• Bulletin of the Korean Mathematical Society
• /
• v.46 no.5
• /
• pp.885-894
• /
• 2009

In this paper, we consider a hybrid projection algorithm for a pair of inverse-strongly monotone mappings and a quasi-$\phi4-nonexpansive mapping. Strong convergence theorems are established in the framework of Banach spaces.

• Kyungpook Mathematical Journal
• /
• v.57 no.2
• /
• pp.193-198
• /
• 2017

In this paper we investigate 2-absorbing ${\delta}$-primary ideals which unify 2-absorbing ideals and 2-absorbing primary ideals. A number of results about 2-absorbing ideals and 2-absorbing primary ideals are extended into this general framework.

• East Asian mathematical journal
• /
• v.24 no.1
• /
• pp.1-6
• /
• 2008

In this paper, we introduce a system of nonlinear variational inclusions involving (A, $\eta$)-monotone mappings in the framework of Hilbert spaces. Based on the generalized resolvent operator technique associated with (A, $\eta$)-monotonicity, the approximation solvability of solutions using an iterative algorithm is investigated. Our results improve and extend the recent ones announced by many others.

• Communications of the Korean Mathematical Society
• /
• v.26 no.3
• /
• pp.473-482
• /
• 2011

In this paper, mappings which are asymptotically pseudo-contractive in the intermediate sense are considered based on a hybrid projection method. Strong convergence theorems of fixed points are established in the framework of Hilbert spaces.

• Kyungpook Mathematical Journal
• /
• v.53 no.1
• /
• pp.143-148
• /
• 2013

The theory of generalized Bessel functions is reformulated within the framework of an operational formalism using the multiplier representation of the Lie group $T_3$ as suggested by Miller. This point of view provides more efficient tools which allow the derivation of generating functions of generalized Bessel functions. A few special cases of interest are also discussed.

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.6
• /
• pp.1521-1537
• /
• 2021

In this paper we consider the global well-posedness of compressible magnetohydrodynamic system in ℝ^d with d ≥ 2, in the framework of the critical Besov spaces. We can show that if the initial data, the shear viscosity and the magnetic diffusion coefficient are small comparing with the volume viscosity, then the compressible magnetohydrodynamic system has a unique global solution. Our result improves the previous one by Danchin and Mucha [10] who considered the compressible Navier-Stokes equations.

• Journal of applied mathematics & informatics
• /
• v.37 no.5_6
• /
• pp.481-489
• /
• 2019

In this manuscript, we provide some new results with short proofs for the existence of Picard-Jungck operators in the framework of generalized metric spaces using $C_G$-simulation functions. An example is also provided to illustrate the usability of the results.

• Korean Journal of Mathematics
• /
• v.30 no.1
• /
• pp.161-173
• /
• 2022

In this paper, we present a fixed point theorem for Meir-Keeler contraction in the framework of Rectangular M_b-metric Space. Our main result improves some existing results in literature. An example is also adopted to exhibit the utility of our main result.

• Korean Journal of Mathematics
• /
• v.31 no.3
• /
• pp.269-294
• /
• 2023

The purpose of this paper is to introduce a new three-step iterative process and show that our iteration scheme is faster than other existing iteration schemes in the literature. We provide a numerical example supported by graphs and tables to validate our proofs. We also prove convergence and stability results for the approximation of fixed points of the contractive-like mapping in the framework of uniformly convex Banach space. In addition, we have established some weak and strong convergence theorems for nonexpansive mappings.

• The Mathematical Education
• /
• v.63 no.2
• /
• pp.295-318
• /
• 2024

This narrative review explores the transformative potential of immersive virtual reality (IVR) in enhancing high school students' mathematics competence, viewed through the lens of the technological, pedagogical, and content knowledge (TPACK) framework. This review comprehensively illustrates how IVR technologies have not only fostered a deeper understanding and engagement with mathematical concepts but have also enhanced the practical application of these skills. Through the careful examination of seminal papers, this study carefully explores the integration of IVR in high school mathematics education. It highlights significant contributions of IVR in improving students' computational proficiency, problem-solving skills, and spatial visualization abilities. These enhancements are crucial for developing a robust mathematical understanding and aptitude, positioning students for success in an increasingly technology-driven educational landscape. This review emphasizes the pivotal role of teachers in facilitating IVR-based learning experiences. It points to the necessity for comprehensive teacher training and professional development to fully harness the educational potential of IVR technologies. Equipping educators with the right tools and knowledge is essential for maximizing the effectiveness of this innovative teaching approach. The findings also indicate that while IVR holds promising prospects for enriching mathematics education, more research is needed to elaborate on instructional integration approaches that effectively overcome existing barriers. This includes technological limitations, access issues, and the need for curriculum adjustments to accommodate new teaching methods. In conclusion, this review calls for continued exploration into the effective use of IVR in educational settings, aiming to inform future practices and contribute to the evolving landscape of educational technology. The potential of IVR to transform educational experiences offers a compelling avenue for research and application in the field of mathematics education.