• Nonlinear Functional Analysis and Applications
• /
• v.26 no.2
• /
• pp.411-432
• /
• 2021

In this paper, an inertial Halpern-type forward backward iterative algorithm for approximating solution of a monotone inclusion problem whose solution is also a fixed point of some nonlinear mapping is introduced and studied. Strong convergence theorem is established in a real Hilbert space. Furthermore, our theorem is applied to variational inequality problems, convex minimization problems and image restoration problems. Finally, numerical illustrations are presented to support the main theorem and its applications.

• Nonlinear Functional Analysis and Applications
• /
• v.29 no.3
• /
• pp.841-865
• /
• 2024

In this research, we propose a new efficient iterative method for fixed point problems of generalized α-nonexpansive mappings. We show the weak and strong convergence analysis of the proposed method under some mild assumptions on the control parameters. We consider the application of the new method to some real world problems such as convex minimization problems, image restoration problems and impulsive fractional differential equations. We carryout a numerical experiment to show the computational advantage of our method over some well known existing methods.

• Nonlinear Functional Analysis and Applications
• /
• v.29 no.1
• /
• pp.131-164
• /
• 2024

In this research, we study a modified relaxed Tseng method with a single projection approach for solving common solution to a fixed point problem involving finite family of τ-demimetric operators and a quasi-monotone variational inequalities in real Hilbert spaces with alternating inertial extrapolation steps and adaptive non-monotonic step sizes. Under some appropriate conditions that are imposed on the parameters, the weak and linear convergence results of the proposed iterative scheme are established. Furthermore, we present some numerical examples and application of our proposed methods in comparison with other existing iterative methods. In order to show the practical applicability of our method to real word problems, we show that our algorithm has better restoration efficiency than many well known methods in image restoration problem. Our proposed iterative method generalizes and extends many existing methods in the literature.

• The Journal of Korean Academy of Prosthodontics
• /
• v.47 no.2
• /
• pp.191-198
• /
• 2009

Statement of problem: Ceramics have been important materials for the restoration of teeth. The demands of patients for tooth-colored restorations and the availability of various dental ceramics has driven the increased use of new types of dental ceramic materials. Improved physical properties of theses materials have expanded its use even in posterior crowns and fixed partial dentures. However, ceramic still has limitation such as low loading capability. This is critical for long-span bridge, because bridge is more subject to tensile force. Purpose: The wire reinforced ceramic was designed to increase the fracture resistance of ceramic restoration. The purpose of this study was to evaluate the fracture resistance of wire reinforced ceramic. Material and methods: Heat pressed ceramic(ingot No.200 : IPS Empress 2, Ivoclar Vivadent, Liechtenstein) and Ni-Cr wire(Alfa Aesar, Johnson Matthey Company, USA) of 0.41 mm diameter were used in this study. Five groups of twelve uniform sized ceramic specimens(width 4 mm, thickness 2 mm, length 15 mm) were fabricated. Each group had different wire arrangement. Wireless ceramic was used as control group. The experimental groups were divided according to wire number and position. One, two and three strands of wires were positioned on the longitudinal axis of specimen. In another experimental group, three strands of wires positioned on the longitudinal axis and five strands of wires positioned on the transverse axis. Three-point bending test was done with universal testing machine(Z020, Zwick, Germany) to compare the flexural modulus, flexural strength, strain at fracture and fracture toughness of each group. Fractured ceramic specimens were cross-sectioned with caborundum disc and grinded with sandpaper to observe interface between ceramic and Ni-Cr wire. The interface between ceramic and Ni-Cr wire was analyzed with scanning electron microscope(JSM-6360, JEOL, Japan) under platinum coating. Results: The results obtained were as follows: 1. The average and standard deviation in flexural modulus, flexural strength and fracture toughness showed no statistical differences between control and experimental groups. However, strain was significantly increased in wire inserted ceramics(P<.001). 2. Control group showed wedge fracture aspects across specimen, while experimental groups showed cracks across specimen. 3. Scanning electron microscopic image of cross-sectioned and longitudinally-sectioned specimens showed no gap at the interface between ceramic and Ni-Cr wire. Conclusion: The results of this study showed that wire inserted ceramics have a high strain characteristic. However, wire inserted ceramics was not enough to use at posterior area of mouth in relation to flexural modulus and flexural strength. Therefore, we need further studies.