The aim of the present paper is to obtain certain new integral inequalities involving the Saigo fractional integral operator. It is also shown how the various inequalities considered in this paper admit themselves of q -extensions which are capable of yielding various results in the theory of q -integral inequalities. Mathematics subject classification (2010): 26D10, 26A33, 05A30.

Abstract. In this note, we give some estimates of the generalized quadrature formula of Gauss-Jacobi type for phi-preinvex functions.

In recent years, a remarkably large number of inequalities involving the fractional q-integral operators have been investigated in the literature by many authors. Here, we aim to present some new fractional integral inequalities involving generalized Erdélyi-Kober fractional q-integral operator due to Gaulué, whose special cases are shown to yield corresponding inequalities associated with Kobe...

We prove two kinds of Lyapunov type inequalities for pseudo-integrals. One discusses pseudo-integrals where pseudo-operations are given by a monotone and continuous function g. The other one focuses on the pseudo-integrals based on a semiring 0; 1 ½ Š; sup; ð Þ , where the pseudo-multiplication is generated. Some examples are given to illustrate the validity of these inequalities. As a generali...

In this paper, we establish some new Grüss type quantum integral inequalities on finite intervals. Furthermore, some related quantum integral inequalities are also considered.

Recently intensive efforts are deployed to establish inequalities involving some bivariate means. In this paper we aim investigate further mean inequalities. The approach employed here is based on a combination of the integral representations involved means with advanced known in literature. particular, applying Gr?ss inequality and Ostrowski derive lot estimations for differences between stand...

Some new inequalities for the q-gamma, the q-beta and the q-analogue of the Psi functions are established via some q-integral inequalities. In classical analysis, integral inequalities have been well-developed and leading to a wide variety of applications in mathematics and physics (see [11–13] and references therein). In a survey paper [4], Dragomir et al. used certain clever integral inequali...

In this paper, we investigate some new Pólya-Szegö type integral inequalities involving the Riemann-Liouville fractional integral operator, and use them to prove some fractional integral inequalities of Chebyshev type, concerning the integral of the product of two functions and the product of two integrals. Certain special cases are also considered. Finally, examples for constructing the boundi...

This paper deals with a special type of delayed integral inequalities of Bihary type for scalar functions of two variables. The integrals involve the maximum of the unknown function over a past time interval. Several nonlinear types of integral inequalities are solved. The importance of these integral inequalities is based on their wide applications to the qualitative investigations of various ...

This paper deals with some nonlinear integral inequalities that involve the maximum of the unknown scalar function of one variable. The considered inequalities are generalizations of the classical integral inequality of Gronwall–Bellman. The importance of these integral inequalities is due to their wide applications in qualitative investigations of differential equations with “maxima”, and it i...