Browsing by Author "Michal Fe_kan"

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    A new Approach of Generalized Fractional Integrals in Multiplicative Calculus and Related Hermite-Hadamard-Type Inequalities with Applications
    (Walter de Gruyter GmbH, 2024) Muhammad Aamir Ali; Michal Fe_kan; Chanon Promsakon; Thanin Sitthiwirattham; M. Fe_kan; Department of Mathematical Analysis and Numerical Mathematics, Comenius University in Bratislava, Bratislava, Mlynsk‡ dolina, 842 48, Slovakia; email: michal.feckan@fmph.uniba.sk
    The primary goal of this paper is to define Katugampola fractional integrals in multiplicative calculus. A novel method for generalizing the multiplicative fractional integrals is the Katugampola fractional integrals in multiplicative calculus. The multiplicative Hadamard fractional integrals are also novel findings of this research and may be derived from the special situations of Katugampola fractional integrals. These integrals generalize to multiplicative Riemann-Liouville fractional integrals and multiplicative Hadamard fractional integrals. Moreover, we use the Katugampola fractional integrals to prove certain new Hermite-Hadamard and trapezoidal-type inequalities for multiplicative convex functions. Additionally, it is demonstrated that several of the previously established inequalities are generalized from the newly derived inequalities. Finally, we give some computational analysis of the inequalities proved in this paper. © 2024 Mathematical Institute Slovak Academy of Sciences.
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    FRACTIONAL HERMITE-HADAMARD INEQUALITY AND ERROR ESTIMATES FOR SIMPSONÕS FORMULA THROUGH CONVEXITY WITH RESPECT TO A PAIR OF FUNCTIONS
    (University of Miskolc, 2023) Muhammad Aamir Ali; Jarunee Soontharanon; HŸseyin Budak; Thanin Sitthiwirattham; Michal Fe_kan; M. Fe_kan; Department of Mathematical Analysis and Numerical Mathematics, Comenius University in Bratislava, Bratislava, Mlynsk‡ dolina, 842 48, Slovakia; email: michal.feckan@fmph.uniba.sk
    In this article, we establish two new and different versions of fractional Hermite-Hadamard type inequality for the convex functions with respect to a pair of functions. Moreover, we establish a new SimpsonÕs type inequalities for differentiable convex functions with respect to a pair of functions. We also prove two more SimpsonÕs type inequalities for differentiable convex functions with respect to a pair of functions using the power mean and HšlderÕs inequalities. It is also shown that the newly established inequalities are the extension of some existing results. Finally, we add some mathematical examples and their graphs to show the validity of newly established results. © 2023 Miskolc University Press
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    FRACTIONAL HERMITEÐHADAMARD INEQUALITY, SIMPSONÕS AND OSTROWSKIÕS TYPE INEQUALITIES FOR CONVEX FUNCTIONS WITH RESPECT TO A PAIR OF FUNCTIONS
    (Rocky Mountain Mathematics Consortium, 2023) Jianqiang Xie; Muhammad Aamir Ali; HŸseyin Budak; Michal Fe_kan; Thanin Sitthiwirattham; M.A. Ali; School of Mathematical Sciences, Nanjing Normal University, Nanjing, China; email: mahr.muhammad.aamir@gmail.com
    We consider the convexity with respect to a pair of functions and establish a HermiteÐHadamard type inequality for RiemannÐLiouville fractional integrals. Moreover, we derive some new SimpsonÕs and OstrowskiÕs type inequalities for differentiable convex mapping with respect to a pair of functions. We also show that the newly established inequalities are the extension of some existing inequalities. Finally, we consider some mathematical examples and graphs to show the validity of the newly established inequalities. © Rocky Mountain Mathematics Consortium.
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    On some NewtonÕs type inequalities for differentiable convex functions via Riemann-Liouville fractional integrals
    (University of Nis, 2023) Muhammad Aamir Ali; HŸseyin Budak; Michal Fe_kan; Nichaphat Patanarapeelert; Thanin Sitthiwirattham
    In this paper, we establish a new integral identity involving Riemann-Liouville fractional integrals and differentiable functions. Then, we use the newly established identity and prove several NewtonÕs type inequalities for differentiable convex functions and functions of bounded variation. Moreover, we give a mathematical example and graphical analysis of newly established inequalities to show their validity. © 2023, University of Nis. All rights reserved.