• Korean Journal of Mathematics
• /
• v.31 no.3
• /
• pp.373-383
• /
• 2023

The aim of this paper is to prove some new approximate best proximity pair theorems on metric spaces using contraction mappings such as P-Bianchini contraction, P - B contraction and so on. A few examples are provided to exemplify our findings. Finally, we discuss some applications that are related to the main results.

• The Pure and Applied Mathematics
• /
• v.30 no.4
• /
• pp.417-427
• /
• 2023

The purpose of this paper is establish the existence of proximity point for the cyclic B-contraction mapping on metric spaces and uniformly convex Banach spaces. Also, we prove the common proximity point for the S-weakly cyclic B-contraction mapping. In addition, a few examples are provided to demonstrate our findings.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.27 no.3
• /
• pp.160-179
• /
• 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.

• Korean Journal of Mathematics
• /
• v.32 no.2
• /
• pp.329-348
• /
• 2024

In this text, we investigate some fixed point results in double-controlled cone metric spaces using several contraction mappings such as the B-contraction, the Hardy-Rogers contraction, and so on. Additionally, we prove the same fixed point results by using rational type contraction mappings, which were discussed by the authors Dass. B. K and Gupta. S. Also, a few examples are included to illustrate the results. Finally, we discuss some applications that support our main results in the field of applied mathematics.

• The Pure and Applied Mathematics
• /
• v.17 no.2
• /
• pp.157-165
• /
• 2010

Let (M,p) be a germ of a $C^{\infty}$ CR manifold of CR dimension n and CR codimension d. Suppose (M,p) admits a $C^{\infty}$ contraction at p. In this paper, we show that (M,p) is CR equivalent to a generic submanifold in $\mathbb{C}^{n+d}$ defined by a vector valued weighted homogeneous polynomial.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.5
• /
• pp.1577-1596
• /
• 2017

We study contraction of points on ${\mathbb{P}}^1({\bar{\mathbb{Q}}})$ with certain control on local ramification indices, with application to the unramified curve correspondence problem initiated by Bogomolov and Tschinkel.

• The Pure and Applied Mathematics
• /
• v.24 no.2
• /
• pp.79-98
• /
• 2017

We establish a coupled coincidence point theorem for generalized compatible pair of mappings $F,G:X{\times}X{\rightarrow}X$ under generalized symmetric Meir-Keeler contraction on a partially ordered metric space. We also deduce certain coupled fixed point results without mixed monotone property of $F:X{\times}X{\rightarrow}X$. An example supporting to our result has also been cited. As an application the solution of integral equations are obtain here to illustrate the usability of the obtained results. We improve, extend and generalize several known results.

• The Pure and Applied Mathematics
• /
• v.25 no.2
• /
• pp.73-94
• /
• 2018

We introduce some new type of admissible mappings and prove a coupled coincidence point theorem by using newly defined concepts for generalized compatible pair of mappings satisfying ${\alpha}-{\psi}$ contraction on partially ordered metric spaces. We also prove the uniqueness of a coupled fixed point for such mappings in this setup. Furthermore, we give an example and an application to integral equations to demonstrate the applicability of the obtained results. Our results generalize some recent results in the literature.

• Journal of the Korea Convergence Society
• /
• v.7 no.1
• /
• pp.105-111
• /
• 2016

The purpose of this study was to investigate effects of three pelvic floor muscle (PFM) exercises on the thickness of PFM and transverse abdominal muscle (TrA), the internal oblique muscle, and the external oblique muscle. The PFM and trunk muscles were measured using ultrasonography in 4 conditions.rest, conventional PFM contraction (Ex A), PFM contraction with hip adductor contraction (Ex B), and PFM contraction with real-time ultrasound imaging (Ex C). The thickness of PFM in Ex C showed a significantly more decrease compared to rest and others (all comparisons, p<.05). The thickness of TrA in Ex C showed a significantly more increase compared to rest and others (all comparisons, p<.05). This study would recommend the use of PFM contraction with real-time ultrasonographic imaging to improve women's incontinence.

• The Pure and Applied Mathematics
• /
• v.27 no.4
• /
• pp.207-229
• /
• 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.