• The Pure and Applied Mathematics
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• v.30 no.4
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• pp.417-427
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• 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
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• v.27 no.3
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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.

• The Pure and Applied Mathematics
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• v.29 no.4
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• pp.335-352
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• 2022

In this paper, we give an extended version of fixed point results for 𝜃-contraction and 𝜃-𝜙-contraction and define a new type of contraction, namely, cyclic 𝜃-contraction and cyclic 𝜃-𝜙-contraction in a complete metric space. Moreover, we prove the existence of best proximity point for cyclic 𝜃-contraction and cyclic 𝜃-𝜙-contraction. Also, we establish best proximity result in the setting of uniformly convex Banach space.

• Korean Journal of Mathematics
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• v.31 no.2
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• pp.123-131
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• 2023

In this paper, we prove existence of best proximity points for 2-convex contraction, 2-sided contraction, and M-weakly cyclic 2-convex contraction mappings in the setting of complete strongly regular generalized modular metric spaces that generalize many results in the literature.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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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.

• Journal of Power System Engineering
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• v.14 no.4
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• pp.37-42
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• 2010

This paper deals with the sealing mechanism of the gasket component and the effects of design parameters for the exhaust manifold. The finite element model includes hot-end exhaust system and a simplified gasket model supplied by ABAQUS software. The mechanical behaviors of bead and body of a gasket are measured after several times of cyclic loads by gasket supplier. From the finite element analysis due to the cyclic thermal loads, the flange of exhaust manifold shows thermal expansion and contraction in longitudinal direction as well as convex and concave deformations with respect to the engine cylinder head. And, the contact pressures of the gasket beads suddenly changes by normal deformation of inlet flanges. Therefore, the magnitudes of contact pressures could be used to determine the sealing characteristics of the exhaust gas in the exhaust system. The distributions of contact pressures in gasket bead lines shows a good agreement with the engine test results.

• Journal of Korean Institute of Industrial Engineers
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• v.5 no.2
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• pp.21-36
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• 1979

Static muscle contractions when prolonged or frequently repeated result in discomfort, fatigue, and musculosketal injuries. An analytic and quantitative model has been developed in order to expand the working knowledge on muscle fatigue. In this paper, three Markov models of muscle fatigue are developed. These models are based on motor unit fatigue-recovery characteristics obtained from information on motor unit behavior as it relates to fatigue and graded exertions. Three successively more realistic models are developed that involve: (1) homogeneous motor units with intensity-dependent fatigue rates and state-independent recovery rates (the HMSI model); (2) homogeneous motor units, intensity-dependent fatigue rates and state-dependent recovery rates (the HMSD model); and (3) non-homogeneous motor units (i.e., Type S and Type F), intensity-dependent fatigue rates and state-dependent recovery rates (the HMSD model). The result indicate that a simple stochastic model provide a means to analyze the complex nature of muscle fatigue in sequential static exertions.