Ismail Naci Cangul

Multivariate interpolation functions of higher-order -Euler numbers and their applications.

The aim of this paper, firstly, is to construct generating functions of 𝑞-Euler numbers and polynomials of higher order by applying the fermionic 𝑝-adic 𝑞-Volkenborn integral, secondly, to define multivariate 𝑞-Euler zeta function (Barnes-type Hurwitz 𝑞-Euler zeta function) and 𝑙-function which interpolate these numbers and polynomials at negative integers, respectively. We give relation between Barnes-type Hurwitz 𝑞-Euler zeta function and multivariate 𝑞-Euler 𝑙-function. Moreover, complete sums of products of these numbers and polynomials are found. We give some applications related to these numbers and functions as well.

The multiplicative Zagreb indices of graph operations

AbstractRecently, Todeschini et al. (Novel Molecular Structure Descriptors - Theory and Applications I, pp. 73-100, 2010), Todeschini and Consonni (MATCH Commun. Math. Comput. Chem. 64:359-372, 2010) have proposed the multiplicative variants of ordinary Zagreb indices, which are defined as follows: ∏1=∏1(G)=∏v∈V(G)dG(v)2,∏2=∏2(G)=∏uv∈E(G)dG(u)dG(v). These two graph invariants are called multiplicative Zagreb indices by Gutman (Bull. Soc. Math. Banja Luka 18:17-23, 2011). In this paper the upper bounds on the multiplicative Zagreb indices of the join, Cartesian product, corona product, composition and disjunction of graphs are derived and the indices are evaluated for some well-known graphs.MSC:05C05, 05C90, 05C07.

On the Zagreb indices of the line graphs of the subdivision graphs

The aim of this paper is to investigate the Zagreb indices of the line graphs of the tadpole graphs, wheel graphs and ladder graphs using the subdivision concepts.

Remarks on Sum of Products of -Twisted Euler Polynomials and Numbers

The main purpose of this paper is to construct generating functions of higher-order twisted -extension of Euler polynomials and numbers, by using -adic, -deformed fermionic integral on . By applying these generating functions, we prove complete sums of products of the twisted -extension of Euler polynomials and numbers. We also define some identities involving twisted -extension of Euler polynomials and numbers.

q-Genocchi Numbers and Polynomials Associated with q-Genocchi-Type l-Functions

The main purpose of this paper is to study on generating functions of the Open image in new window -Genocchi numbers and polynomials. We prove new relation for the generalized Open image in new window -Genocchi numbers which is related to the Open image in new window -Genocchi numbers and Open image in new window -Bernoulli numbers. By applying Mellin transformation and derivative operator to the generating functions, we define Open image in new window -Genocchi zeta and Open image in new window -functions, which are interpolated Open image in new window -Genocchi numbers and polynomials at negative integers. We also give some applications of generalized Open image in new window -Genocchi numbers.The main purpose of this paper is to study on generating functions of the -Genocchi numbers and polynomials. We prove new relation for the generalized -Genocchi numbers which is related to the -Genocchi numbers and -Bernoulli numbers. By applying Mellin transformation and derivative operator to the generating functions, we define -Genocchi zeta and -functions, which are interpolated -Genocchi numbers and polynomials at negative integers. We also give some applications of generalized -Genocchi numbers.

On the Harary index of graph operations

The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. In this paper, expressions for the Harary indices of the join, corona product, Cartesian product, composition and disjunction of graphs are derived and the indices for some well-known graphs are evaluated. In derivations some terms appear which are similar to the Harary index and we name them the second and third Harary index.MSC:05C05, 05C07, 05C90.

A note on the (h,q)-zeta-type function with weight α

The objective of this paper is to derive the symmetric property of an (h,q)-zeta function with weight α. By using this property, we give some interesting identities for (h,q)-Genocchi polynomials with weight α. As a result, our applications possess a number of interesting properties which we state in this paper.MSC:11S80, 11B68.The objective of this paper is to derive the symmetric property of an ( h , q ) Open image in new window-zeta function with weight α. By using this property, we give some interesting identities for ( h , q ) Open image in new window-Genocchi polynomials with weight α. As a result, our applications possess a number of interesting properties which we state in this paper.

A note on the modified q-Bernstein polynomials for functions of several variables and their reflections on q-Volkenborn integration

Abstract In this paper, we consider the modified q -Bernstein polynomials for functions of several variables on q -Volkenborn integral and investigate some new interesting properties of these polynomials related to q -Stirling numbers, Hermite polynomials and Carlitz’s type q -Bernoulli numbers.

A unified presentation of certain meromorphic functions related to the families of the partial zeta type functions and the L-functions

Abstract The aim of this paper is to construct a unified family of meromorphic functions, which is related to many known functions such as a unified family of partial zeta type functions, a unified family of L -functions, and so on. We investigate and derive many properties of this family of meromorphic functions. Moreover, we compute the residues of this family of meromorphic functions at their poles. We also give some applications and remarks involving this family of meromorphic functions.

On the Kirchhoff matrix, a new Kirchhoff index and the Kirchhoff energy

AbstractAbstractThe main purpose of this paper is to define and investigate the Kirchhoff matrix, a new Kirchhoff index, the Kirchhoff energy and the Kirchhoff Estrada index of a graph. In addition, we establish upper and lower bounds for these new indexes and energy. In the final section, we point out a new possible application area for graphs by considering this new Kirchhoff matrix. Since graph theoretical studies (including graph parameters) consist of some fixed point techniques, they have been applied in the fields such as chemistry (in the meaning of atoms, molecules, energy etc.) and engineering (in the meaning of signal processing etc.), game theory, and physics. MSC: 05C12, 05C50, 05C90.