• 한국수학교육학회지시리즈B:순수및응용수학
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• 제30권3호
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• pp.309-336
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• 2023

We establish some common fixed point theorems satisfying weak ψ - ϕ contraction on partially ordered non-Archimedean fuzzy metric spaces. By using this results we show the existence of fixed point on the domain of words and apply this approach to deduce the existence of solution for some recurrence equations associated to the analysis of Quicksort algorithms and divide and Conquer algorithms, respectively and also give an example to show the usefulness of our hypothesis. Our results generalize, extend and improve several well-known results of the existing literature in fixed point theory.

• East Asian mathematical journal
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• 제16권2호
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• pp.339-354
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• 2000

• 한국수학사학회지
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• 제28권3호
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• pp.133-149
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• 2015

Arrivals of Hilbert and Minkowski at $G\ddot{o}ttingen$ put mathematical science there in full flourish. They further extended its strong mathematical tradition of Gauss and Riemann. Though Riemann envisioned Finsler metric and gave an example of it in his inaugural lecture of 1854, Finsler geometry was officially named after Minkowski's academic grandson Finsler. His tool to generalize Riemannian geometry was the calculus of variations of which his advisor $Carath\acute{e}odory$ was a master. Another $G\ddot{o}ttingen$ graduate Busemann regraded Finsler geometry as a special case of geometry of metric spaces. He was a student of Courant who was a student of Hilbert. These figures all at $G\ddot{o}ttingen$ created and developed Finsler geometry in its early stages. In this paper, we investigate history of works on Finsler geometry contributed by these frontiers.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제2권1호
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• pp.31-34
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• 1995

Let R$^n$be n-th Euclidean space. Let be the n-th spere embeded as a subspace in R$\^$n+1/ centered at the origin. In this paper, we are going to consider the function space F = {f│f : S$^n$\longrightarrow S$^n$} metrized by as follow D(f,g)=d(f($\chi$), g($\chi$)) where f, g $\in$ F and d is the metric in S$^n$. Finally we want to find certain relation these spaces.(omitted)

• 대한수학회논문집
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• 제22권3호
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• pp.391-399
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• 2007

The purpose of this paper is to obtain some common fixed point theorems for multivalued mappings in intuitionistic fuzzy metric space. We extend some earlier results.

• Nonlinear Functional Analysis and Applications
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• 제26권1호
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• pp.177-195
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• 2021

In this paper, we introduce the modification of a generalized (Ψ, L)-weak contraction and we prove some coincidence point results for self-mappings G, T and S, and some fixed point results for some maps by using a (c)-comparison function and a comparison function in the sense of a b-metric space.

• Nonlinear Functional Analysis and Applications
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• 제26권5호
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• pp.949-959
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• 2021

In this paper, some fixed point theorems for new type of (𝜉, 𝛽)-expansive mappings of type (S) and type (T) using control function and 𝛽-admissible function in 𝒢-metric spaces are proved. Further, we prove certain fixed point results by relaxing the continuity condition.

• 대한수학회보
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• 제40권3호
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• pp.351-363
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• 2003

In the present paper, some general convergence principles are established in metric spaces and then theses principles are applied to the convergence of the iterative sequences for approximating fixed points of certain classes of mappings. By virtue of our principles, most of the latest results obtained by several authors can be deduced easily.

• Nonlinear Functional Analysis and Applications
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• 제26권3호
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• pp.565-580
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• 2021

In this paper, first of all we prove a fixed point theorem for 𝜓_∫𝜑-weakly contractive mapping. Next, we prove some common fixed point theorems for a pair of weakly compatible self maps along with E.A. property and (CLR) property. An example is also given to support our results.

• 대한수학회보
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• 제53권1호
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• pp.61-81
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• 2016

In this paper, we prove some existence and uniqueness results on coincidence points for g-monotone mappings satisfying linear as well as generalized nonlinear contractivity conditions in ordered metric spaces. Our results generalize and extend two classical and well known results due to Ran and Reurings (Proc. Amer. Math. Soc. 132 (2004), no. 5, 1435-1443) and Nieto and $Rodr{\acute{i}}guez$-$L{\acute{o}}pez$ (Acta Math. Sin. 23 (2007), no. 12, 2205-2212) besides similar other ones. Finally, as an application of one of our newly proved results, we establish the existence and uniqueness of solution of a first order periodic boundary value problem.