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

Yıl 2019, Cilt: 9 Sayı: 1, 142 - 150, 01.03.2019

Ahmet Ocak Akdemir Erhan Set Alper Ekinci

Öz

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.

Anahtar Kelimeler

Convex function, s-convex function, Hermite-Hadamard type inequalities, new conformable fractional integral.

Kaynakça

• 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.