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    New version of midpoint-type inequalities for co-ordinated convex functions via generalized conformable integrals
    (Springer, 2024) Kiris, Mehmet Eyup; Vivas-Cortez, Miguel; Uzun, Tugba Yalcin; Bayrak, Gozde; Budak, Hüseyin
    In the current research, some midpoint-type inequalities are generalized for co-ordinated convex functions with the help of generalized conformable fractional integrals. Moreover, some findings of this paper include results based on Riemann-Liouville fractional integrals and Riemann integrals.
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    On Fejer type inequalities for co-ordinated hyperbolic rho-convex functions
    (Amer Inst Mathematical Sciences-Aims, 2020) Kara, Hasan; Budak, Hüseyin; Kiris, Mehmet Eyup
    In this study, we first establish some Hermite-Hadamard-Fejer type inequalities for coordinated hyperbolic rho-convex functions. Then, by utilizing these inequalities, we also give some fractional Fejer type inequalities for co-ordinated hyperbolic rho-convex functions. The inequalities obtained in this study provide generalizations of some result given in earlier works.
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    On Hermite-Hadamard type inequalities for co-ordinated convex function via conformable fractional integrals
    (Amer Inst Mathematical Sciences-Aims, 2024) Kiris, Mehmet Eyup; Vivas-Cortez, Miguel; Bayrak, Gozde; Cmar, Tugba; Budak, Hüseyin
    In this study, some new Hermite-Hadamard type inequalities for co-ordinated convex functions were obtained with the help of conformable fractional integrals. We have presented some remarks to give the relation between our results and earlier obtained results. Moreover, an identity for partial differentiable functions has been established. By using this equality and concept of co-ordinated convexity, we have proven a trapezoid type inequality for conformable fractional integrals.
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    On Hermite-Hadamard type inequalities for co-ordinated trigonometrically rho-convex functions
    (Tbilisi Centre Math Sci, 2020) Budak, Hüseyin; Kara, Hasan; Kiris, Mehmet Eyup
    In this study, we first introduce the co-ordinated trigonometrically rho-convex functions. Then we establish some Hermite-Hadamard type inequalities for this kind of functions. We also give refinement of the obtained inequalities by using the result given by Budak. The inequalities obtained in this study provide generalizations of some result given in earlier works.