• Nonlinear Functional Analysis and Applications
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• v.26 no.3
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• pp.553-563
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• 2021

As hypergeometric meromorphic multivalent functions of the form $$L^{t,{\rho}}_{{\varpi},{\sigma}}f(\zeta)=\frac{1}{{\zeta}^{\rho}}+{\sum\limits_{{\kappa}=0}^{\infty}}{\frac{(\varpi)_{{\kappa}+2}}{{(\sigma)_{{\kappa}+2}}}}\;{\cdot}\;{\frac{({\rho}-({\kappa}+2{\rho})t)}{{\rho}}}{\alpha}_{\kappa}+_{\rho}{\zeta}^{{\kappa}+{\rho}}$$ contains a new subclass in the punctured unit disk ${\sum_{{\varpi},{\sigma}}^{S,D}}(t,{\kappa},{\rho})$ for -1 ≤ D < S ≤ 1, this paper aims to determine sufficient conditions, distortion properties and radii of starlikeness and convexity for functions in the subclass $L^{t,{\rho}}_{{\varpi},{\sigma}}f(\zeta)$.

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.515-526
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• 2021

The paper has been devoted to study the uniqueness problem of meromorphic function and its linear differential polynomial sharing two values. We have pointed out gaps in one of the theorem due to [1]. We have further extended the corrected form of Chen-Li-Li's result which in turn extend the an earlier result of [8] in a large extent. In fact, we have subtly use the notion of weighted sharing of values in this particular section of literature which was unexplored till now. A handful number of examples have been provided by us pertinent to different discussions. Specially we have given an example to show that one condition in a theorem can not be dropped.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.827-841
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• 2022

In this paper, we study the uniqueness of two finite order transcendental meromorphic solutions f(z) and g(z) of the following complex difference equation A₁(z)f(z + 1) + A₀(z)f(z) = F(z)e^𝛼(z) when they share 0, ∞ CM, where A₁(z), A₀(z), F(z) are non-zero polynomials, 𝛼(z) is a polynomial. Our result generalizes and complements some known results given recently by Cui and Chen, Li and Chen. Examples for the precision of our result are also supplied.

• Korean Journal of Mathematics
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• v.31 no.2
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• pp.229-242
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• 2023

In this paper, we investigate the [p, q] - φ order and [p, q] - φ type of f₁ + f₁, ${\frac{f_1}{f_2}}$ and f₁ f₁, where f₁ and f₁ are analytic or meromorphic functions with the same [p, q]-φ order and different [p, q]-φ type in the unit disc. Also, we study the [p, q]-φ order and [p, q]-φ type of different f and its derivative. At the end, we investigate the relationship between two different [p, q] - φ convergence exponents of f. We extend some earlier precedent well known results.

• Journal of applied mathematics & informatics
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• v.41 no.4
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• pp.765-780
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• 2023

In this paper, we explore the uniqueness property between the transcendental meromorphic functions and differential polynomial. With the notion of weighted sharing, we generalised the many previous results on uniqueness property. Here we discussed the uniqueness of [P(f)(αf^m + β)^s]^(k) - η(z) and [P(g)(αg^m + β)^s]^(k) - η(z). Meanwhile, we generalised the result of Harina P. waghamore and Rajeshwari S[1].

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.229-246
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• 2024

We consider the delay differential equations $$b(z)w(z+1)+c(z)w(z-1)+a(z)\frac{w'(z)}{w^k(z)}=\frac{P(z, w(z))}{Q(z, w(z))}$$, where k ∈ {1, 2}, a(z), b(z) ≢ 0, c(z) ≢ 0 are rational functions, and P(z, w(z)) and Q(z, w(z)) are polynomials in w(z) with rational coefficients satisfying certain natural conditions regarding their roots. It is shown that if this equation has a non-rational meromorphic solution w with hyper-order ρ2(w) < 1, then either deg_w(P) = deg_w(Q) + 1 ≤ 3 or max{deg_w(P), deg_w(Q)} ≤ 1. In addition, it is shown that in the case max{deg_w(P), deg_w(Q)} = 0 the equations above can have such a solution, with an additional zero density requirement, only if the coefficients of the equation satisfy certain strict conditions.

• Honam Mathematical Journal
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• v.46 no.2
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• pp.267-278
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• 2024

In this paper, we investigate the uniqueness of a meromorphic function f(z) and its difference polynomial of difference operator with two sharing values counting multiplicities. Our two results improve and generalize the recent results of Barki Mahesh, Dyavanal Renukadevi S and Bhoosnurmath Subhas S [4] and for the case q ≥ 2, this allows for a highly unique generalization. To further demonstrate the validity of our main result, we provide an example.

• Journal of the Chungcheong Mathematical Society
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• v.15 no.2
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• pp.47-56
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• 2003

This note is concerned with some properties of fixed points and periodic points. First, we have constructed a generalized continuous function to give a proof for the fact that, as the reverse of the Sharkovsky theorem[16], for a given positive integer n, there exists a continuous function with a period-n point but no period-m points wherem is a predecessor of n in the Sharkovsky ordering. Also we show that the composition of two transcendental meromorphic functions, one of which has at least three poles, has infinitely many fixed points.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.1-11
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• 2015

This paper is devoted to investigate the singular directions of meromorphic functions in some angular domains. We will confirm the existence of Hayman T directions in some angular domains. This is a continuous work of Yang [8] and Zheng [10].

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.529-542
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• 2017

In this paper, using the notion of weakly weighted sharing and relaxed weighted sharing, we investigate the uniqueness problems of certain differential polynomials sharing a small function. The results obtained in this paper extend the theorem obtained by Jianren Long [9].