Integral inequalities via harmonically h-convexity

Merad, Meriem; Meftah, Badreddine; Souahi, Abdourazek

doi:10.2478/mjpaa-2021-0026

Abstract

In this paper, we establish some estimates of the left side of the generalized Gauss-Jacobi quadrature formula for harmonic h-preinvex functions involving Euler’s beta and hypergeometric functions. The obtained results are mainly based on the identity given by M. A. Noor, K. I. Noor and S. Iftikhar in [17].

References

[1] I. Ahmad, Integral inequalities under beta function and preinvex type functions. SpringerPlus. 5 (2016), no. 1, p. 1-6.
Search in Google Scholar Back to article
[2] J. Chen and X. Huang, Some integral inequalities via (h – (α, m))-logarithmically convexity. J. Comput. Anal. Appl. 20 (2016), no. 2, 374–380.
Search in Google Scholar Back to article
[3] İ. İşcan, M. Aydin and S. Dikmenoglu, New integral inequalities via harmonically convex functions. Mathematics and Statistics 3 (2015), no. 5, 134-140.
Search in Google Scholar Back to article
[4] A. Kashuri and R. Liko, Hermite-Hadamard type fractional integral inequalities for generalized (r, s, m, φ)-preinvex functions. European Journal of Pure and Applied Mathematics. 10 (2017), no. 3, 495-505.
Search in Google Scholar Back to article
[5] A. Kashuri and R. Liko, Generalizations of Hermite-Hadamard and Ostrowski type inequalities for MTm−preinvex functions. Proyecciones 36 (2017), no. 1, 45–80.
Search in Google Scholar Back to article
[6] W. Liu, New integral inequalities via (α, m)-convexity and quasi-convexity. Hacet. J. Math. Stat. 42 (2013), no. 3, 289–297.
Search in Google Scholar Back to article
[7] W. Liu, New integral inequalities involving beta function via P-convexity. Miskolc Math. Notes 15 (2014), no. 2, 585–591.
Search in Google Scholar Back to article
[8] B. Meftah, New integral inequalities via strongly convexity. Electronic Journal of Mathematical Analysis and Applications. 5 (2017), no. 2, 266–270.
Search in Google Scholar Back to article
[9] B. Meftah, New integral inequalities for s-preinvex functions. Int. J. Nonlinear Anal. Appl, 8 (2017), no. 1, 331–336.
Search in Google Scholar Back to article
[10] B. Meftah and N. Aouissi, New integral inequalities for (s, m)-and (α, m)-preinvex functions. Revista De Matemáticas De la Universidad del Atlántico Páginas. 5 (2018), no. 1, 87–99.
Search in Google Scholar Back to article
[11] B. Meftah, New integral inequalities Through the φ-preinvexity. Iranian Journal of Mathematical Sciences and Informatics. 15 (2020), no. 1, 79-83.
Search in Google Scholar Back to article
[12] P. O. Mohammed, New integral inequalities for preinvex functions via generalized beta function. Journal of Interdisciplinary Mathematics, 22 (2019), no. 4, 539-549.
Search in Google Scholar Back to article
[13] M. Muddassar and A. Ali, New integral inequalities through generalized convex functions. Punjab Univ. J. Math. (Lahore) 46 (2014), no. 2, 47–51.
Search in Google Scholar Back to article
[14] M. A. Noor, K. I. Noor and S. Iftikhar, Hermite-Hadamard inequalities for harmonic preinvex functions, SAUSSUREA. 6 (2016), no. 2, 34-53.
Search in Google Scholar Back to article
[15] M. A. Noor, K. I. Noor and S. Iftikhar, Fractional Ostrowski inequalities for harmonic h-preinvex functions. Facta Univ. Ser. Math. Inform. 31 (2016), no. 2, 417–445.
Search in Google Scholar Back to article
[16] M. A. Noor, K. I. Noor and S. Iftikhar, Harmonic MT-preinvex functions and integral inequalities. Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. 20 (2016), no. 528, 51–70.
Search in Google Scholar Back to article
[17] M. A. Noor, K. I. Noor and S. Iftikhar, Harmonic beta-preinvex functions and inequalities. International Journal of Analysis and Applications. 13 (2017), no. 2, 144-160.
Search in Google Scholar Back to article
[18] M. A. Noor, K. I. Noor and S. Iftikhar, Harmonic beta-convex functions involving hypergeometric functions. Publ. Inst. Math. (Beograd) (N.S.) 104(118) (2018), 241–249.10.2298/PIM1818241N
Search in Google Scholar Back to article
[19] M. E.Özdemir, E. Set and M. Alomari, Integral inequalities via several kinds of convexity. Creat. Math. Inform. 20 (2011), no. 1, 62–73.
Search in Google Scholar Back to article
[20] A. Ralston and P. Rabinowitz, A first course in numerical analysis. Reprint of the 1978 second edition. Dover Publications, Inc., Mineola, NY, 2001.
Search in Google Scholar Back to article
[21] H.-N. Shi and J. Zhang, Some new judgement theorems of Schur geometric and Schur harmonic convexities for a class of symmetric functions. J. Inequal. Appl. 2013, 2013:527.10.1186/1029-242X-2013-527
Search in Google Scholar Back to article

Integral inequalities via harmonically h-convexity

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