38 research outputs found

    Some New Hermite–Hadamard Type Inequalities Pertaining to Generalized Multiplicative Fractional Integrals

    Get PDF
    There is significant interaction between the class of symmetric functions and other types of functions. The multiplicative convex function class, which is intimately related to the idea of symmetry, is one of them. In this paper, we obtain some new generalized multiplicative fractional Hermite–Hadamard type inequalities for multiplicative convex functions and for their product. Additionally, we derive a number of inequalities for multiplicative convex functions related to generalized multiplicative fractional integrals utilising a novel identity as an auxiliary result. We provide some examples for the appropriate selections of multiplicative convex functions and their graphical representations to verify the authenticity of our main results.Basque Government: Grants IT1555-22 and KK-2022/00090; and MCIN/AEI 269.10.13039/501100011033 for Grant PID2021-1235430B-C21/C22

    On Ostrowski–Mercer’s Type Fractional Inequalities for Convex Functions and Applications

    Get PDF
    This research focuses on the Ostrowski–Mercer inequalities, which are presented as variants of Jensen’s inequality for differentiable convex functions. The main findings were effectively composed of convex functions and their properties. The results were directed by Riemann–Liouville fractional integral operators. Furthermore, using special means, q-digamma functions and modified Bessel functions, some applications of the acquired results were obtained.Basque Government: Grants IT1555-22 and KK-2022/00090; and MCIN/AEI 269.10.13039/501100011033 for Grant PID2021-1235430B-C21/C22

    Fractional Hermite-Hadamard integral inequalities for a new class of convex functions

    Get PDF
    Fractional integral inequality plays a significant role in pure and applied mathematicsfields. It aims to develop and extend various mathematical methods. Therefore, nowadays weneed to seek accurate fractional integral inequalities in obtaining the existence and uniqueness of thefractional methods. Besides, the convexity theory plays a concrete role in the field of fractional integralinequalities due to the behavior of its definition and properties. There is also a strong relationshipbetween convexity and symmetric theories. So, whichever one we work on, we can then apply itto the other one due to the strong correlation produced between them, specifically in the last fewdecades. First, we recall the definition ofφ-Riemann–Liouville fractional integral operators and therecently defined class of convex functions, namely the ̆σ-convex functions. Based on these, we willobtain few integral inequalities of Hermite–Hadamard’s type for a ̆σ-convex function with respectto an increasing function involving theφ-Riemann–Liouville fractional integral operator. We canconclude that all derived inequalities in our study generalize numerous well-known inequalitiesinvolving both classical and Riemann–Liouville fractional integral inequalities. Finally, application tocertain special functions are pointed out

    On Hermite-Hadamard-Fejér type inequalities for convex functions via fractional integrals

    Full text link

    Fractional Calculus Operators and the Mittag-Leffler Function

    Get PDF
    This book focuses on applications of the theory of fractional calculus in numerical analysis and various fields of physics and engineering. Inequalities involving fractional calculus operators containing the Mittag–Leffler function in their kernels are of particular interest. Special attention is given to dynamical models, magnetization, hypergeometric series, initial and boundary value problems, and fractional differential equations, among others

    Advances in Optimization and Nonlinear Analysis

    Get PDF
    The present book focuses on that part of calculus of variations, optimization, nonlinear analysis and related applications which combines tools and methods from partial differential equations with geometrical techniques. More precisely, this work is devoted to nonlinear problems coming from different areas, with particular reference to those introducing new techniques capable of solving a wide range of problems. The book is a valuable guide for researchers, engineers and students in the field of mathematics, operations research, optimal control science, artificial intelligence, management science and economics

    Inequalities for α-fractional differentiable functions

    Get PDF
    Abstract In this article, we present an identity and several Hermite-Hadamard type inequalities for conformable fractional integrals. As applications, we establish some inequalities for certain special means of two positive real numbers and give the error estimations for the trapezoidal formula

    Hermite–Hadamard Type Inequalities Involving k-Fractional Operator for (h¯,m)-Convex Functions

    Get PDF
    The principal motivation of this paper is to establish a new integral equality related to k-Riemann Liouville fractional operator. Employing this equality, we present several new inequalities for twice differentiable convex functions that are associated with Hermite–Hadamard integral inequality. Additionally, some novel cases of the established results for different kinds of convex functions are derived. This fractional integral sums up Riemann–Liouville and Hermite–Hadamard’s inequality, which have a symmetric property. Scientific inequalities of this nature and, particularly, the methods included have applications in different fields in which symmetry plays a notable role. Finally, applications of q-digamma and q -polygamma special functions are presented.This work was funded by the Basque Government for Grant IT1207-19

    Integral inequalities of hermite-hadamard type and their applications

    Get PDF
    A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, South Africa, in fulfilment of the requirements for the degree of Doctor of Philosophy. Johannesburg, 17 October 2016.The role of mathematical inequalities in the growth of different branches of mathematics as well as in other areas of science is well recognized in the past several years. The uses of contributions of Newton and Euler in mathematical analysis have resulted in a numerous applications of modern mathematics in physical sciences, engineering and other areas sciences and hence have employed a dominat effect on mathematical inequalities. Mathematical inequalities play a dynamic role in numerical analysis for approximation of errors in some quadrature rules. Speaking more specifically, the error approximation in quadrature rules such as the mid-point rule, trapezoidal rule and Simpson rule etc. have been investigated extensively and hence, a number of bounds for these quadrature rules in terms of at most second derivative are proven by a number of researchers during the past few years. The theorey of mathematical inequalities heavily based on theory of convex functions. Actually, the theory of convex functions is very old and its commencement is found to be the end of the nineteenth century. The fundamental contributions of the theory of convex functions can be found in the in the works of O. Hölder [50], O. Stolz [151] and J. Hadamard [48]. At the beginning of the last century J. L. W. V. Jensen [72] first realized the importance convex functions and commenced the symmetric study of the convex functions. In years thereafter this research resulted in the appearance of the theory of convex functions as an independent domain of mathematical analysis. Although, there are a number of results based on convex function but the most celebrated results about convex functions is the Hermite-Hadamard inequality, due to its rich geometrical significance and many applications in the theory of means and in numerical analysis. A huge number of research articles have been written during the last decade by a number of mathematicians which give new proofs, generalizations, extensions and refitments of the Hermite-Hadamard inequality. Applications of the results for these classes of functions are given. The research upshots of this thesis make significant contributions in the theory of means and the theory of inequalities.MT 201

    Fejér and Hermite-Hadamard Type Inequalities for Harmonically Convex Functions

    Get PDF
    We establish a Fejér type inequality for harmonically convex functions. Our results are the generalizations of some known results. Moreover, some properties of the mappings in connection with Hermite-Hadamard and Fejér type inequalities for harmonically convex functions are also considered
    corecore