• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1111-1126
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• 2023

In this paper, we define a new subclass of k-uniformly starlike functions of order γ (0 ≤ γ < 1) by using certain generalized q-integral operator. We explore geometric interpretation of the functions in this class by connecting it with conic domains. We also investigate q-sufficient coefficient condition, q-Fekete-Szegö inequalities, q-Bieberbach-De Branges type coefficient estimates and radius problem for functions in this class. We conclude this paper by introducing an analogous subclass of k-uniformly convex functions of order γ by using the generalized q-integral operator. We omit the results for this new class because they can be directly translated from the corresponding results of our main class.

• Honam Mathematical Journal
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• v.45 no.4
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• pp.689-700
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• 2023

In this note, we establish a new subfamily of spirallike functions by making use of a generalized q-integral operator. We examine characterization rule for functions which are member of this subclass. We further obtain coefficient estimate, subordination results and integral mean inequalities for functions in this class. The Fekete-Szegö inequalities are also derived.

• Journal of applied mathematics & informatics
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• v.37 no.3_4
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• pp.295-305
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• 2019

In the present paper, we introduce (p, q)-Frobenius-Genocchi numbers and polynomials and investigate some basic identities and properties for these polynomials and numbers including addition theorems, difference equations, derivative properties, recurrence relations and so on. Then, we provide integral representations, implicit and explicit formulas and relations for these polynomials and numbers. We consider some relationships for (p, q)-Frobenius-Genocchi polynomials of order ${\alpha}$ associated with (p, q)-Bernoulli polynomials, (p, q)-Euler polynomials and (p, q)-Genocchi polynomials.

• Kyungpook Mathematical Journal
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• v.52 no.4
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• pp.397-404
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• 2012

In this article, the reverse q-H$\ddot{o}$lder type inequality and two dimensional q-H$\ddot{o}$lder's inequality are established. We also obtain some q-integral inequalities by using q-H$\ddot{o}$lder's inequality which give q-Hardy's inequalities as spacial cases.

• Honam Mathematical Journal
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• v.33 no.4
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• pp.519-527
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• 2011

Recently, the modified q-Bernoulli numbers and polynomials with weight ${\alpha}$ are introduced in [3]: In this paper we give some interesting p-adic integral representation on $\mathbb{Z}_p$ of the weighted q-Bernstein polynomials related to the modified q-Bernoulli numbers and polynomials with weight ${\alpha}$. From those integral representation on $\mathbb{Z}_p$ of the weighted q-Bernstein polynomials, we can derive some identities on the modified q-Bernoulli numbers and polynomials with weight ${\alpha}$.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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• pp.349-362
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• 2010

We establish the various relationships among the integral transform ${\mathcal{F}}_{{\alpha},{\beta}}F$, the convolution product $(F*G)_{\alpha}$ and the first variation ${\delta}F$ for a class of functionals defined on K(Q), the space of complex-valued continuous functions on $Q=[0,S]{\times}[0,T]$ which satisfy x(s, 0) = x(0, t) = 0 for all $(s,t){\in}Q$. And also we obtain Parseval's and Plancherel's relations for the integral transform of some functionals defined on K(Q).

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.167-179
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• 2023

In this paper, we investigate solutions of equations which are linear (p, q)-difference equation of higher order by using (p, q)-derivative and integral. We also derive the solution of equation in the case of second order.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1149-1156
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• 2016

In this paper, we introduce the degenerate Carlitz q-Bernoulli numbers and polynomials and give some interesting identities and properties of these numbers and polynomials which are derived from the generating functions and p-adic integral equations.

• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.671-694
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• 2018

In this paper, we investigate the weighted vector-valued bounds for a class of multilinear singular integral operators, and its commutators, from $L^{p_1}(l^{q_1};\;{\mathbb{R}}^n,\;w_1){\times}{\cdots}{\times}L^{p_m}(l^{q_m};\;{\mathbb{R}}^n,\;w_m)$ to $L^p(l^q;\;{\mathbb{R}}^n,\;{\nu}_{\vec{w}})$, with $p_1,{\cdots},p_m$, $q_1,{\cdots},q_m{\in}(1,\;{\infty})$, $1/p=1/p_1+{\cdots}+1/p_m$, $1/q=1/q_1+{\cdots}+1/q_m$ and ${\vec{w}}=(w_1,{\cdots},w_m)$ a multiple $A_{\vec{P}}$ weights. Our argument also leads to the weighted weak type endpoint estimates for the commutators. As applications, we obtain some new weighted estimates for the $Calder{\acute{o}}n$ commutator.

• Korean Journal of Mathematics
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• v.29 no.1
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• pp.193-209
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• 2021

In this research, we offer two new quantum integral equalities for recently defined qε2-integral and derivative, the derived equalities then used to prove quantum integral inequalities of Simpson's and Newton's type for preinvex functions. We also considered the special cases of established results and offer several new and existing results inside the literature of Simpson's and Newton's type inequalities.