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ON NEW CONFORMABLE FRACTIONAL INTEGRAL INEQUALITIES FOR PRODUCT OF DIFFERENT KINDS OF CONVEXITY

Year 2019, Volume: 9 Issue: 1, 142 - 150, 01.03.2019

Abstract

Certain Hermite-Hadamard type inequalities involving various fractional integral operators for products of two functions have, recently, been presented. We aim to establish several Hermite-Hadamard type inequalities for products of two convex and s-convex functions via new conformable fractional integral operators.

References

  • Abdeljawad, T., (2015), On conformable fractional calculus, Journal of Computational and Applied Mathematics, 279, 57-66.
  • Avci, M., Kavurmaci, H., ¨Ozdemir, M.E., (2011), New inequalities of HermiteHadamard type via s-convex functions in the second sense with applications, Applied Mathematics and Computation, 217(12), 5171-5176.
  • Breckner, W.W., (1978), Stetigkeitsaussagen fr eine Klasse verallgemeinerter konvexer funktionen in topologischen linearen Raumen, Pupl. Inst. Math. 23, 1320.
  • Chen, F., and Wu, S., (2016), Several complementary inequalities to inequalities of Hermite-Hadamard type for s-convex functions, J. Nonlinear Sci. Appl., 9, 705-716.
  • Dragomir, W.W. and Fitzpatrik, S., (1999), The Hadamard’s inequality for s -convex functions in the second sense, Demonstratio Math. 32(4), 687-696.
  • Hudzik, H., Maligranda, L., (1994), Some remarks on s-convex functions, Aequationes Math. 48, 100-111.
  • Jarad, F., U˘gurlu, E., Abdeljawad, T. and Baleanu, D., (2017), On a new class of fractional operators, Advances in Difference Equations, (1), 2017:247, DOI 10.1186/s13662-017-1306-z.
  • Katugampola, U.N., (2014), New approach to generalized fractional derivatives, Bull. Math. Anal. Appl., 6(4), 1-15.
  • Kilbas, A. A., (2001), Hadamard-type fractional calculus, Journal of the Korean Mathematical Society 38(6), 1191-1204.
  • Rainville, E.D., (1960),Special Functions, The Mcmillan Company, New York.
  • Set, E. and C¸ elik, B., (2017), Certain Hermite-Hadamard type inequalities associated with conformable fractional integral operators, Creative Math. Inform., 26(3), 321-330.
  • Set, E., Akdemir, A.O., Mumcu, ˙I., (2018), The Hermite-Hadamard’s inequaly and its extentions for conformable fractional integrals of any order α > 0, Creative Math. Inform., 27(2), 197-206.
  • Set, E., G¨ozpınar, A., Mumcu, A., (2018), The Hermite-Hadamard Inequality For s-convex Functions In The Second Sense Via Conformable Fractional Integrals And Related Inequalities, Thai J. Math., accepted.
  • Set, E., Akdemir, A., C¸ elik, B., (2016), Some Hermite-Hadamard Type Inequalities for Products of Two Different Convex Functions via Conformable Fractional Integrals, X. Statistical Days, 11-15 November 2016, Giresun-Turkey.
  • Srivastava, H.M. and Choi, J., (2012), Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Science Publishers, Amsterdam, London and New York.
Year 2019, Volume: 9 Issue: 1, 142 - 150, 01.03.2019

Abstract

References

  • Abdeljawad, T., (2015), On conformable fractional calculus, Journal of Computational and Applied Mathematics, 279, 57-66.
  • Avci, M., Kavurmaci, H., ¨Ozdemir, M.E., (2011), New inequalities of HermiteHadamard type via s-convex functions in the second sense with applications, Applied Mathematics and Computation, 217(12), 5171-5176.
  • Breckner, W.W., (1978), Stetigkeitsaussagen fr eine Klasse verallgemeinerter konvexer funktionen in topologischen linearen Raumen, Pupl. Inst. Math. 23, 1320.
  • Chen, F., and Wu, S., (2016), Several complementary inequalities to inequalities of Hermite-Hadamard type for s-convex functions, J. Nonlinear Sci. Appl., 9, 705-716.
  • Dragomir, W.W. and Fitzpatrik, S., (1999), The Hadamard’s inequality for s -convex functions in the second sense, Demonstratio Math. 32(4), 687-696.
  • Hudzik, H., Maligranda, L., (1994), Some remarks on s-convex functions, Aequationes Math. 48, 100-111.
  • Jarad, F., U˘gurlu, E., Abdeljawad, T. and Baleanu, D., (2017), On a new class of fractional operators, Advances in Difference Equations, (1), 2017:247, DOI 10.1186/s13662-017-1306-z.
  • Katugampola, U.N., (2014), New approach to generalized fractional derivatives, Bull. Math. Anal. Appl., 6(4), 1-15.
  • Kilbas, A. A., (2001), Hadamard-type fractional calculus, Journal of the Korean Mathematical Society 38(6), 1191-1204.
  • Rainville, E.D., (1960),Special Functions, The Mcmillan Company, New York.
  • Set, E. and C¸ elik, B., (2017), Certain Hermite-Hadamard type inequalities associated with conformable fractional integral operators, Creative Math. Inform., 26(3), 321-330.
  • Set, E., Akdemir, A.O., Mumcu, ˙I., (2018), The Hermite-Hadamard’s inequaly and its extentions for conformable fractional integrals of any order α > 0, Creative Math. Inform., 27(2), 197-206.
  • Set, E., G¨ozpınar, A., Mumcu, A., (2018), The Hermite-Hadamard Inequality For s-convex Functions In The Second Sense Via Conformable Fractional Integrals And Related Inequalities, Thai J. Math., accepted.
  • Set, E., Akdemir, A., C¸ elik, B., (2016), Some Hermite-Hadamard Type Inequalities for Products of Two Different Convex Functions via Conformable Fractional Integrals, X. Statistical Days, 11-15 November 2016, Giresun-Turkey.
  • Srivastava, H.M. and Choi, J., (2012), Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Science Publishers, Amsterdam, London and New York.
There are 15 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Ahmet Ocak Akdemir This is me

Erhan Set This is me

Alper Ekinci This is me

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

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