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On some k-fractional integral inequalities of Hermite-Hadamard type for twice differentiable generalized beta (r, g)-preinvex functions

Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In the present paper, a new class of generalized beta (r, g)-preinvex functions is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving generalized beta (r, g)-preinvex functions are given. Moreover, some generalizations of Hermite-Hadamard type inequalities for generalized beta (r, g)-preinvex functions that are twice differentiable via k-fractional integrals are established. These general inequalities give us some new estimates for Hermite-Hadamard type k-fractional integral inequalities and also extend some results appeared in the literature; see [A. Kashuri and R. Liko, Ostrowski type fractional integral inequalities for generalized (s, m, φ)-preinvex functions, Aust. J. Math. Anal. Appl. 13 (2016), no. 1, Article ID 16]. At the end, some applications to special means are given.
Wydawca
Rocznik
Strony
59--72
Opis fizyczny
Bibliogr. 24 poz.
Twórcy
  • Department of Mathematics, Faculty of Technical Science, University Ismail Qemali, Vlora, Albania
autor
  • Department of Mathematics, Faculty of Technical Science, University Ismail Qemali, Vlora, Albania
Bibliografia
  • [1] T. Antczak, Mean value in invexity analysis, Nonlinear Anal. 60 (2005), no. 8, 1473-1484.
  • [2] P. S. Bullen, Handbook of Means and Their Inequalities, Math. Appl. 560, Kluwer Academic, Dordrecht, 2003.
  • [3] F. Chen and S. Wu, Several complementary inequalities to inequalities of Hermite-Hadamard type for s-convex functions, J. Nonlinear Sci. Appl. 9 (2016), no. 2, 705-716.
  • [4] Y. Chu, G.Wang and X. Zhang, Schur convexity and Hadamard’s inequality,Math. Inequal. Appl. 13 (2010), no. 4, 725-731.
  • [5] Y.-M. Chu, M. A. Khan, T. U. Khan and T. Ali, Generalizations of Hermite-Hadamard type inequalities for MT-convex functions, J. Nonlinear Sci. Appl. 9 (2016), no. 6, 4305-4316.
  • [6] R. Díaz and E. Pariguan, On hypergeometric functions and Pochhammer k-symbol, Divulg. Mat. 15 (2007), no. 2, 179-192.
  • [7] S. S. Dragomir, J. Pečarić and L. E. Persson, Some inequalities of Hadamard type, Soochow J. Math. 21 (1995), no. 3, 335-341.
  • [8] T.-S. Du, J.-G. Liao and Y.-J. Li, Properties and integral inequalities of Hadamard-Simpson type for the generalized (s, m)-preinvex functions, J. Nonlinear Sci. Appl. 9 (2016), no. 5, 3112-3126.
  • [9] H. Hudzik and L. Maligranda, Some remarks on s-convex functions, Aequationes Math. 48 (1994), no. 1, 100-111.
  • [10] W.-D. Jiang, D.-W. Niu and F. Qi, Some inequalities of Hermite-Hadamard type for r-ϕ-preinvex functions, Tamkang J. Math. 45 (2014), no. 1, 31-38.
  • [11] A. Kashuri and R. Liko, Ostrowski type fractional integral inequalities for generalized (s, m, φ)-preinvex functions, Aust. J. Math. Anal. Appl. 13 (2016), no. 1, Article ID 16.
  • [12] H. Kavurmaci, M. Avci and M. E. Özdemir, New inequalities of Hermite-Hadamard type for convex functions with applications, J. Inequal. Appl. 2011 (2011), Article ID 86.
  • [13] M. A. Khan, Y. Khurshid and T. Ali, Hermite-Hadamard inequality for fractional integrals via η-convex functions, Acta Math. Univ. Comenian. (N. S.) 86 (2017), no. 1, 153-164.
  • [14] M. A. Khan, Y. Khurshid, T. Ali and N. Rehman, Inequalities for three times differentiable functions, Punjab Univ. J. Math. (Lahore) 48 (2016), no. 2, 35-48.
  • [15] W. Liu, New integral inequalities involving beta function via P-convexity, Miskolc Math. Notes 15 (2014), no. 2, 585-591.
  • [16] W. Liu, W. Wen and J. Park, Hermite-Hadamard type inequalities for MT-convex functions via classical integrals and fractional integrals, J. Nonlinear Sci. Appl. 9 (2016), no. 3, 766-777.
  • [17] S. Mubeen and G. M. Habibullah, k-fractional integrals and application, Int. J. Contemp. Math. Sci. 7 (2012), no. 1-4, 89-94.
  • [18] M. E. Özdemir, E. Set and M. Alomari, Integral inequalities via several kinds of convexity, Creat. Math. Inform. 20 (2011), no. 1, 62-73.
  • [19] R. Pini, Invexity and generalized convexity, Optimization 22 (1991), no. 4, 513-525.
  • [20] F. Qi and B.-Y. Xi, Some integral inequalities of Simpson type for GA-ε-convex functions, Georgian Math. J. 20 (2013), no. 4, 775-788.
  • [21] H.-N. Shi, Two Schur-convex functions related to Hadamard-type integral inequalities, Publ. Math. Debrecen 78 (2011), no. 2, 393-403.
  • [22] D. D. Stancu, G. Coman and P. Blaga, Numerical Analysis and Approximation Theory Vol. II, Presa Universitară Clujeană, Cluj-Napoca, 2002.
  • [23] X. M. Yang, X. Q. Yang and K. L. Teo, Generalized invexity and generalized invariant monotonicity, J. Optim. Theory Appl. 117 (2003), no. 3, 607-625.
  • [24] X.-M. Zhang, Y.-M. Chu and X.-H. Zhang, The Hermite-Hadamard type inequality of GA-convex functions and its applications, J. Inequal. Appl. 2010 (2010), Article ID 507560.
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-95456183-4802-4da6-8d21-c1f5bfdafc75
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