We present symmetric Rogers--Hölder's inequalities on time scales when $frac{1}{p}+frac{1}{q}+frac{1}{r}=0$ and $frac{r}{p}+frac{r}{q}$ is not necessarily equal to $1$ where $p,$ $q$ and $r$ are nonzero real numbers.

Algorithms and identities for (p, q)-Bézier curves via (p, q)-Blossom Abstract In this paper, a new variant of the blossom, the (p, q)-blossom, is introduced, by altering the diagonal property of the standard blossom. This (p, q)-blossom is has been adapted for developing identities and algorithms for (p, q)-Bernstein bases and (p, q)-Bézier curves. We generate several new identities including ...

For a simple connected graph G, Eccentric connectivity index denoted by ( ) c G 7 is defined as: ( ) ( ) ( ( ) ( )) c i V G G E i d i 7 , where E(i) is the eccentricity of vertex i, d(i) is the degree of vertex i and V(G) is the set of vertices of G. Eccentricity of vertex i in a graph G is the path length from verte i to vertex j that is farthest from i. In this paper, an algorithm is presente...

Riordan arrays are useful for solving the combinatorial sums by the help of generating functions. Many theorems can be easily proved by Riordan arrays. In this paper we consider the Pascal matrix and define a new generalization of Fibonacci polynomials called p, q -Fibonacci polynomials. We obtain combinatorial identities and by using Riordanmethodwe get factorizations of Pascal matrix involvin...

Utilizing p,q-numbers and p,q-concepts, in 2016, Duran et al. considered p,q-Genocchi numbers polynomials, p,q-Bernoulli polynomials p,q-Euler provided multifarious formulas properties for these polynomials. Inspired motivated by this consideration, many authors have introduced (p,q)-special described some of their applications. In paper, using the (p,q)-cosine (p,q)-sine we consider a novel ki...