• Korean Journal of Mathematics
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• v.26 no.2
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• pp.215-269
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• 2018

Orders and types of entire functions have been actively investigated by many authors. In this paper, we investigate some basic properties in connection with sum and product of relative (p, q, t) L-th order, relative (p, q, t) L-th type, and relative (p, q, t) L-th weak type of entire functions with respect to another entire function where $p,q{\in}{\mathbb{N}}$ and $t{\in}{\mathbb{N}}{\cup}\{-1,0\}$.

• Korean Journal of Mathematics
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• v.28 no.1
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• pp.149-157
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• 2020

Some basic properties in connection with generalized relative order and generalized relative lower order of analytic functions in the unit disc have been dicussed in this article.

• Honam Mathematical Journal
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• v.44 no.1
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• pp.135-145
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• 2022

This paper aims to investigate characterizations on parameters k₁, k₂, k₃, k₄, k₅, l₁, l₂, l₃, and l₄ to find relation between the class of 𝓗(k, l, m, n, o) hypergeometric functions defined by $$5_F_4\[{\array{k_1,\;k_2,\;k_3,\;k_4,\;k_5\\l_1,\;l_2,\;l_3,\;l_4}}\;:\;z\]=\sum\limits_{n=2}^{\infty}\frac{(k_1)_n(k_2)_n(k_3)_n(k_4)_n(k_5)_n}{(l_1)_n(l_2)_n(l_3)_n(l_4)_n(1)_n}z^n$$. We need to find k, l, m and n that lead to the necessary and sufficient condition for the function zF([W]), G = z(2 - F([W])) and $H_1[W]=z^2{\frac{d}{dz}}(ln(z)-h(z))$ to be in 𝓢^*(2^-r), r is a positive integer in the open unit disc 𝒟 = {z : |z| < 1, z ∈ ℂ} with $$h(z)=\sum\limits_{n=0}^{\infty}\frac{(k)_n(l)_n(m)_n(n)_n(1+\frac{k}{2})_n}{(\frac{k}{2})_n(1+k-l)_n(1+k-m)_n(1+k-n)_nn(1)_n}z^n$$ and $$[W]=\[{\array{k,\;1+{\frac{k}{2}},\;l,\;m,\;n\\{\frac{k}{2}},\;1+k-l,\;1+k-m,\;1+k-n}}\;:\;z\]$$.

• Bulletin of the Korean Mathematical Society
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• v.44 no.3
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• pp.507-516
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• 2007

Let M be a complete Riemannian manifold and L be a $Schr\"{o}dinger$ operator on M. We prove that if M has finitely many L-nonparabolic ends, then the space of bounded L-harmonic functions on M has the same dimension as the sum of dimensions of the spaces of bounded L-harmonic functions on the L-nonparabolic end, which vanish at the boundary of the end.

• Honam Mathematical Journal
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• v.41 no.3
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• pp.463-487
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• 2019

In the paper we establish some new results depending on the comparative growth properties of composite entire and meromorphic functions using relative (p, q, t)L-th order and relative (p, q, t)L-th type of entire and meromorphic function with respect to another entire function.

• Korean Journal of Mathematics
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• v.14 no.2
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• pp.137-160
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• 2006

We describe the weight functions for which Hardy's inequality of nonincreasing functions is satisfied. Further we characterize the pairs of weight functions $(w,v)$ for which the Laplace transform $\mathcal{L}f(x)={\int}^{\infty}_0e^{-xy}f(y)dy$, with monotone function $f$, is bounded from the weighted Lebesgue space $L^p(w)$ to $L^q(v)$.

• Kyungpook Mathematical Journal
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• v.58 no.4
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• pp.677-688
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• 2018

In this paper, we introduce and investigate a new subclass of bi-univalent functions defined by $S{\breve{a}}l{\breve{a}}gean$ q-calculus operator in the open disk ${\mathbb{U}}$. For functions belonging to the subclass, we obtain estimates on the first two Taylor-Maclaurin coefficients ${\mid}a_2{\mid}$ and ${\mid}a_3{\mid}$. Some consequences of the main results are also observed.

• The Pure and Applied Mathematics
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• v.25 no.3
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• pp.193-201
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• 2018

In this paper, we discuss central index oriented and slowly changing function based some growth properties of composite entire functions.

• Kyungpook Mathematical Journal
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• v.49 no.1
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• pp.47-55
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• 2009

In the present investigation sufficient conditions are found for certain subclass of normalized analytic functions defined by Hadamard product. Differential sandwich theorems are also obtained. As a special case of this we obtain results involving Ruscheweyh derivative, S$\u{a}$l$\u{a}$gean derivative, Carlson-shaffer operator, Dziok-Srivatsava linear operator, Multiplier transformation.

• East Asian mathematical journal
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• v.31 no.5
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• pp.667-675
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• 2015

In this paper, we provide some properties of several left regular functions in Clifford analysis. We find the corresponding Cauchy-Riemann system and conjugate harmonic functions of the harmonic functions, for each left regular function in the sense of several complex variables. And we investigate certain properties of generalized quaternions in Clifford analysis.