As indicated by Pachpatte [15], this result has been frequently used by authors to obtain global existence, uniqueness and stability of solutions of various nonlinear integral and differential equations. On the other hand, Theorem 1.1 has also been extended and generalized by many authors; see, for example, the reference [2, 3, 6, 7, 8, 9, 13, 14, 15, 17, 18]. Like Gronwall type inequalities, (...

The fuzzy integrals are a kind of fuzzy measures acting on fuzzy sets. They can be viewed as an average membershipvalue of fuzzy sets. The value of the fuzzy integral in a decision making environment where uncertainty is presenthas been well established. Most of the integral inequalities studied in the fuzzy integration context normally considerconditions such as monotonicity or comonotonicity....

The integral inequalities play a fundamental role in the study of existence, uniqueness, boundedness, stability, invariant manifolds, and other qualitative properties of solutions of the theory of differential and integral equations. There are a lot of papers investigating them such as [1–8]. In particular, Pachpatte [2] discovered some new integral inequalities involving functions of two varia...

Abstract. We discuss the inequalities for q-integrals because of the fact that the inequalities can be very useful in the future mathematical research. Since q-integral of a function over an interval [a, b] is defined by the difference of two infinite sums, there a lot of unexpected troubles in analyzing analogs of well-known integral inequalities. In this paper, we will signify to some directi...

It is well known that the integral inequalities involving functions of one and more than one independent variables which provide explicit bounds on unknown functions play a fundamental role in the development of the theory of differential equations. In the past few years, a number of integral inequalities had been established by many scholars, which are motivated by certain applications. For de...

Recently, a general class of the Hermit--Hadamard-Fejer inequality on convex functions is studied in [H. Budak, March 2019, 74:29, textit{Results in Mathematics}]. In this paper, we establish a generalization of Hermit--Hadamard--Fejer inequality for fractional integral based on co-ordinated convex functions.Our results generalize and improve several inequalities obtained in earlier studies.

In this paper we study systems of the form b ≤ Mx ≤ d, l ≤ x ≤ u, where M is obtained from a totally unimodular matrix with two nonzero elements per row by multiplying by 2 some of its columns, and b, d, l, u are integral vectors. We give an explicit description of a totally dual integral system that describes the integer hull of the polyhedron P defined by the above inequalities. Since the ine...

Muhammad I. Bhatti Department of Mathematics University of Engineering and Technology, Lahore. Pakistan Email: [email protected] Abstract. In this paper, we establish various inequalities for some differentiable mappings that are linked with the illustrious HermiteHadamard integral inequality for mappings whose derivatives are (h−(α, m))-convex.The generalized integral inequalities contribute...

In the paper Several integral inequalities published in J. Inequal. Pure Appl. Math. 1 (2000), no. 2, Art. 19 (http://jipam.vu.edu.au/v1n2.html.001_00.html) and RGMIA Res. Rep. Coll. 2(7) (1999), Art. 9, 1039–1042 (http://rgmia.vu.edu.au/ v2n7.html) by F. Qi, an open problem was posed. In this article we give the solution and further generalizations of this problem. Reverse inequalities to the ...

In the present paper, the notion of generalized $(r;g,s,m,varphi)$-preinvex function is applied to establish some new generalizations of Ostrowski type integral inequalities via Caputo $k$-fractional derivatives. At the end, some applications to special means are given.