Browsing by Author "Sotiris K. Ntouyas"

Now showing 1 - 6 of 6
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    Fractional ostrowski type inequalities for differentiable harmonically convex functions
    (American Institute of Mathematical Sciences, 2022) Thanin Sitthiwirattham; Muhammad Aamir Ali; HŸseyin Budak; Sotiris K. Ntouyas; Chanon Promsakon; M.A. Ali; Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China; email: mahr.muhammad.aamir@gmail.com
    In this paper, we prove some new Ostrowski type inequalities for differentiable harmonically convex functions using generalized fractional integrals. Since we are using generalized fractional integrals to establish these inequalities, therefore we obtain some new inequalities of Ostrowski type for Riemann-Liouville fractional integrals and k-Riemann-Liouville fractional integrals in special cases. Finally, we give some applications to special means of real numbers for newly established inequalities. © 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0).
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    On a boundary value problem for fractional hahn integro-difference equations with four-point fractional integral boundary conditions
    (American Institute of Mathematical Sciences, 2022) Varaporn Wattanakejorn; Sotiris K. Ntouyas; Thanin Sitthiwirattham; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.th
    In this paper, we study a boundary value problem consisting of Hahn integro-difference equation supplemented with four-point fractional Hahn integral boundary conditions. The novelty of this problem lies in the fact that it contains two fractional Hahn difference operators and three fractional Hahn integrals with different quantum numbers and orders. Firstly, we convert the given nonlinear problem into a fixed point problem, by considering a linear variant of the problem at hand. Once the fixed point operator is available, we make use the classical BanachÕs and SchauderÕs fixed point theorems to establish existence and uniqueness results. An example is also constructed to illustrate the main results. Several properties of fractional Hahn integral that will be used in our study are also discussed. © 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0).
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    On some new inequalities of hermiteÐhadamard midpoint and trapezoid type for preinvex functions in (P, q)-calculus
    (MDPI, 2021) Ifra Bashir Sial; Muhammad Aamir Ali; Ghulam Murtaza; Sotiris K. Ntouyas; Jarunee Soontharanon; Thanin Sitthiwirattham; M.A. Ali; Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China; email: mahr.muhammad.aamir@gmail.com; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.th
    In this paper, we establish some new HermiteÐHadamard type inequalities for preinvex functions and left-right estimates of newly established inequalities for (p, q)-differentiable preinvex functions in the context of (p, q)-calculus. We also show that the results established in this paper are generalizations of comparable results in the literature of integral inequalities. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.
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    On some new trapezoidal type inequalities for twice (P, q) differentiable convex functions in post-quantum calculus
    (MDPI, 2021) Thanin Sitthiwirattham; Ghulam Murtaza; Muhammad Aamir Ali; Sotiris K. Ntouyas; Muhammad Adeel; Jarunee Soontharanon; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.th
    Quantum information theory, an interdisciplinary field that includes computer science, information theory, philosophy, cryptography, and symmetry, has various applications for quantum calculus. Inequalities has a strong association with convex and symmetric convex functions. In this study, first we establish a (p,q)-integral identity involving the second (p,q)-derivative and then we used this result to prove some new trapezoidal type inequalities for twice (p,q)-differentiable convex functions. It is also shown that the newly established results are the refinements of some existing results in the field of integral inequalities. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role. © 2021 by the authors.
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    Post-quantum simpsonÕs type inequalities for coordinated convex functions
    (American Institute of Mathematical Sciences, 2022) Xue-Xiao You; Muhammad Aamir Ali; Ghulam Murtaza; Saowaluck Chasreechai; Sotiris K. Ntouyas; Thanin Sitthiwirattham; M.A. Ali; Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China; email: mahr.muhammad.aamir@gmail.com; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.th
    In this paper, we prove some new SimpsonÕs type inequalities for partial (p, q)-differentiable convex functions of two variables in the context of (p, q)-calculus. We also show that the findings in this paper are generalizations of comparable findings in the literature. © 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0).
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    Separate fractional (P, q)-integrodifference equations via nonlocal fractional (p, q)-integral boundary conditions
    (MDPI, 2021) Thongchai Dumrongpokaphan; Sotiris K. Ntouyas; Thanin Sitthiwirattham; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.th
    In this paper, we study a boundary value problem involving (p, q)-integrodifference equations, supplemented with nonlocal fractional (p, q)-integral boundary conditions with respect to asymmetric operators. First, we convert the given nonlinear problem into a fixed-point problem, by considering a linear variant of the problem at hand. Once the fixed-point operator is available, existence and uniqueness results are established using the classical BanachÕs and SchaeferÕs fixedpoint theorems. The application of the main results is demonstrated by presenting numerical examples. Moreover, we study some properties of (p, q)-integral that are used in our study. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.