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In this paper, firstly, we review the notion of the SO-complete metric spaces. This notion let us to consider some fixed point theorems for single-valued mappings in incomplete metric spaces. Secondly, as motivated by the recent work of A.H. Ansari et al. [J. Fixed Point Theory Appl. (2017), 1145–1163], we obtain that an existence and uniqueness result for the following problem: finding x ∈ X such that x = T x, Ax R₁ Bx and Cx R₂ Dx, where (X, d) is an incomplete metric space equipped with the two binary relations R₁ and R₂, A, B, C, D : X → X are discontinuous mappings and T : X → X satisfies in a new contractive condition. This result is a real generalization of main theorem of A.H. Ansari’s. Finally, we provide some examples for our results and as an application, we find that the solutions of a differential equation. Publisher's Version

Intraoperative electron radiotherapy is one of the radiotherapy methods that delivers a high single fraction of radiation dose to the patient in one session during the surgery. Beam shaper applicator is one of the applicators that is recently employed with this radiotherapy method. This applicator has a considerable application in treatment of large tumors. In this study, the dosimetric characteristics of the electron beam produced by LIAC intraoperative radiotherapy accelerator in conjunction with this applicator have been evaluated through Monte Carlo simulation by MCNP code. The results showed that the electron beam produced by the beam shaper applicator would have the desirable dosimetric characteristics, so that the mentioned applicator can be considered for clinical purposes. Furthermore, the good agreement between the results of simulation and practical dosimetry, confirms the applicability of Monte Carlo method in determining the dosimetric parameters of electron beam intraoperative radiotherapy

Background and Objective: The most common intravascular brachytherapy sources include 32P, 188Re, 106Rh and 90Sr/90Y. In this research, skin absorbed dose for different covering materials in dealing with these sources were evaluated and the best covering material for skin protection and reduction of absorbed dose by radiation staff was recognized and recommended. Method: Four materials including polyethylene, cotton and two different kinds of plastic were proposed as skin covers and skin absorbed dose at different depths for each kind of the materials was calculated separately using the VARSKIN3 code. Results: The results suggested that for all sources, skin absorbed dose was minimized when using polyethylene. Considering this material as skin cover, maximum and minimum doses at skin surface were related to 90Sr/90Y and 106Rh, respectively. Conclusion: polyethylene was found the most effective cover in reducing skin dose and protecting the skin. Furthermore, proper agreement between the results of VARSKIN3 and other experimental measurements indicated that VRASKIN3 is a powerful tool for skin dose calculations when working with beta emitter sources. Therefore, it can be utilized in dealing with the issue of radiation protection.

Background: One of the main problems of dedicated IORT accelerators is to determine dosimetric characteristics of the electron beams. Monte Carlo simulation of IORT accelerator head and produced beam will be useful to improve the accuracy of beam dosimetry. Materials and Methods: Liac accelerator head was modeled using the BEAMnrcMonte Carlo simulation system. Phase-space files were generated at the bottom of the applicators. These phase-space files were used as an input source in DOSXYZnrc and BEAMDP codes for dose calculation and analysis of the characteristic of the electron beams in all applicators and energies. Results: The results of Monte Carlo calculations are in very close agreement with the measurements. There is a decrease in the peak of the initial spectrum when electrons come from the end of accelerator wave guide to the end of applicator. By decreasing the applicator diameter, the mean energy of electron beam decreased. Using applicators and increasing their size, X-ray contamination will increase. The percentage of X-ray contamination increases by applicator diameter. This is related to the increase of the mean energy of electron beams. Conclusion: Application of PMMA collimator leads to, although well below accepted level, the production of bremsstrahlung. The results of this study showed that special design of LIAC head accompanying by PMMA collimator system cause to produce an electron beam with an individual dosimetric characteristic making it a useful tool for intraoperative radiotherapy purposes.