• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1231-1240
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• 2018

In this paper, we characterize the conformal transformations between two almost regular (${\alpha},{\beta}$)-metrics. Suppose that F is a non-Riemannian (${\alpha},{\beta}$)-metric and is conformally related to ${\widetilde{F}}$, that is, ${\widetilde{F}}=e^{{\kappa}(x)}F$, where ${\kappa}:={\kappa}(x)$ is a scalar function on the manifold. We obtain the necessary and sufficient conditions of the conformal transformation between F and ${\widetilde{F}}$ preserving the mean Landsberg curvature. Further, when both F and ${\widetilde{F}}$ are regular, the conformal transformation between F and ${\widetilde{F}}$ preserving the mean Landsberg curvature must be a homothety.

• Journal of the Korean Mathematical Society
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• v.38 no.3
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• pp.503-521
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• 2001

A change of Finsler metric L(x,y)longrightarrowL(x,y) is called a Randers change of L, if L(x,y) = L(x,y) +$\rho$(x,y), where $\rho$(x,y) = $\rho$(sub)i(x)y(sup)i is a 1-form on a smooth manifold M(sup)n. Let us consider the special Randers change of Finsler metric LlongrightarrowL = L + $\beta$ by $\beta$. On the basis of this special Randers change, the purpose of the present paper is devoted to studying the conditions for Finsler space F(sup)n which are transformed by a special Randers change of Finsler spaces F(sup)n with ($\alpha$,$\beta$)-metrics of Douglas type to be also of Douglas type, and vice versa.

• Honam Mathematical Journal
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• v.37 no.4
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• pp.457-468
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• 2015

The aim of present paper is to investigate 3-dimensional ${\xi}$-projectively flt and $\tilde{\varphi}$-projectively flt normal almost paracontact metric manifolds. As a first step, we proved that if the 3-dimensional normal almost paracontact metric manifold is ${\xi}$-projectively flt then ${\Delta}{\beta}=0$. If additionally ${\beta}$ is constant then the manifold is ${\beta}$-para-Sasakian. Later, we proved that a 3-dimensional normal almost paracontact metric manifold is $\tilde{\varphi}$-projectively flt if and only if it is an Einstein manifold for ${\alpha},{\beta}=const$. Finally, we constructed an example to illustrate the results obtained in previous sections.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.639-648
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• 2013

In this paper, we study Finsler metrics of constant S-curvature. First we produce infinitely many Randers metrics with non-zero (constant) S-curvature which have vanishing H-curvature. They are counterexamples to Theorem 1.2 in [20]. Then we show that the existence of (${\alpha}$, ${\beta}$)-metrics with arbitrary constant S-curvature in each dimension which is not Randers type by extending Li-Shen' construction.

• Kyungpook Mathematical Journal
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• v.63 no.4
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• pp.611-622
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• 2023

In this paper, we prove that every weakly Einstein slope metric, which is conformally flat on a manifold M of dimension n ≥ 3, is either a locally Minkowski metric or a Riemannian metric. We also prove the same result for conformally flat weakly Einstein Kropina metrics.

• Honam Mathematical Journal
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• v.46 no.2
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• pp.198-208
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• 2024

In this paper, we find the conditions for a homogeneous Finsler space with an invariant infinite series (α, β)-metric to be of Berwald type. Also, we derive the necessary and sufficient condition for such a metric to be a Douglas metric.

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.157-171
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• 2014

We show that the recurrence rates of Laurent series about continued fractions almost surely coincide with their pointwise dimensions of the Haar measure. Moreover, let $E_{{\alpha},{\beta}}$ be the set of points with lower and upper recurrence rates ${\alpha},{\beta}$, ($0{\leq}{\alpha}{\leq}{\beta}{\leq}{\infty}$), we prove that all the sets $E_{{\alpha},{\beta}}$, are of full Hausdorff dimension. Then the recurrence sets $E_{{\alpha},{\beta}}$ have constant multifractal spectra.

• Bulletin of the Korean Mathematical Society
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• v.39 no.1
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• pp.153-163
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• 2002

The present paper is devoted to studying the condition for a Finsler space with the second approximate Matsumoto metric to be a Berwald space and to be a Douglas space.

• Communications of the Korean Mathematical Society
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• v.23 no.3
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• pp.427-446
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• 2008

In this paper, we give some new definitions of compatible mappings in intuitionistic fuzzy metric spaces and we prove a common fixed point theorem for four mappings under the condition of compatible mappings of type (I) and of type (II) in complete intuitionistic fuzzy metric spaces.

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.571-587
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• 2023

In this paper, we have developed the idea of α-β-ψ-contractive mapping in S-metric space and renamed it α_s-β_s-ψ-contractive mapping. We have proved some results of fixed point present in literature in partially ordered S-metric space using α_s-β_s-admissible and α_s-β_s-ψ-contractive mapping.