In this manuscript, we investigate Random fixed points by examining Random mappings that satisfy Random Sehgal-type inequalities within the framework of separable complete metric spaces.  The principal contributions of this study both encompass and significantly broaden a range of existing results in the pertinent literature.  There is a novel approach to finding the Random fixed points as the proposed results in the Random setting. To demonstrate the effectiveness and strength of our results, we also provide illustrative examples. Moreover, the results are also applied to Ulam Hyers Stability (UHS) and the Limit Shadowing Properties (LSP) of Random fixed point problems. Subsequently, we utilize the derived results to systematically consolidate and affirm the existence and uniqueness of Random solutions for nonlinear Random Fredholm integral equations.

The accuracy and reliance increase and consequently reduction of uncertainty of spatial prediction maps of environmental hazards including landslides is one of the challenges facing with in such studies Therefore, the objective of this research is to introduce a hybrid model of data mining algorithm named Random Forest (RF) -Random Subspace (RF-RS) in order to enhance the accuracy of spatial prediction map of landslide prone areas around the city of Bijar, Kurdistan province, Iran. Firstly, 19 affecting factors on shallow landslides in the study area including slope degree, slope aspect, elevation, curvature, profile curvature, plan curvature, solar radiation, stream power index (SPI), topographic wetness index (TWI), length-angle of slope (LS), land use, normalized difference vegetation index (NDVI), litho logy, distance to fault, fault density, rainfall, distance to stream, stream density and distance to road were identified. Then based on Information Gain Ratio (IGR), twelve factors among them were selected to be used in modeling. The elative importance of each factor was assessed by Random Forest (RF) model as well as Random Forest-Random Subspace (RF-RS) hybrid model. Kappa, Precision, Recall, and AUROC indices were used to evaluate the models not only for training dataset but also for testing dataset. Shallow landslide susceptibility maps of the study area were prepared using both models. The results showed that slope aspect in the RF model and slope degree in the RF-RS hybrid model is the most important affecting factor on landslide occurrence in the area. The model evaluation results indicated that both models are reasonable in application for shallow landslide susceptibility mapping. The findings also indicated that the percentage of area under the curve of ROC (AUROC) was 0.729 and 0.784 for training dataset by RF and RF-RS hybrid model, respectively, while these values were 0.717 and 0.771 for testing dataset. In conclusion, it can be claimed that the new technique (RF-RS hybrid model) is able to increase the accuracy of spatial prediction map of shallow landslides in the study area. This accurate map will help decision-makers to protect infrastructures of an area, to develop better land-use planning programs and to more effectively control sediments.

In a fuzzy metric space (X, M,*), where * is a continuous t-norm, a locally fuzzy Contraction mapping is defined. It is proved that any locally fuzzy Contraction mapping is a global fuzzy contractive. Also, if f satisfies the locally fuzzy contractivity condition then it satisfies the global fuzzy contractivity condition.

Background and Aim: Whole Body Vibration (WBV) is more attended as a new exercise modality helping improvement in neuro-muscular performance, but so far, its immediate effect indirectly concurrent with different external load (EL) on maximum voluntary Contraction (MVC) and upper limb electromyography (EMG) in not known. The purpose of the spresent study was to investigate the immediate effect of WBV on maximumisometric Contraction and upper limb EMG indifferent Contraction forces.Materials and Methods: In 15 young healthy men, dominant biceps Randomly underwent isometric contaction with supination of forearm and 90 degrees of elbow flexion while receiving no WBV or WBV with a frequency of 50 Hz and low amplitude (4 mm) for 60 seconds (i.e. two thirty-second phase with an interval of 20-second-rest) in three different modes: without EL, with an EL of 10% of primary MVC, and finally with an EL of 20% of primary MVC. In the meantime, EMG activity of the muscle was recorded and once the whole exercise protocol was terminated, MVC was measured and its EMG activity was recorded simultaneously with MVC.Results: WBV without EL showed a significant increase in biceps MVC compared with no WBV and no EL (P=0.006), wheras in WBV the comparison of an EL of 10% of primary MVC and that of 20%, despite rendering higher rate of MVC, is not statistically significant. On the other hand, WBV without EL revealed a significant improvement in biceps RMS (P=0.001). The same was true in WBV with an EL of 20% of MVC (P=0.032). The rate of ΔFMED with WBV or without WBV, and with an EL of 20%, was statistically more significant than without WBV, with an external load of 10%, and this significancy with vibration was P=0.011 and without vibration was P=0.016. Meanwhile, ΔFMED was significant with WBV and with an external load of 20% of MVC compared with WBV and 10% of MVC (P=0.023).Conclusion: It seems that a single session of WBV reults in an immediate increase of MVC and EMG of biceps bracheiand applying ELs of 10% and 20% of MVC with WBV did not significantly increase in the present study, but it leadsto more increase of MVC and EMG. Also, the effect of an EL of 20% of MVC in this increase is more tangible than 10% of MVC.