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Hermite-Hadamard type fractional integral inequalities for generalized (s,m,φ)-preinvex functions

Yıl 2017, Cilt: 5 Sayı: 3, 97 - 106, 01.07.2017

Öz

In the present paper, by using new identity for fractional integrals some new estimates on generalizations of Hermite-Hadamard type inequalities for the class of generalized (s,m,φ)-preinvex functions via Riemann-Liouville fractional integral are established. These results not only extend the results appeared in the literature (see [2]), but also provide new estimates on these types. At the end, some applications to special means are given.

Kaynakça

  • A. Kashuri and R. Liko, Ostrowski type fractional integral inequalities for generalized (s,m,φ)-preinvex functions, Aust. J. Math. Anal. Appl., 13, (1) (2016), Article 16, 1-11.
  • V. M. Mihai, Some Hermite-Hadamard type inequalities via Riemann-Liouville fractional calculus, Tamkang J. Math., 44, (4) (2013), 411-416.
  • 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), 3112-3126.
  • S. S. Dragomir, J. Pečarić and L. E. Persson, Some inequalities of Hadamard type, Soochow J. Math., 21, (1995), 335-341.
  • H. Hudzik and L. Maligranda, Some remarks on s-convex functions, Aequationes Math., 48, (1994), 100-111.
  • T. Antczak, Mean value in invexity analysis, Nonlinear Anal., 60, (2005), 1473-1484.
  • X. M. Yang, X. Q. Yang and K. L. Teo, Generalized invexity and generalized invariant monotonicity, J. Optim. Theory Appl., 117, (2003), 607-625.
  • R. Pini, Invexity and generalized convexity, Optimization., 22, (1991), 513-525.
  • H. Kavurmaci, M. Avci and M. E. Özdemir, New inequalities of Hermite-Hadamard type for convex functions with applications, arXiv:1006.1593v1 [math. CA], (2010), 1-10.
  • Y. M. Chu, G. D. Wang and X. H. Zhang, Schur convexity and Hadamard’s inequality, Math. Inequal. Appl., 13, (4) (2010), 725-731.
  • 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), Article ID 507560, 11 pages.
  • 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, (5) (2016), 4305-4316.
  • M. Adil Khan, Y. Khurshid, T. Ali and N. Rehman, Inequalities for three times differentiable functions, J. Math., Punjab Univ., 48, (2) (2016), 35-48.
  • M. Adil Khan, Y. Khurshid and T. Ali, Hermite-Hadamard inequality for fractional integrals via α-convex functions, Acta Math. Univ. Comenianae, 79, (1) (2017), 153-164.
  • Y. M. Chu, M. Adil Khan, T. Ullah Khan and T. Ali, Generalizations of Hermite-Hadamard type inequalities for MT-convex functions, J. Nonlinear Sci. Appl., 9, (2016), 4305-4316.
  • H. N. Shi, Two Schur-convex functions related to Hadamard-type integral inequalities, Publ. Math. Debrecen, 78, (2) (2011), 393-403.
  • F. X. Chen and S. H. Wu, Several complementary inequalities to inequalities of Hermite-Hadamard type for s-convex functions, J. Nonlinear Sci. Appl., 9, (2) (2016), 705-716.
  • 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), 766-777.
  • W. Liu, W. Wen and J. Park, Ostrowski type fractional integral inequalities for MT-convex functions, Miskolc Mathematical Notes., 16, (1) (2015), 249-256.
  • Y. M. Chu, G. D. Wang and X. H. Zhang, Schur convexity and Hadamard’s inequality, Math. Inequal. Appl., 13, (4) (2010), 725-731.
  • 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), Article ID 507560, 11 pages.
  • 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, (5) (2016), 4305-4316.
  • M. Tunç, Ostrowski type inequalities for functions whose derivatives are MT-convex, J. Comput. Anal. Appl., 17, (4) (2014), 691-696.
  • W. J. Liu, Some Simpson type inequalities for h-convex and (α,m)-convex functions, J. Comput. Anal. Appl., 16, (5) (2014), 1005-1012.
  • F. Qi and B. Y. Xi, Some integral inequalities of Simpson type for GA-ϵ-convex functions, Georgian Math. J., 20, (5) (2013), 775-788.
  • P. S. Bullen, Handbook of Means and Their Inequalities, Kluwer Academic Publishers, Dordrecht, (2003).
Yıl 2017, Cilt: 5 Sayı: 3, 97 - 106, 01.07.2017

Öz

Kaynakça

  • A. Kashuri and R. Liko, Ostrowski type fractional integral inequalities for generalized (s,m,φ)-preinvex functions, Aust. J. Math. Anal. Appl., 13, (1) (2016), Article 16, 1-11.
  • V. M. Mihai, Some Hermite-Hadamard type inequalities via Riemann-Liouville fractional calculus, Tamkang J. Math., 44, (4) (2013), 411-416.
  • 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), 3112-3126.
  • S. S. Dragomir, J. Pečarić and L. E. Persson, Some inequalities of Hadamard type, Soochow J. Math., 21, (1995), 335-341.
  • H. Hudzik and L. Maligranda, Some remarks on s-convex functions, Aequationes Math., 48, (1994), 100-111.
  • T. Antczak, Mean value in invexity analysis, Nonlinear Anal., 60, (2005), 1473-1484.
  • X. M. Yang, X. Q. Yang and K. L. Teo, Generalized invexity and generalized invariant monotonicity, J. Optim. Theory Appl., 117, (2003), 607-625.
  • R. Pini, Invexity and generalized convexity, Optimization., 22, (1991), 513-525.
  • H. Kavurmaci, M. Avci and M. E. Özdemir, New inequalities of Hermite-Hadamard type for convex functions with applications, arXiv:1006.1593v1 [math. CA], (2010), 1-10.
  • Y. M. Chu, G. D. Wang and X. H. Zhang, Schur convexity and Hadamard’s inequality, Math. Inequal. Appl., 13, (4) (2010), 725-731.
  • 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), Article ID 507560, 11 pages.
  • 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, (5) (2016), 4305-4316.
  • M. Adil Khan, Y. Khurshid, T. Ali and N. Rehman, Inequalities for three times differentiable functions, J. Math., Punjab Univ., 48, (2) (2016), 35-48.
  • M. Adil Khan, Y. Khurshid and T. Ali, Hermite-Hadamard inequality for fractional integrals via α-convex functions, Acta Math. Univ. Comenianae, 79, (1) (2017), 153-164.
  • Y. M. Chu, M. Adil Khan, T. Ullah Khan and T. Ali, Generalizations of Hermite-Hadamard type inequalities for MT-convex functions, J. Nonlinear Sci. Appl., 9, (2016), 4305-4316.
  • H. N. Shi, Two Schur-convex functions related to Hadamard-type integral inequalities, Publ. Math. Debrecen, 78, (2) (2011), 393-403.
  • F. X. Chen and S. H. Wu, Several complementary inequalities to inequalities of Hermite-Hadamard type for s-convex functions, J. Nonlinear Sci. Appl., 9, (2) (2016), 705-716.
  • 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), 766-777.
  • W. Liu, W. Wen and J. Park, Ostrowski type fractional integral inequalities for MT-convex functions, Miskolc Mathematical Notes., 16, (1) (2015), 249-256.
  • Y. M. Chu, G. D. Wang and X. H. Zhang, Schur convexity and Hadamard’s inequality, Math. Inequal. Appl., 13, (4) (2010), 725-731.
  • 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), Article ID 507560, 11 pages.
  • 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, (5) (2016), 4305-4316.
  • M. Tunç, Ostrowski type inequalities for functions whose derivatives are MT-convex, J. Comput. Anal. Appl., 17, (4) (2014), 691-696.
  • W. J. Liu, Some Simpson type inequalities for h-convex and (α,m)-convex functions, J. Comput. Anal. Appl., 16, (5) (2014), 1005-1012.
  • F. Qi and B. Y. Xi, Some integral inequalities of Simpson type for GA-ϵ-convex functions, Georgian Math. J., 20, (5) (2013), 775-788.
  • P. S. Bullen, Handbook of Means and Their Inequalities, Kluwer Academic Publishers, Dordrecht, (2003).
Toplam 26 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

Artion Kashuri

Rozana Liko Bu kişi benim

Yayımlanma Tarihi 1 Temmuz 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 5 Sayı: 3

Kaynak Göster

APA Kashuri, A., & Liko, R. (2017). Hermite-Hadamard type fractional integral inequalities for generalized (s,m,φ)-preinvex functions. New Trends in Mathematical Sciences, 5(3), 97-106.
AMA Kashuri A, Liko R. Hermite-Hadamard type fractional integral inequalities for generalized (s,m,φ)-preinvex functions. New Trends in Mathematical Sciences. Temmuz 2017;5(3):97-106.
Chicago Kashuri, Artion, ve Rozana Liko. “Hermite-Hadamard Type Fractional Integral Inequalities for Generalized (s,m,φ)-Preinvex Functions”. New Trends in Mathematical Sciences 5, sy. 3 (Temmuz 2017): 97-106.
EndNote Kashuri A, Liko R (01 Temmuz 2017) Hermite-Hadamard type fractional integral inequalities for generalized (s,m,φ)-preinvex functions. New Trends in Mathematical Sciences 5 3 97–106.
IEEE A. Kashuri ve R. Liko, “Hermite-Hadamard type fractional integral inequalities for generalized (s,m,φ)-preinvex functions”, New Trends in Mathematical Sciences, c. 5, sy. 3, ss. 97–106, 2017.
ISNAD Kashuri, Artion - Liko, Rozana. “Hermite-Hadamard Type Fractional Integral Inequalities for Generalized (s,m,φ)-Preinvex Functions”. New Trends in Mathematical Sciences 5/3 (Temmuz 2017), 97-106.
JAMA Kashuri A, Liko R. Hermite-Hadamard type fractional integral inequalities for generalized (s,m,φ)-preinvex functions. New Trends in Mathematical Sciences. 2017;5:97–106.
MLA Kashuri, Artion ve Rozana Liko. “Hermite-Hadamard Type Fractional Integral Inequalities for Generalized (s,m,φ)-Preinvex Functions”. New Trends in Mathematical Sciences, c. 5, sy. 3, 2017, ss. 97-106.
Vancouver Kashuri A, Liko R. Hermite-Hadamard type fractional integral inequalities for generalized (s,m,φ)-preinvex functions. New Trends in Mathematical Sciences. 2017;5(3):97-106.