequalities of composite convex functions, South East Asian J. of Mathematics and Mathematical Sciences Vol. 20, No. 2 (2024), 133-142.
Publiée
2025-07-13
Numéro
Rubrique
Research Articles
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