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Research Article
A New Discussion on Banach-Type Fixed Point Result in Double-Composed Metric Spaces
Issue:
Volume 9, Issue 2, December 2025
Pages:
26-30
Received:
4 September 2025
Accepted:
30 September 2025
Published:
30 October 2025
Abstract: One of the important research directions of fixed point theory is the generalization of metric spaces. An interesting generalization of metric space is the modification of triangular inequality. In the last few decades, many generalizations of metric space have been introduced in the field of fixed point theory by changing triangle inequality using multiplication of constants or functions. Recently, a new generalization of metric space with changing triangle inequality using the composition of two functions, namely, a double-composed metric space, has been introduced. A double-composed metric space is a new concept using the composition of functions, unlike the previous generalizations of metric space that modify the triangular inequality using the multiplication of functions. And, Banach-type fixed point result and Kanan-type fixed point result are established under certain assumptions in the setting of double-composed metric spaces. In this paper, we reconsider the Banach-type fixed point result in the setting of double-composed metric spaces under new and simple conditions. We have proved the fixed point theorem by using a new proof method and, consequently, we have demonstrated that Banach’s contractions in double-composed metric spaces have a unique fixed point under different assumptions from the previous one. We also present an example showing the validity of our fixed point result. Finally, we apply our fixed point result to show the existence of solution of Fredholm integral equations.
Abstract: One of the important research directions of fixed point theory is the generalization of metric spaces. An interesting generalization of metric space is the modification of triangular inequality. In the last few decades, many generalizations of metric space have been introduced in the field of fixed point theory by changing triangle inequality using...
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Research Article
Parameter Identification of Fractional-order Systems with Unknown Both State and Input Delays Based on Block Pulse Functions
Yu-Gang Hyon,
Hyon-Ju Sin,
Myong-Hyok Sin*
,
Chol Min Sin,
Hun Kim
Issue:
Volume 9, Issue 2, December 2025
Pages:
31-44
Received:
27 October 2025
Accepted:
22 November 2025
Published:
29 December 2025
Abstract: In this paper, we propose a method for identification of continuous-time fractional-order systems with unknown states and input delays. In practice, many systems are modeled accurately with fractional differential equations. In particular, many systems are modeled as fractional differential equations with input delay and state delay. Since the geometric and physical meaning of fractional calculus is not clear, it is difficult to model the real system directly to fractional order systems based on mechanical analysis. Thus, the identification of fractional order systems is the main method for constructing fractional order models and is the subject of the main research by many scientists. To solve the identification problem of systems with input delay and state delay, we use the fact that the fractional integral operator matrix by the block pulse functions is an upper triangular Toeplitz matrix. We have presented an efficient method to identify the linear and nonlinear parameters separably by using the commutativity and nilpotent property for multiplication between upper triangular Toeplitz matrices. We also have presented an efficient algorithm to newly approximate the Jacobian of the variable projection functional to solve the least squares problem with nonlinear parameters. Several simulation examples have been used to verify the effectiveness of the proposed method. It is shown that the input delay and the state delay have a significant effect on the output characteristics of the system, especially the state delay has a larger effect than the input delay.
Abstract: In this paper, we propose a method for identification of continuous-time fractional-order systems with unknown states and input delays. In practice, many systems are modeled accurately with fractional differential equations. In particular, many systems are modeled as fractional differential equations with input delay and state delay. Since the geom...
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Research Article
Interacting Multi-Model Strong Robust Adaptive Unscented Kalman Filter to Bearing only Tracking of Underwater Vehicle Approaching the Observer
Kang Song Ju,
Myong Hyok Sin*
Issue:
Volume 9, Issue 2, December 2025
Pages:
46-67
Received:
4 November 2025
Accepted:
22 November 2025
Published:
29 December 2025
Abstract: We have designed an interacting multi-model strong robust adaptive unscented Kalman filter for bearing only tracking of an underwater vehicle approaching the observer. To solve the problem of tracking an approaching underwater vehicle to the observer based on only its bearing, an interactive multi-model robust adaptive unscented Kalman filter is proposed in this paper. First, a new model of the bearing sense motion towards the observer is proposed to construct a set of realistic target motion modes consisting of linear and curved motion modes. In addition, to account for the influence of outliers in the target bearing measurements, the distribution of measurement noise is assumed to have a Student’s t-distribution, and the probability distribution of the degree of function and the scaling matrix of this distribution is assumed to have a gamma distribution and an inverse Wishart distribution. Thus, the model interaction step is to factorize the mixed probability density function using variational Bayesian method and, based on this, a predictive update method is proposed. In the measurement update phase, the posterior probability density function is obtained in factorization form using variational Bayesian method, and based on this, a posteriori mode probability calculation method is proposed. Simulation results show that our proposed method greatly improves the convergence rate of target tracking error.
Abstract: We have designed an interacting multi-model strong robust adaptive unscented Kalman filter for bearing only tracking of an underwater vehicle approaching the observer. To solve the problem of tracking an approaching underwater vehicle to the observer based on only its bearing, an interactive multi-model robust adaptive unscented Kalman filter is pr...
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