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

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

Hermite-hadamard type integral inequalities for convex functions and their applications

In this paper we establish new generalizations of Hermite-Hadamard type inequalitie

Symmetry in the Mathematical Inequalities

This Special Issue brings together original research papers, in all areas of mathematics, that are concerned with inequalities or the role of inequalities. The research results presented in this Special Issue are related to improvements in classical inequalities, highlighting their applications and promoting an exchange of ideas between mathematicians from many parts of the world dedicated to the theory of inequalities. This volume will be of interest to mathematicians specializing in inequality theory and beyond. Many of the studies presented here can be very useful in demonstrating new results. It is our great pleasure to publish this book. All contents were peer-reviewed by multiple referees and published as papers in our Special Issue in the journal Symmetry. These studies give new and interesting results in mathematical inequalities enabling readers to obtain the latest developments in the fields of mathematical inequalities. Finally, we would like to thank all the authors who have published their valuable work in this Special Issue. We would also like to thank the editors of the journal Symmetry for their help in making this volume, especially Mrs. Teresa Yu

Some well known inequalities for (h1, h2)-convex stochastic process via interval set inclusion relation

This note introduces the concept of (h1, h2)-convex stochastic processes using intervalvalued functions. First we develop Hermite-Hadmard (H.H) type inequalities, then we check the results for the product of two convex stochastic process mappings, and finally we develop Ostrowski and Jensen type inequalities for (h1, h2)-convex stochastic process. Also, we have shown that this is a more generalized and larger class of convex stochastic processes with some remark. Furthermore, we validate our main findings by providing some non-trivial examples.http://www.aimspress.com/journal/MathMathematics and Applied Mathematic

Computation of Generalized Averaged Gaussian Quadrature Rules

The estimation of the quadrature error of a Gauss quadrature rule when applied to the approximation of an integral determined by a real-valued integrand and a real-valued nonnegative measure with support on the real axis is an important problem in scientific computing. Laurie [2] developed anti-Gauss quadrature rules as an aid to estimate this error. Under suitable conditions the Gauss and associated anti-Gauss rules give upper and lower bounds for the value of the desired integral. It is then natural to use the average of Gauss and anti-Gauss rules as an improved approximation of the integral. Laurie also introduced these averaged rules. More recently, the author derived new averaged Gauss quadrature rules that have higher degree of exactness for the same number of nodes as the averaged rules proposed by Laurie. In [2], [5], [3] stable numerical procedures for computation of the corresponding averaged Gaussian rules are proposed. An analogous procedure can be applied also for a more general class of weighted averaged Gaussian rules introduced in [1]. Those results are presented in [4]. Here we we give a survey of the quoted results, which are obtained jointly with L. Reichel (Kent State Univ., OH (U.S.)

Integral inequalities of hermite-hadamard type and their applications

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

Inequalities

Inequalities appear in various fields of natural science and engineering. Classical inequalities are still being improved and/or generalized by many researchers. That is, inequalities have been actively studied by mathematicians. In this book, we selected the papers that were published as the Special Issue ‘’Inequalities’’ in the journal Mathematics (MDPI publisher). They were ordered by similar topics for readers’ convenience and to give new and interesting results in mathematical inequalities, such as the improvements in famous inequalities, the results of Frame theory, the coefficient inequalities of functions, and the kind of convex functions used for Hermite–Hadamard inequalities. The editor believes that the contents of this book will be useful to study the latest results for researchers of this field

Advances in Optimization and Nonlinear Analysis

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