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GENERALIZATION MITTAG-LEFFLER FUNCTION ASSOCIATED WITH OF THE HADAMARD AND FEJER HADAMARD INEQUALITIES FOR (h-m)-STRONGLY CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS

Year 2019, , 8 - 15, 30.01.2019
https://doi.org/10.33773/jum.506507

Abstract

The aim of this paper, Hadamard and Fejer Hadamard _nequalities for (h -m)-strongly convex functions via
generalizeed fractional integral operators involving the generalized
Mittag-Le_er function are established. In particular several knows results are
mentioned.




References

  • Ozdemir M, Akdemri A, Set E. On (h - m)-convexity and hadamard-type inequalities. Transylvanian Journal of Mathematics and Mechanics. 2016;8(1):51- 58.Varosanec S. On h-convexity. Journal of Mathematical Analysis and Applications.2007;326(1):303-311.Kilbas A, Srivastava H, Trujillo J. Theory and applications of fractional di_erential equations. Elsevier, Amsterdam; 2006.C. R. Bector and C. Singh, B-Vex functions, J. Optim. Theory. Appl. 71 (2) (1991) 237-253Podlubni I. Fractional di_erential equations. Academic press. San Diego; 1999. Farid G. Weighted opial inequalities for fractional integral and di_erential operators involving generalized Mittag-Le_er function. European Journal of Pure and Applied Mathematics. 2017;10(3):419-439.Srivastava H, Tomovski Z. Fractional calculus with an integral operator containing generalized Mittagle_er function in the kernel. Applied Mathematics and Computation. 2009;211(1):198-210.Prabhakar T. A singular integral equation with a generalized Mittag-le_er function in the kernel. Yokohama Mathematical Journal. 1971;19:7-15. Chen F. On Hermite-Hadamard type inequalities for Riemann-Liouville fractional integrals via two kinds of convexity. Chinese Journal of Mathematics. 2014; Article ID 173293.Chen H, Katugampola U. Hermite-Hadamard-Fejr type inequalities for generalized fractional integrals. Journal of Mathematical Analysis and Applications. 2017;446:1274-1291.Farid G. A Treatment of the Hadamard inequality due to m- convexity via generalized fractional integral. Fractional Calculus and Applied Analysis. In press.Farid G, Rehman AU, Tariq B. On Hadamard-type inequalities for m-convex functions via Riemann-Liouville fractional integrals. Studia Universitatis Babes_-Bolyai Mathematica. 2017;62(2):141-150.Loverro A. Fractional calculus: history, de_nitions and applications for the engineers. Rapport technique. University of Notre Dame: Department of Aerospace and Mechanical Engineering. 2004:1-28.Arqub O, El-Ajou A, Momani S. Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial di_erential equations. Journal of Computational Physics. 2015;293:385-399.El-Ajou A, Arqub O, Momani S. Approximate analytical solution of the nonlinear fractional KdV-burgers equation : a new iterative algorithm. Journal of Computational Physics. 2015;293 :81-95.El-Ajou A, Arqub O, Momani S, Baleanu D, Alsaedi A. A novel expansion iterative method for solving linear partial di_erential equations of fractional order. Applied Mathematics and Computation. 2015;257:119-133.Arqub O. Fitted reproducing kernel hilbert space method for the solutions of some certain classes of time-fractional partial di_erential equations subject to initial and neumann boundary conditions. Computers & Mathematics with Applications. 2017;73:1243-1261.M. E.ozdemir, M. Avci and H. Kavurmaci, Hermite-Hadamard-type inequalities via ( _;m)- convexity. Comput. Math. Appl. 61 (2011), no. 9, 2614-2620Farid G. Hadamard and Fej _er-Hadamard inequalities for generalized fractional integral involving special functions. Konuralp Journal of Mathematics. 2016;4(1):108-113.Sarikaya M, Set E, Yaldiz H, Basak N. Hermite-Hadamards inequalities for fractional integrals and related fractional inequalities. Mathematical and Computer Modelling. 2013;57:2403- 2407.Sarikaya M, Yildirim H. On Hermite-Hadamard type inequalities for Riemann-Liouville fractional integrals. Miskolc Mathematical Notes. 2016;17(2):1049-1059.A. U. Rehman, G.Farid and Q.U. Ain Hadamard and Fej_er Hadamard Inequalities for (h -m)- Convex Functions Via Fractional Integral Containing the Generalized Mittag-Le_er Function Journal of Scienti_c Research reports 2018; 18(5); 1-8.
Year 2019, , 8 - 15, 30.01.2019
https://doi.org/10.33773/jum.506507

Abstract

References

  • Ozdemir M, Akdemri A, Set E. On (h - m)-convexity and hadamard-type inequalities. Transylvanian Journal of Mathematics and Mechanics. 2016;8(1):51- 58.Varosanec S. On h-convexity. Journal of Mathematical Analysis and Applications.2007;326(1):303-311.Kilbas A, Srivastava H, Trujillo J. Theory and applications of fractional di_erential equations. Elsevier, Amsterdam; 2006.C. R. Bector and C. Singh, B-Vex functions, J. Optim. Theory. Appl. 71 (2) (1991) 237-253Podlubni I. Fractional di_erential equations. Academic press. San Diego; 1999. Farid G. Weighted opial inequalities for fractional integral and di_erential operators involving generalized Mittag-Le_er function. European Journal of Pure and Applied Mathematics. 2017;10(3):419-439.Srivastava H, Tomovski Z. Fractional calculus with an integral operator containing generalized Mittagle_er function in the kernel. Applied Mathematics and Computation. 2009;211(1):198-210.Prabhakar T. A singular integral equation with a generalized Mittag-le_er function in the kernel. Yokohama Mathematical Journal. 1971;19:7-15. Chen F. On Hermite-Hadamard type inequalities for Riemann-Liouville fractional integrals via two kinds of convexity. Chinese Journal of Mathematics. 2014; Article ID 173293.Chen H, Katugampola U. Hermite-Hadamard-Fejr type inequalities for generalized fractional integrals. Journal of Mathematical Analysis and Applications. 2017;446:1274-1291.Farid G. A Treatment of the Hadamard inequality due to m- convexity via generalized fractional integral. Fractional Calculus and Applied Analysis. In press.Farid G, Rehman AU, Tariq B. On Hadamard-type inequalities for m-convex functions via Riemann-Liouville fractional integrals. Studia Universitatis Babes_-Bolyai Mathematica. 2017;62(2):141-150.Loverro A. Fractional calculus: history, de_nitions and applications for the engineers. Rapport technique. University of Notre Dame: Department of Aerospace and Mechanical Engineering. 2004:1-28.Arqub O, El-Ajou A, Momani S. Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial di_erential equations. Journal of Computational Physics. 2015;293:385-399.El-Ajou A, Arqub O, Momani S. Approximate analytical solution of the nonlinear fractional KdV-burgers equation : a new iterative algorithm. Journal of Computational Physics. 2015;293 :81-95.El-Ajou A, Arqub O, Momani S, Baleanu D, Alsaedi A. A novel expansion iterative method for solving linear partial di_erential equations of fractional order. Applied Mathematics and Computation. 2015;257:119-133.Arqub O. Fitted reproducing kernel hilbert space method for the solutions of some certain classes of time-fractional partial di_erential equations subject to initial and neumann boundary conditions. Computers & Mathematics with Applications. 2017;73:1243-1261.M. E.ozdemir, M. Avci and H. Kavurmaci, Hermite-Hadamard-type inequalities via ( _;m)- convexity. Comput. Math. Appl. 61 (2011), no. 9, 2614-2620Farid G. Hadamard and Fej _er-Hadamard inequalities for generalized fractional integral involving special functions. Konuralp Journal of Mathematics. 2016;4(1):108-113.Sarikaya M, Set E, Yaldiz H, Basak N. Hermite-Hadamards inequalities for fractional integrals and related fractional inequalities. Mathematical and Computer Modelling. 2013;57:2403- 2407.Sarikaya M, Yildirim H. On Hermite-Hadamard type inequalities for Riemann-Liouville fractional integrals. Miskolc Mathematical Notes. 2016;17(2):1049-1059.A. U. Rehman, G.Farid and Q.U. Ain Hadamard and Fej_er Hadamard Inequalities for (h -m)- Convex Functions Via Fractional Integral Containing the Generalized Mittag-Le_er Function Journal of Scienti_c Research reports 2018; 18(5); 1-8.
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Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Seda Kılınç This is me

Abdullah Akkurt

Hüseyin Yıldırım

Publication Date January 30, 2019
Submission Date January 2, 2019
Acceptance Date January 26, 2019
Published in Issue Year 2019

Cite

APA Kılınç, S., Akkurt, A., & Yıldırım, H. (2019). GENERALIZATION MITTAG-LEFFLER FUNCTION ASSOCIATED WITH OF THE HADAMARD AND FEJER HADAMARD INEQUALITIES FOR (h-m)-STRONGLY CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS. Journal of Universal Mathematics, 2(1), 8-15. https://doi.org/10.33773/jum.506507
AMA Kılınç S, Akkurt A, Yıldırım H. GENERALIZATION MITTAG-LEFFLER FUNCTION ASSOCIATED WITH OF THE HADAMARD AND FEJER HADAMARD INEQUALITIES FOR (h-m)-STRONGLY CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS. JUM. January 2019;2(1):8-15. doi:10.33773/jum.506507
Chicago Kılınç, Seda, Abdullah Akkurt, and Hüseyin Yıldırım. “GENERALIZATION MITTAG-LEFFLER FUNCTION ASSOCIATED WITH OF THE HADAMARD AND FEJER HADAMARD INEQUALITIES FOR (h-M)-STRONGLY CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS”. Journal of Universal Mathematics 2, no. 1 (January 2019): 8-15. https://doi.org/10.33773/jum.506507.
EndNote Kılınç S, Akkurt A, Yıldırım H (January 1, 2019) GENERALIZATION MITTAG-LEFFLER FUNCTION ASSOCIATED WITH OF THE HADAMARD AND FEJER HADAMARD INEQUALITIES FOR (h-m)-STRONGLY CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS. Journal of Universal Mathematics 2 1 8–15.
IEEE S. Kılınç, A. Akkurt, and H. Yıldırım, “GENERALIZATION MITTAG-LEFFLER FUNCTION ASSOCIATED WITH OF THE HADAMARD AND FEJER HADAMARD INEQUALITIES FOR (h-m)-STRONGLY CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS”, JUM, vol. 2, no. 1, pp. 8–15, 2019, doi: 10.33773/jum.506507.
ISNAD Kılınç, Seda et al. “GENERALIZATION MITTAG-LEFFLER FUNCTION ASSOCIATED WITH OF THE HADAMARD AND FEJER HADAMARD INEQUALITIES FOR (h-M)-STRONGLY CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS”. Journal of Universal Mathematics 2/1 (January 2019), 8-15. https://doi.org/10.33773/jum.506507.
JAMA Kılınç S, Akkurt A, Yıldırım H. GENERALIZATION MITTAG-LEFFLER FUNCTION ASSOCIATED WITH OF THE HADAMARD AND FEJER HADAMARD INEQUALITIES FOR (h-m)-STRONGLY CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS. JUM. 2019;2:8–15.
MLA Kılınç, Seda et al. “GENERALIZATION MITTAG-LEFFLER FUNCTION ASSOCIATED WITH OF THE HADAMARD AND FEJER HADAMARD INEQUALITIES FOR (h-M)-STRONGLY CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS”. Journal of Universal Mathematics, vol. 2, no. 1, 2019, pp. 8-15, doi:10.33773/jum.506507.
Vancouver Kılınç S, Akkurt A, Yıldırım H. GENERALIZATION MITTAG-LEFFLER FUNCTION ASSOCIATED WITH OF THE HADAMARD AND FEJER HADAMARD INEQUALITIES FOR (h-m)-STRONGLY CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS. JUM. 2019;2(1):8-15.