In this paper, we present some existence and uniqueness results for coupled coincidence point and common fixed point of θ -ψ -contraction mappings in complete metric spaces endowed with a directed graph. Our results generalize the results obtained by Kadelburg et al. (Fixed Point Theory Appl. 2015:27, 2015, doi:10.1007. We also have an application to some integral system to support the results.
In this paper, we pursue further analysis of the performance of a compact structure-preserving finite difference scheme. The convergence, stability, and accuracy of the approximate solution with respect to grid refinement are discussed. The compact difference approach to precisely preserving invariants on any time-space regions gives a three-level linear-implicit scheme with the spatial accuracy, found to be fourth order on a uniform grid. The method is verified by comparison with a solution of the Rosenau-Kawahara equation just obtained with second-order finite difference schemes recently. Also, the efficiency of the present algorithm is confirmed by simulations of the problem at a long time. Details of CPU time are examined in order to assess the usefulness of the compact scheme for determining an approximate solution.
We introduce a new self-adaptive algorithm for applications to image restoration problems. In order to study an image restoration, we consider the algorithm that contains inertial effects and step sizes, which is independent from the norm of the bounded linear operator. With some control conditions, the strong convergence to the minimum norm solution of the algorithm is obtained. Convergence analysis of the proposed algorithm is also discussed. Moreover, numerical results of image restoration problems illustrate that the proposed algorithm is efficient and outperforms other ones.
KEYWORDSdemicontractive operator, image restoration problem, inertial algorithm, self-adaptive algorithm
MSC CLASSIFICATION
47J25; 65K10wherex is an original image, y is the observed image, A is a blurring matrix, and is a noise term.The split common fixed point problem has received much attention due to its applications in image reconstruction, signal processing, intensity-modulated radiation therapy, computed tomography, control theory, approximation theory, Math Meth Appl Sci. 2019;42:7268-7284.
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