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SOME INEQUALITIES FOR B -1 -CONVEX FUNCTIONS VIA FRACTIONAL INTEGRAL OPERATOR

Year 2019, Volume: 9 Issue: 3, 620 - 625, 01.09.2019

Abstract

In this paper, B-1-convexity which is an abstract convexity type is studied. In addition, some new Hermite-Hadamard type inequalities for B-1-convex functions involving Riemann-Liouville type integral operators that are more general from classic integral operators are proven.

References

  • [1] G. Adilov, (2011), Increasing Co-radiant Functions and Hermite-Hadamard Type Inequalities, Mathematical Inequalities and Applications, 14 (1), pp. 45-60.
  • [2] G. Adilov, S. Kemali, (2009), Abstract convexity and Hermite-Hadamard Type Inequalities, Journal of Inequalities and Applications, 2009, 13 pages.
  • [3] G. Adilov, S. Kemali, (2007), Hermite-Hadamard-Type Inequalities For Increasing Positively Homogeneous Functions, Journal of Inequalities and Applications, 2007, 10 pages.
  • [4] G. Adilov and A. Rubinov, (2006), B-convex Sets and Functions, Numerical Functional Analysis and Optimization, 27 (3-4), pp. 237-257.
  • [5] G. Adilov and G. Tinaztepe, (2009), The Sharpening of Some Inequalities via Abstract Convexity, Mathematical Inequalities and Applications, 12 (1), pp. 33-51.
  • [6] G. Adilov and I. Yesilce, (2017), B −1−convex Functions, Journal of Convex Analysis, 24 (2), pp. 505-517.
  • [7] G. Adilov and I. Yesilce, (2012), B −1−convex Sets and B −1−measurable Maps, Numerical Functional Analysis and Optimization, 33 (2), pp. 131-141.
  • [8] G. Adilov and I. Yesilce, (2012), On Generalization of the Concept of Convexity, Hacettepe Journal of Mathematics and Statistics, 41 (5), pp. 723-730.
  • [9] W. Briec, Q.B. Liang, (2011), On Some Semilattice Structures for Production Technologies, Eur. J. Oper. Res., 215, pp. 740749.
  • [10] Z. Dahmani, (2010), On Minkowski and Hermite-Hadamard Integral Inequalities via Fractional Integration, Ann. Funct. Anal, 1 (1), pp. 51-58.
  • [11] S.S. Dragomir, C.E.M. Pearce, (2000), Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University.
  • [12] J. Hadamard, (1893), Etude sur les proprietes des fonctions entieres et en particulier d’une fonction consideree par Riemann, Journal des Mathematiques Pures et Appliquees, 58, pp. 171-215.
  • [13] Ch. Hermite, (1883), Sur deux limites d’une integrale define, Mathesis, 3, pp. 82.
  • [14] S. Kemali, I. Yesilce, G. Adilov, (2015), B-convexity, B −1 -convexity, and Their Comparison, Numerical Functional Analysis and Optimization, 36 (2), pp. 133-146.
  • [15] A. A. Kilbas, O. I. Marichev, S. G. Samko, (1993), Fractional Integrals and Derivatives. Theory and Applications, Gordon and Breach, Switzerland.
  • [16] C.P. Niculescu, L.-E. Persson, (2003), Old and New on the Hermite-Hadamard Inequality, Real Analysis Exchange, 29 (2), pp. 663-685.
  • [17] M.Z. Sarikaya, E. Set, H. Yaldiz, N. Basak, (2013), HermiteHadamards Inequalities for Fractional Integrals and Related Fractional Inequalities, Mathematical and Computer Modelling, 57 (9), pp. 2403-2407.
  • [18] G. Tinaztepe, I. Yesilce and G. Adilov, (2014), Separation of B −1−convex Sets by B −1−measurable Maps, Journal of Convex Analysis, 21 (2), pp. 571-580.
  • [19] I. Yesilce, (2018), Inequalities for B-convex Functions via Generalized Fractional Integral, Journal of Inequalities and Applications (submitted).
  • [20] I. Yesilce, G. Adilov, (2017), Hermite-Hadamard Inequalities for B-convex and B −1 -convex Functions, International Journal of Nonlinear Analysis and Applications, 8 (1), pp. 225-233.
Year 2019, Volume: 9 Issue: 3, 620 - 625, 01.09.2019

Abstract

References

  • [1] G. Adilov, (2011), Increasing Co-radiant Functions and Hermite-Hadamard Type Inequalities, Mathematical Inequalities and Applications, 14 (1), pp. 45-60.
  • [2] G. Adilov, S. Kemali, (2009), Abstract convexity and Hermite-Hadamard Type Inequalities, Journal of Inequalities and Applications, 2009, 13 pages.
  • [3] G. Adilov, S. Kemali, (2007), Hermite-Hadamard-Type Inequalities For Increasing Positively Homogeneous Functions, Journal of Inequalities and Applications, 2007, 10 pages.
  • [4] G. Adilov and A. Rubinov, (2006), B-convex Sets and Functions, Numerical Functional Analysis and Optimization, 27 (3-4), pp. 237-257.
  • [5] G. Adilov and G. Tinaztepe, (2009), The Sharpening of Some Inequalities via Abstract Convexity, Mathematical Inequalities and Applications, 12 (1), pp. 33-51.
  • [6] G. Adilov and I. Yesilce, (2017), B −1−convex Functions, Journal of Convex Analysis, 24 (2), pp. 505-517.
  • [7] G. Adilov and I. Yesilce, (2012), B −1−convex Sets and B −1−measurable Maps, Numerical Functional Analysis and Optimization, 33 (2), pp. 131-141.
  • [8] G. Adilov and I. Yesilce, (2012), On Generalization of the Concept of Convexity, Hacettepe Journal of Mathematics and Statistics, 41 (5), pp. 723-730.
  • [9] W. Briec, Q.B. Liang, (2011), On Some Semilattice Structures for Production Technologies, Eur. J. Oper. Res., 215, pp. 740749.
  • [10] Z. Dahmani, (2010), On Minkowski and Hermite-Hadamard Integral Inequalities via Fractional Integration, Ann. Funct. Anal, 1 (1), pp. 51-58.
  • [11] S.S. Dragomir, C.E.M. Pearce, (2000), Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University.
  • [12] J. Hadamard, (1893), Etude sur les proprietes des fonctions entieres et en particulier d’une fonction consideree par Riemann, Journal des Mathematiques Pures et Appliquees, 58, pp. 171-215.
  • [13] Ch. Hermite, (1883), Sur deux limites d’une integrale define, Mathesis, 3, pp. 82.
  • [14] S. Kemali, I. Yesilce, G. Adilov, (2015), B-convexity, B −1 -convexity, and Their Comparison, Numerical Functional Analysis and Optimization, 36 (2), pp. 133-146.
  • [15] A. A. Kilbas, O. I. Marichev, S. G. Samko, (1993), Fractional Integrals and Derivatives. Theory and Applications, Gordon and Breach, Switzerland.
  • [16] C.P. Niculescu, L.-E. Persson, (2003), Old and New on the Hermite-Hadamard Inequality, Real Analysis Exchange, 29 (2), pp. 663-685.
  • [17] M.Z. Sarikaya, E. Set, H. Yaldiz, N. Basak, (2013), HermiteHadamards Inequalities for Fractional Integrals and Related Fractional Inequalities, Mathematical and Computer Modelling, 57 (9), pp. 2403-2407.
  • [18] G. Tinaztepe, I. Yesilce and G. Adilov, (2014), Separation of B −1−convex Sets by B −1−measurable Maps, Journal of Convex Analysis, 21 (2), pp. 571-580.
  • [19] I. Yesilce, (2018), Inequalities for B-convex Functions via Generalized Fractional Integral, Journal of Inequalities and Applications (submitted).
  • [20] I. Yesilce, G. Adilov, (2017), Hermite-Hadamard Inequalities for B-convex and B −1 -convex Functions, International Journal of Nonlinear Analysis and Applications, 8 (1), pp. 225-233.
There are 20 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

I. Yesilce This is me

Publication Date September 1, 2019
Published in Issue Year 2019 Volume: 9 Issue: 3

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