• Nonlinear Functional Analysis and Applications
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• v.26 no.3
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• pp.451-474
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• 2021

In this paper, we investigate a hybrid algorithm for finding zeros of the sum of maximal monotone operators and Lipschitz continuous monotone operators which is also a common fixed point problem for finite family of relatively quasi-nonexpansive mappings and split feasibility problem in uniformly convex real Banach spaces which are also uniformly smooth. The iterative algorithm employed in this paper is design in such a way that it does not require prior knowledge of operator norm. We prove a strong convergence result for approximating the solutions of the aforementioned problems and give applications of our main result to minimization problem and convexly constrained linear inverse problem.

• Nonlinear Functional Analysis and Applications
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• v.26 no.4
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• pp.839-853
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• 2021

Let 𝕽ⁿ be an Euclidean space and g : 𝕽ⁿ → 𝕽ⁿ be a monotone and continuous mapping. Suppose the convex constrained nonlinear monotone equation problem x ∈ 𝕮 s.t g(x) = 0 has a solution. In this paper, we construct an inertial-type algorithm based on the three-term derivative-free projection method (TTMDY) for convex constrained monotone nonlinear equations. Under some standard assumptions, we establish its global convergence to a solution of the convex constrained nonlinear monotone equation. Furthermore, the proposed algorithm converges much faster than the existing non-inertial algorithm (TTMDY) for convex constrained monotone equations.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.1129-1135
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• 2022

The purpose of this research is to find an extension of the renowned Chernoff theorem on standard operator algebra. Infact, we prove the following result: Let H be a real (or complex) Banach space and 𝓛(H) be the algebra of bounded linear operators on H. Let 𝓐(H) ⊂ 𝓛(H) be a standard operator algebra. Suppose that D : 𝓐(H) → 𝓛(H) is a linear mapping satisfying the relation D(AⁿBⁿ) = D(Aⁿ)Bⁿ + AⁿD(Bⁿ) for all A, B ∈ 𝓐(H). Then D is a linear derivation on 𝓐(H). In particular, D is continuous. We also present the limitations on such identity by an example.

• Structural Engineering and Mechanics
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• v.81 no.5
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• pp.647-664
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• 2022

The powerful data mapping capability of computational deep learning methods has been recently explored in academic works to develop strategies for structural health monitoring through appropriate characterization of dynamic responses. In many cases, these studies concern laboratory prototypes and finite element models to validate the proposed methodologies. Therefore, the present work aims to investigate the capability of a deep learning algorithm called Sparse Autoencoder (SAE) specifically focused on detecting structural alterations in real-case studies. The idea is to characterize the dynamic responses via SAE models and, subsequently, to detect the onset of abnormal behavior through the Shewhart T control chart, calculated with SAE extracted features. The anomaly detection approach is exemplified using data from the Z24 bridge, a classical benchmark, and data from the continuous monitoring of the San Vittore bell-tower, Italy. In both cases, the influence of temperature is also evaluated. The proposed approach achieved good performance, detecting structural changes even under temperature variations.

• Nonlinear Functional Analysis and Applications
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• v.28 no.1
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• pp.135-173
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• 2023

The purpose of this paper is to introduce and study a method for solving the split equality of variational inequality and f, g-fixed point problems in reflexive real Banach spaces, where the variational inequality problems are for uniformly continuous pseudomonotone mappings and the fixed point problems are for Bregman relatively f, g-nonexpansive mappings. A strong convergence theorem is proved under some mild conditions. Finally, a numerical example is provided to demonstrate the effectiveness of the algorithm.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.6
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• pp.128-136
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• 1995

The problem addressed in this paper is that of the on-line computational burden of time-optimal control laws for quick, strongly nonlinear systems like revolute robots. It will be demonstrated that a large amount of off-line computation can be substituted for most of the on-line burden in cases of time optimization with constrained inputs if differential point-to- point specifications can be relaxed to cell-to-cell transitions. These cells result from a coarse discretization of likely swaths of state space into a set of nonuniform, contiguous volumes of relatively simple shapes. The cell boundaries approximate stream surfaces of the phase fluid and surfaces of equal transit times. Once the cells have been designed, the bang- bang schedules for the inputs are determined for all likely starting cells and terminating cells. The scheduling process is completed by treating all cells into which the trajectories might unex- pectedly stray as additional starting cells. Then an efficient-to-compute control law can be based on the resulting table of optimal strategies.

• Kyungpook Mathematical Journal
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• v.63 no.1
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• pp.45-60
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• 2023

In this paper we suggest an enhanced Geraghty-type contractive mapping for examining the existence properties of classical nonlinear operators with or without prior degenerates. The nonlinear operators are proved to exist with the imposition of the Geraghty-type condition in a non-empty closed subset of complete metric spaces. To showcase some efficacies of the Geraghty-type condition, convergent rate and stability are deduced. The results are used to study some asymptotic properties of perturbed integral and hypergeometric operators. The results also extend and generalize some existing Geraghty-type conditions.

• The Pure and Applied Mathematics
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• v.30 no.4
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• pp.357-375
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• 2023

In this paper, we introduce the concept of bipolar soft supra topological space and provide a characterization of the related concepts of bipolar soft supra closure and bipolar soft supra interior. We also establish a connection between bipolar soft supra topology and bipolar soft topology. Additionally, we present the concept of bipolar soft supra continuous mapping and examine the concept of bipolar soft supra compact topological space. A related result concerning the image of the bipolar soft supra compact space is proved. Finally, we identify the concepts of disconnected (connected) and strongly disconnected (strongly connected) space and derive several results linking them together. Relationships among these concepts are clarified with the aid of examples.

• Journal of the Korean Mathematical Society
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• v.36 no.6
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• pp.1061-1073
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• 1999

Let X be a real normed linear space. Let T : D(T) ⊂ X \longrightarrow X be a uniformly continuous and ∮-strongly quasi-accretive mapping. Let {${\alpha}$n}{{{{ { }`_{n=0 } ^{$\infty$ } }}}} , {${\beta}$n}{{{{ { }`_{n=0 } ^{$\infty$ } }}}} be two real sequences in [0, 1] satisfying the following conditions: (ⅰ) ${\alpha}$n \longrightarrow0, ${\beta}$n \longrightarrow0, as n \longrightarrow$\infty$ (ⅱ) {{{{ SUM from { { n}=0} to inf }}}} ${\alpha}$=$\infty$. Set Sx=x-Tx for all x $\in$D(T). Assume that {u}{{{{ { }`_{n=0 } ^{$\infty$ } }}}} and {v}{{{{ { }`_{n=0 } ^{$\infty$ } }}}} are two sequences in D(T) satisfying {{{{ SUM from { { n}=0} to inf }}}}∥un∥<$\infty$ and vn\longrightarrow0 as n\longrightarrow$\infty$. Suppose that, for any given x0$\in$X, the Ishikawa type iteration sequence {xn}{{{{ { }`_{n=0 } ^{$\infty$ } }}}} with errors defined by (IS)1 xn+1=(1-${\alpha}$n)xn+${\alpha}$nSyn+un, yn=(1-${\beta}$n)x+${\beta}$nSxn+vn for all n=0, 1, 2 … is well-defined. we prove that {xn}{{{{ { }`_{n=0 } ^{$\infty$ } }}}} converges strongly to the unique zero of T if and only if {Syn}{{{{ { }`_{n=0 } ^{$\infty$ } }}}} is bounded. Several related results deal with iterative approximations of fixed points of ∮-hemicontractions by the ishikawa iteration with errors in a normed linear space. Certain conditions on the iterative parameters {${\alpha}$n}{{{{ { }`_{n=0 } ^{$\infty$ } }}}} , {${\beta}$n}{{{{ { }`_{n=0 } ^{$\infty$ } }}}} and t are also given which guarantee the strong convergence of the iteration processes.

• The Journal of Engineering Geology
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• v.17 no.4
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• pp.555-566
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• 2007

In general, RMR classification system is used for the support design of a tunnel. Face mapping during excavation and RMR-based rock classifications are conducted in order to provide information for complementary changes to preliminary survey plans and for continuous geological estimations in direction of tunnel route. Although they are ever so important, there are not enough time for survey in general and sometimes even face mapping is not available. Linear regression analysis for the estimation of mediating RQD and condition of discontinuities, which require longer time and more detailed observation in RMR, was performed and optimum regression equations are suggest as the result. The geological data collected from tunnels were analyzed in accordance with three rock types as sedimentary rock, phyllite and granite to see geological effects, generally not been considered in previous researches. Parameters for the regression analysis were set another RMR factor.