The purpose of this paper is to introduce the some interesting properties of q-Euler numbers and ... more The purpose of this paper is to introduce the some interesting properties of q-Euler numbers and polynomials, cf. [1, 2, 5]. Finally, we will consider the " sums of products of q-Euler polynomials".
We investigate several arithmetic properties of h, q -Genocchi polynomials and numbers of higher ... more We investigate several arithmetic properties of h, q -Genocchi polynomials and numbers of higher order.
Advanced Studies in Contemporary Mathematics, Sep 2, 2007
In this paper we study q-Euler numbers and polynomials by using p-adic q-fermionic integrals on Z... more In this paper we study q-Euler numbers and polynomials by using p-adic q-fermionic integrals on Z_p. The methods to study q-Euler numbers and polynomials in this paper are new.
We construct the q-Euler numbers and polynomials of higher order, which are related to Barnes' ty... more We construct the q-Euler numbers and polynomials of higher order, which are related to Barnes' type multiple Euler polynomials. We also derive many properties and formulae for our q-Euler polynomials of higher order by using the multiple integral equations on Z p .
In [14] Ozden-Simsek-Cangul constructed generating functions of higher-order twisted $(h,q)$-exte... more In [14] Ozden-Simsek-Cangul constructed generating functions of higher-order twisted $(h,q)$-extension of Euler polynomials and numbers, by using $p$-adic q-deformed fermionic integral on $\Bbb Z_p$. By applying their generating functions, they derived the complete sums of products of the twisted $(h,q)$-extension of Euler polynomials and numbers, see[13, 14]. In this paper we cosider the new $q$-extension of Euler numbers and polynomials to be different which is treated by Ozden-Simsek-Cangul. From our $q$-Euler numbers and polynomials we derive some interesting identities and we construct $q$-Euler zeta functions which interpolate the new $q$-Euler numbers and polynomials at a negative integer. Furthermore we study Barnes' type $q$-Euler zeta functions. Finally we will derive the new formula for " sums products of $q$-Euler numbers and polynomials" by using fermionic $p$-adic $q$-integral on $\Bbb Z_p$.
Recently Kim [2,6] has introduced an interesting Euler-Barnes' numbers and polynomials. In this p... more Recently Kim [2,6] has introduced an interesting Euler-Barnes' numbers and polynomials. In this paper, we construct the q-analogue of Euler-Barnes'numbers and polynomials, and investigate their some properties.
In this paper, we consider higher order Barnes-type q-Bernoulli polynomials and numbers and inves... more In this paper, we consider higher order Barnes-type q-Bernoulli polynomials and numbers and investigate some identities of them. Furthermore, we discuss some identities of higher order Barnes-type q-Euler polynomials and numbers.
Atanassov [1,2] and Szmidt and Kacprzyk[7,8] studied various methods for measuring distances betw... more Atanassov [1,2] and Szmidt and Kacprzyk[7,8] studied various methods for measuring distances between intuitionistic fuzzy sets. In this paper, we consider interval-valued intuitionistic fuzzy sets and discuss these methods for measuring distances between interval-valued intuitionistic fuzzy sets.
In this paper, we consider fuzzy complex valued fuzzy measures and Choquet integrals with respect... more In this paper, we consider fuzzy complex valued fuzzy measures and Choquet integrals with respect to a fuzzy measure of real-valued measurable functions. In doing so, we investigate some basic properties and convergence theorems.
Recently, the Von Staudt-Clausen theorem for q-Euler numbers was introduced by Kim (Russ. J. Math... more Recently, the Von Staudt-Clausen theorem for q-Euler numbers was introduced by Kim (Russ. J. Math. Phys. 20(1):33-38, 2013) and Araci et al. have also studied this theorem for q-Genocchi numbers (see Araci et al. in Appl. Math. Comput. 247:780-785, 2014) based on the work of Kim et al. In this paper, we give the corresponding Von Staudt-Clausen theorem for the weighted q-Genocchi numbers and also prove the Kummer-type congruences for the generated weighted q-Genocchi numbers. MSC: 11B68; 11S40
The purpose of this paper is to introduce the some interesting properties of q-Euler numbers and ... more The purpose of this paper is to introduce the some interesting properties of q-Euler numbers and polynomials, cf. [1, 2, 5]. Finally, we will consider the " sums of products of q-Euler polynomials".
The purpose of this paper is to introduce the some interesting properties of q-Euler numbers and ... more The purpose of this paper is to introduce the some interesting properties of q-Euler numbers and polynomials, cf. [1, 2, 5]. Finally, we will consider the " sums of products of q-Euler polynomials".
We investigate several arithmetic properties of h, q -Genocchi polynomials and numbers of higher ... more We investigate several arithmetic properties of h, q -Genocchi polynomials and numbers of higher order.
Advanced Studies in Contemporary Mathematics, Sep 2, 2007
In this paper we study q-Euler numbers and polynomials by using p-adic q-fermionic integrals on Z... more In this paper we study q-Euler numbers and polynomials by using p-adic q-fermionic integrals on Z_p. The methods to study q-Euler numbers and polynomials in this paper are new.
We construct the q-Euler numbers and polynomials of higher order, which are related to Barnes' ty... more We construct the q-Euler numbers and polynomials of higher order, which are related to Barnes' type multiple Euler polynomials. We also derive many properties and formulae for our q-Euler polynomials of higher order by using the multiple integral equations on Z p .
In [14] Ozden-Simsek-Cangul constructed generating functions of higher-order twisted $(h,q)$-exte... more In [14] Ozden-Simsek-Cangul constructed generating functions of higher-order twisted $(h,q)$-extension of Euler polynomials and numbers, by using $p$-adic q-deformed fermionic integral on $\Bbb Z_p$. By applying their generating functions, they derived the complete sums of products of the twisted $(h,q)$-extension of Euler polynomials and numbers, see[13, 14]. In this paper we cosider the new $q$-extension of Euler numbers and polynomials to be different which is treated by Ozden-Simsek-Cangul. From our $q$-Euler numbers and polynomials we derive some interesting identities and we construct $q$-Euler zeta functions which interpolate the new $q$-Euler numbers and polynomials at a negative integer. Furthermore we study Barnes' type $q$-Euler zeta functions. Finally we will derive the new formula for " sums products of $q$-Euler numbers and polynomials" by using fermionic $p$-adic $q$-integral on $\Bbb Z_p$.
Recently Kim [2,6] has introduced an interesting Euler-Barnes' numbers and polynomials. In this p... more Recently Kim [2,6] has introduced an interesting Euler-Barnes' numbers and polynomials. In this paper, we construct the q-analogue of Euler-Barnes'numbers and polynomials, and investigate their some properties.
In this paper, we consider higher order Barnes-type q-Bernoulli polynomials and numbers and inves... more In this paper, we consider higher order Barnes-type q-Bernoulli polynomials and numbers and investigate some identities of them. Furthermore, we discuss some identities of higher order Barnes-type q-Euler polynomials and numbers.
Atanassov [1,2] and Szmidt and Kacprzyk[7,8] studied various methods for measuring distances betw... more Atanassov [1,2] and Szmidt and Kacprzyk[7,8] studied various methods for measuring distances between intuitionistic fuzzy sets. In this paper, we consider interval-valued intuitionistic fuzzy sets and discuss these methods for measuring distances between interval-valued intuitionistic fuzzy sets.
In this paper, we consider fuzzy complex valued fuzzy measures and Choquet integrals with respect... more In this paper, we consider fuzzy complex valued fuzzy measures and Choquet integrals with respect to a fuzzy measure of real-valued measurable functions. In doing so, we investigate some basic properties and convergence theorems.
Recently, the Von Staudt-Clausen theorem for q-Euler numbers was introduced by Kim (Russ. J. Math... more Recently, the Von Staudt-Clausen theorem for q-Euler numbers was introduced by Kim (Russ. J. Math. Phys. 20(1):33-38, 2013) and Araci et al. have also studied this theorem for q-Genocchi numbers (see Araci et al. in Appl. Math. Comput. 247:780-785, 2014) based on the work of Kim et al. In this paper, we give the corresponding Von Staudt-Clausen theorem for the weighted q-Genocchi numbers and also prove the Kummer-type congruences for the generated weighted q-Genocchi numbers. MSC: 11B68; 11S40
The purpose of this paper is to introduce the some interesting properties of q-Euler numbers and ... more The purpose of this paper is to introduce the some interesting properties of q-Euler numbers and polynomials, cf. [1, 2, 5]. Finally, we will consider the " sums of products of q-Euler polynomials".
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