Related papers: On generalized trigonometric functions with two pa…

We introduce a notion of $(p,q)$-dominated multilinear operators which stems from the geometrical approach provided by $\Sigma$-operators. We prove that $(p,q)$-dominated multilinear operators can be characterized in terms of their behavior…

In this paper, the author introduces the concept of the quasi-geometrically convex and defines a new identity for fractional integrals. By using of this identity, author obtains new estimates on generalization of Hadamard, Ostrowski and…

We define generalizations of the multiple elliptic gamma functions and the multiple sine functions, labelled by rational cones in $\mathbb{R}^r$. For $r=2,3$ we prove that the generalized multiple elliptic gamma functions enjoy a modular…

By introducing a parameter, we give a unified generalization of some quadrature rules, which not only unify the recent results about error bounds for generalized mid-point, trapezoid and Simpson's rules, but also give some new error bounds…

We introduce the q,k-generalized Pochhammer symbol. We construct $\Gamma_{q,k}$ and $B_{q,k}$, the q,k-generalized gamma and beta fuctions, and show that they satisfy properties that generalize those satisfied by the classical gamma and…

In this paper, some monotonicity and concavity results of several functions involving the psi and polygamma functions are proved, and then some known inequalities are extended and generalized.

We deduce some growth properties of composite entire functions in the light of their relative $(p,q)$\ th order by extending some results of J. Tu, Z. X. Chen and X. M. Zheng.

We extend the theorem by Olmsted (1945) and Carlitz-Thomas (1963) on rational values of trigonometric functions to powers of trigonometric functions.

We generalize generating functions for hypergeometric orthogonal polynomials, namely Jacobi, Gegenbauer, Laguerre, and Wilson polynomials. These generalizations of generating functions are accomplished through series rearrangement using…

In this papaer, we put forward some new definitions and integral inequalities by using fairly elementary analysis.

Several integrals involving powers and ordinary hypergeometric functions are rederived by means of a generalized hypergeometric function of two variables (Appell's function) recovering some well-known expressions as particular cases. Simple…

In this paper we solve the following problems: (i) find two differential operators P and Q satisfying [P,Q]=P, where P flows according to the KP hierarchy \partial P/\partial t_n = [(P^{n/p})_+,P], with p := \ord P\ge 2; (ii) find a matrix…

In 2007, \'A. Baricz put forward a conjecture concerning Tur\'an-type inequalities for Gaussian hypergeometric functions (see Conjecture \ref{ConjA} in Section \ref{Sec1}). In this paper, the authors disprove this conjecture with several…

We prove that the generalized Hilbert-Kunz function of a graded module $M$ over a two-dimensional standard graded normal $K$-domain over an algebraically closed field $K$ of prime characteristic $p$ has the form…

In a joint paper [4] by Otsubo, Terasoma and the first author, we proved that the special value 3F2(a,b,q;a+b,q;1) of the generalized hypergeometric function is a linear combination of log of algebraic numbers if the triplet (a,b,q) of…

The n-point correlation functions introduced by Bloch and Okounkov have already found several geometric connections and algebraic generalizations. In this Note we formulate a q,t-deformation of this n-point function. The key operator used…

In this article we give some improvements and generalizations of the famous Jensen's and Jensen-Mercer inequalities for twice differentiable functions, where convexity property of the target function is not assumed in advance. They…

In this paper, we investigate the various different generalized inverses in a Banach algebra with respect to prescribed two idempotents $p$ and $q$. Some new characterizations and explicit representations for these generalized inverses,…

Recently, Mursaleen et al applied (p,q)-calculus in approximation theory and introduced (p,q)-analogue of Bernstein operators in [16]. In this paper, we construct and introduce a generalization of the bivariate Bleimann-Butzer-Hahn…

In this paper, we derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are ({\alpha},m)-convex.