Hermite-Hadamard Inequalities for Generalized $\zeta -$Conformable Integrals Generated by Co-Ordinated Functions

Year 2025, Volume: 13 Issue: 1, 36 - 53, 08.03.2025

Sümeyye Ermeydan Çiriş , Hüseyin Yıldırım

https://doi.org/10.36753/mathenot.1500238

Abstract

In this article, we introduce generalized $\zeta -$ conformable fractional integrals on co-ordinated functions and for the functions of two variables. Additionally, we derive a new Hermite-Hadamard inequality by utilizing the generalized Riemann-Liouville integrals, utilizing the generalized $\zeta -$conformable integral definition. Furthermore, we demonstrate some implications of the Hermite-Hadamard inequality and definitions introduced in this study. Consequently, we state and prove several related inequalities.

Keywords

Co-ordinated functions, Generalized conformable integrals, Hermite-Hadamard inequality

References

• [1] Sarikaya, M. Z., Büyükeken, M., Kiriş, M. E.: On some generalized integral inequalities for φ−convex functions. Studia Universitatis Babeş-Bolyai Mathematica. 60(3), 367-377 (2015).
• [2] Cristescu, G.: Hadamard type inequalities for ϕ-convex functions. Annals of the University of Oradea, Fascicle of Management and Technological Engineering, C-Rom Edition, III (XIII), (2004).
• [3] Akkurt, A., Sarikaya, M. Z., Budak, Yildirim, H.: On the Hadamard’s type inequalities for co-ordinated convex functions via fractional integrals. Journal of King Saud University-Science. 29(2017), 380-387 (2017).
• [4] Sarikaya, M. Z., Set, E., Ozdemir, M. E., Dragomir, S. S.: New some Hadamard’s type inequalities for co-ordinated convex functions. Tamsui Oxford Journal of Mathematical Sciences. 28(2), 137-152 (2012).
• [5] Bakula, M. K.: An improvement of the Hermite-Hadamard inequality for functions convex on the coordinates. Australian Journal of Mathematical Analysis and Applications. 11( 1), 1-7 (2014).
• [6] Set, E., Sarıkaya, M.Z., Akdemir, A. O.: Hadamard type inequalities for φ−convex functions on the co-ordinates. Tbilisi Mathematical Journal. 7(2), 51-60 (2014).
• [7] Yıldırım, H., Kırtay, Z.: Ostrowski inequality for generalized fractional integral and related inequalities. Malaya Journal of Matematik. 2(3), 322-329 (2014).
• [8] Kaçar, E., Kaçar, Z., Yildirim, H.: Integral inequalities for Riemann-Liouville fractional integral of a function with respect to another function. Iranian Journal of Mathematical Sciences and Informatics. 13, 1-13 (2018).
• [9] Bozkurt, M., Akkurt, A., Yildirim, H.: Conformable derivatives and integrals for the functions of two variables. Konuralp Journal of Mathematics. 9(1), 49-59 (2021).
• [10] Sarikaya, M. Z.: On the Hermite-Hadamard-type inequalities for co-ordinated convex function via fractional integral. Integral Transforms and Special Functions. 25(2), 134-147 (2014).
• [11] Kiriş, M.E., Bayrak, G.: New version of Hermite-Hadamard inequality for co-ordinated convex function via generalized conformable integrals. Filomat. 38(16), 5575-5589 (2024).
• [12] Çiriş, S. E., Yildirim, H.: Hermite-Hadamard inequalities for generalized σ−conformable integrals generated by co-ordinated functions. Chaos, Solitons & Fractals. 181, 114628 (2024).
• [13] Hyder, A. A., Almoneef, A. A., Budak, H., Barakat, M. A.: On new fractional version of generalized Hermite- Hadamard inequalities. Mathematics. 10(18), 33-37 (2022).
• [14] Celik, B., Set, E., Akdemir, A. O., Ozdemir, M. E.: Novel Generalizations for Gruss type inequalities pertaining to the constant proportional fractional integrals. Applied and Computational Mathematics. 22(2), 275-291 (2023).
• [15] Yıldız, C., Bakan, E., Donmez, H. : New general inequalities for exponential type convex function. Turkish Journal of Science. 8(1), 11-18 (2023).
• [16] Andric, M.: Fejer type inequalities for (h, g; m)-convex functions. TWMS Journal of Pure and Applied Mathematics. 14(2), 185-194 (2023).
• [17] Desta, H. D., Budak, H., Kara, H.: New perspectives on fractional Milne-type inequalities: Insights from twice-differentiable functions. Universal Journal of Mathematics and Applications. 7(1), 30-37 (2024).
• [18] Dragomir, S.: Refinements and reverses of tensorial and Hadamard product inequalities for Selfadjoint operators in Hilbert Spaces related to Young’s result. Communications in Advanced Mathematical Sciences. 7(1), 56-70 (2024).
• [19] Turker, R. Kavurmacı, Onalan, H.: Generalized inequalities for Quasi-Convex functions via generalized Riemann-Liouville fractional integrals. Turkish Journal of Science.7(3), 219-230 (2022).
• [20] Kırmacı, U. S.: On some Cauchy type mean-value theorems with applications. Communications in Advanced Mathematical Sciences. 7(3), 147-156 (2024).