Q integral inequalities pdf

In this paper, qcalculus analogues of some classical and some recent integral inequalities are found. There are qanalogs for the fractional, binomial coefficient, derivative, integral, fibonacci numbers and so on. In the article, we present several conformable fractional integrals versions of the hermitehadamard type inequalities for gg and gaconvex functions and provide their applications in special bivariate means. Quantum integral inequalities of simpsontype for strongly. Some weighted integral inequalities for differentiable. Our results, on the one hand, give a weighted generalization of recent results for preinvex functions and, on the other hand, extend several results connected with the hermitehadamard type integral inequalities. Pdf in the present paper, several qintegral inequalities are shown, which stem from f. The definite qintegral definzd above is too general for our purpose of studying inequalities. To rewrite an inequality, switch the numbers and reverse the direction of the inequality symbol. Quantum montgomery identity and some quantum integral inequalities.

In this paper, we present weighted integral inequalities of hermitehadamard type for differentiable preinvex and prequasiinvex functions. Quantum hermitehadamard inequalities for double integral. Consequently we have equality in 1 if, and only if. Integral inequalities play an essential role in the stability analysis of continuoustime systems with time delay. Otherwise, using the young inequality, we have jfxj kfk lp jgxj kgk. In the case of a closed curve it is also called a contour integral.

Finally, we prove the lyapunov inequality for the solutions of the qnon uniform sturm. If f or g is zero almost everywhere, then the second inequality is trivial. Type in any integral to get the solution, steps and graph this website. Fror 1 p q triangle inequality for arbitrarily many terms and integrals. The analysis relies on the notions of qderivative and qintegral on finite intervals introduced by the authors in tariboon and. In this paper, we consider a general form of nonlinear integral inequalities with the unknown function composed with a given function on the left hand side, more than one distinct nonlinear integrals on its ri. J ournal of mathematical i nequalities volume 3, number 1 2009, 115121 several q integral inequalities y u m iao and f eng q i communicated. Df fq the qderi vative reduces to the usual derivative as q 1.

The basic observation is the fact that f 0 and z x f d 0 imply f 0 almost everywhere. In this paper, we establish some new quantum analogue of hermitehadamard in. We establish some inequalities involving saigo fractionalqintegral operator in the theory of quantum calculus by using the two parameters of deformation,q1and q2, whose special cases are shown to yield corresponding inequalities associated with. There are other special symbols that show in what way things are not equal. Classical examples of such inequalities include hardys inequality and opia. Here, we aim to establish some new fractional qintegral inequality by using fractional qintegral operators. Quantum hermitehadamard inequalities for double integral and qdifferentiable convex functions julalakprabseang,kamsing nonlaopon andjessadatariboon abstract. Siyavulas open mathematics grade 11 textbook, chapter 2 on equations and inequalities covering quadratic inequalities. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. Some new fejer type inequalities via quantum calculus on. Previous asked questions with solutions for cat 2018.

Free integral calculator solve indefinite, definite and multiple integrals with all the steps. The applications pertain to relations among integrals involving first and second differences of lp functions. The aim of this problemoriented book is to present elementary techniques in the theory of inequalities. Topics in inequalities theorems and techniques hojoo lee. Conformable integral inequalities of the hermitehadamard. Pdf several qintegral inequalities feng qi academia. Applications to estimation of sums of some convergent. Pdf quantum integral inequalities on finite intervals researchgate. Integral inequalities via fractional quantum calculus. In this paper, we establish a new qintegral identity, the result is then used to derive two qintegral inequalities of simpsontype involving strongly preinvex functions. The purpose of this paper is to present a general integral inequality concerning subadditive functions and to make applications of this inequality.

If the minimum perimeter of the rectangle is 160 cm, then a breadth 20 cm b length qanalog, also called a qextension or qgeneralization is a mathematical expression parameterized by a quantity q that generalized a known expression and reduces to the known expression in the limit q 1. Pdf certain inequalities involving the fractional q. The function to be integrated may be a scalar field or a vector field. A line integral sometimes called a path integral is an integral where the function to be integrated is evaluated along a curve. Mildorf december 22, 2005 it is the purpose of this document to familiarize the reader with a wide range of theorems and techniques that can be used to solve inequalities of the variety typically appearing on mathematical olympiads or. Topics in inequalities theorems and techniques hojoo lee introduction inequalities are useful in all elds of mathematics. On some new weakly singular volterra integral inequalities with maxima and their applications. We define an l2 function by its fourier coefficients. From now on, we will use a special type of the definite qintegral, which we will call the restricted definite qintegral. Example 11 the length of a rectangle is three times the breadth. Introduction for 01 q, the qanalog of the derivative of the function f x, denoted by df xq is defined see 5 by,0 q 1 fx fqx df x x qx 1.

Applications to estimation of sums of some convergent series are also given. In recent years fractional qintegral inequalities have been investigated by many authors. In this chapter, we will focus on the study of integral inequalities. Recent developments of integral inequalities and its. There are examples of functions for which the left side of 4 is finite while the right side is infinite. The qcalculus analogs of some classical integral inequalities, such as holder, hermitehadamard. For example, if f x 2 0, it is not necessarily true that jab fx d,x 2 0. Some special cases of the obtained results are also considered, it is shown that several new and previously known results can be derived via generalized strongly preinvex functions and quantum integrals. Download fulltext pdf download fulltext pdf download. Linear inequalities 105 solution b is the correct choice. Quadratic inequalities equations and inequalities siyavula. So, developing an accurate integral inequality is of particular importance. Inequalities and modulus questions and answers for cat. Available formats pdf please select a format to send.