• 한국수학교육학회지시리즈B:순수및응용수학
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• 제30권1호
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• pp.25-34
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• 2023

Popa [14] proved the common fixed point theorem using implicit relations. Saluja [17] proved a fixed point theorem on complete partial metric spaces satisfying an implicit relation. In this paper, we prove a fixed point theorem on complete partial metric space satisfying another implicit relation.

• 호남수학학술지
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• 제45권3호
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• pp.491-502
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• 2023

As a generalization of Berwald spaces, we have the ideas of Douglas spaces and Landsberg spaces. S. Bacso defined a weakly-Berwald space as another generalization of Berwald spaces. In 1972, Matsumoto proposed the (α, β) metric, which is a Finsler metric derived from a Riemannian metric α and a differential 1-form β. In this paper, we investigated an important class of (α, β)-metrics of the form $F={\mu}_1\alpha+{\mu}_2\beta+{\mu}_3\frac{\beta^2}{\alpha}$, which is recognized as a special form of the first approximate Matsumoto metric on an n-dimensional manifold, and we obtain the criteria for such metrics to be weakly-Berwald metrics. A Finsler space with a special (α, β)-metric is a weakly Berwald space if and only if B^m_m is a 1-form. We have shown that under certain geometric and algebraic circumstances, it transforms into a weakly Berwald space.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제27권3호
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• pp.160-179
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• 2023

In this paper, we investigate the existence and diameter of the approximate fixed point results on E-metric spaces (not necessarily complete) by using various cyclic contraction mappings, including the B-cyclic contraction, the Bianchini cyclic contraction, the Hardy-Rogers cyclic contraction, and so on. Additionally, we prove the approximate fixed point results for rational type cyclic contraction mappings, which were discussed mainly in [35] and [37], in the setting of E-metric space. Also, a few examples are provided to demonstrate our findings. Subsequently, we discuss some applications of approximate fixed point results in the field of applied mathematics rigorously.

• 대한수학회지
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• 제37권6호
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• pp.885-899
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• 2000

We obtain generalized versions of the Fan-Browder fixed point theorem for G-convex spaces. We define the class B of better admissible multimaps on G-convex spaces and show that any closed compact map in b fro ma locally G-convex uniform space into itself has a fixed point.

• East Asian mathematical journal
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• 제17권2호
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• pp.325-337
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• 2001

We consider the special hypersurface of the first approximate Matsumoto metric with $b_i(x)={\partial}_ib$ being the gradient of a scalar function b(x). In this paper, we consider the hypersurface of the first approximate Matsumoto space with the same equation b(x)=constant. We are devoted to finding the condition for this hypersurface to be a hyperplane of the first or second kind. We show that this hypersurface is not a hyper-plane of third kind.

• Nonlinear Functional Analysis and Applications
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• 제26권2호
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• pp.289-301
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• 2021

In this research, we interpret the notion of a b-cyclic (𝚽, C, D)-contraction for the pair (g, S) of self-mappings on the set Y. We employ our definition to introduce some common fixed point theorems for the two mappings g and S under a set of conditions. Also we introduce an example to support our results.

• 호남수학학술지
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• 제45권1호
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• pp.1-24
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• 2023

In the present paper, we prove common fixed point theorems for a pair of weakly compatible mappings under implicit contractive relation in quasi-partial S_b-metric spaces. We also provide an illustrative example to support our results. Furthermore, we will use the results obtained for application to two boundary value problems for the second-order differential equation. Also, we prove a common solution for the nonlinear fractional differential equation.

• Nonlinear Functional Analysis and Applications
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• 제29권2호
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• pp.477-485
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• 2024

In this work, we will generalize the notion of multivalued (ν, 𝒞)-contraction mapping in 𝑏-Menger spaces and we shall give a new fixed point result of this type of mappings. As a consequence of our main result, we obtained the corresponding fixed point theorem in fuzzy 𝑏-metric spaces. Also, an example will be given to illustrate the main theorem in ordinary 𝑏-metric spaces.

• 대한수학회보
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• 제60권6호
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• pp.1641-1650
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• 2023

It is our goal in this study to present the structure of isotropic mean Berwald Finsler warped product metrics. We bring out the rich class of warped product Finsler metrics behaviour under this condition. We show that every Finsler warped product metric of dimension n ≥ 2 is of isotropic mean Berwald curvature if and only if it is a weakly Berwald metric. Also, we prove that every locally dually flat Finsler warped product metric is weakly Berwaldian. Finally, we prove that every Finsler warped product metric is of isotropic Berwald curvature if and only if it is a Berwald metric.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제27권4호
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• pp.207-229
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• 2020

We establish fixed point and multidimensional fixed point results satisfying generalized (𝜓, 𝜃, 𝜑)-contraction on partially ordered non-Archimedean fuzzy metric spaces. By using this result we obtain the solution for periodic boundary value problems and give an example to show the degree of validity of our hypothesis. Our results generalize, extend and modify several well-known results in the literature.