In this paper, we discuss some Iterations and apply it to $d/BCK$-algebras and semigroups. Given a $BCK$-algebra $(X,*, 0)$, we construct an edge $d$-algebra by using the notion of Iterations.

This paper extends the notion of weak convergence in metric spaces to the case of S-metric spaces. Moreover, some results on the weak convergence of fixed point Iterations of Banach's, Kannan's, Chatterjee's, Reich's, Hardy and Roger's types of contractions on S-metric spaces are obtained. In addition, an example is presented to demonstrate our primary result.

We introduce a modified Noor iteration scheme generated by an infinite family of strict pseudo-contractive mappings and prove the strong convergence theorems of the scheme in the framework of q-uniformly smooth and strictly convex Banach space. Results shown here are extensions and refinements of previously known results.

In this paper, we propose a novel Mann iterative algorithm for discovering a shared fixed point of two nonexpansive mappings in real Hilbert spaces. We establish the weak convergence of this fixed-point approach under new conditions, and additionally demonstrate its strong convergence with the inclusion of an additional requirement. Our findings expand upon previous results presented by Kanzow and Shehu, as well as by Cho et al. Furthermore, we showcase the versatility of our main results through the presentation of various applications in the last section, accompanied by illustrative examples.

Background: The image quality of PET/CT is affected by various factors which include technical errors, Biological factors, and Physical factors. The errors due to physical factors can be reduced by using standardized image reconstruction parameters. The choice of reconstruction parameters is a trade‐off between resolution and noise and has a major impact on the performance of clinically important tasks such as lesion detection. Moreover, these image reconstruction parameters are highly specific to manufacturer and scanner type thus making generalizations difficult.Materials and Methods: PET/CT scan of Deluxe Jaszczak phantom filled with water having 74 MBq F‐ 18 FDG was acquired on Biograph mCT (Siemens Healthcare) PET/CT scanner. PET scan was acquired in one bed for 5 minutes. Transverse slices were reconstructed using OSEM reconstruction method by varying FWHM from 1mm to 8 mm and for each FWHM, Iterations (IT) varied from 1 to 10. The image quality of 240 mages was assessed by two nuclear medicine physicians based on 4 point scale.Results: At constant iteration, increase in FWHM resulted in smooth images, but gradual decrease in image quality seen because of edge blurring. At constant FWHM, increase in number of iteration improved the contrast in the image but at the cost of inclusion of noise.Conclusion: Optimized value of iteration and FWHM were found to be 4 and 2 mm respectively.