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.

In this paper, we introduce the notions of FUZZY a-Geraghty con- traction type mapping and FUZZY b- j -contractive mapping and establish some interesting results on the existence and uniqueness of xed points for these two types of mappings in the setting of FUZZY metric spaces and non-Archimedean FUZZY metric spaces. The main results of our work generalize and extend some known comparable results in the literature. Furthermore, several illustrative examples are given to support the usability of our obtained results.

In this paper, a new type of equation namely FUZZY fractional stochastic Pantograph delay differential system (FSPDDS) is proposed. In our previous work, a first extension of FUZZY stochastic differential system into FUZZY fractional stochastic differential system by using Granular differentiability has been established. Here we study the existence and uniqueness results for the FUZZY FSPDDS which are obtained by using generalized Granular differentiability and CONTRACTION principle with weaker conditions. This kind of equation is used in many real world problems. Finally, we provide two numerical examples for the effectiveness of the theoretical results.

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.

FUZZY analytical hierarchy process (FUZZY-AHP) technique as a knowledge-driven approach relies on the geologist’ s input to weight the importance of each evidence layer is applied for prospectivity modeling of Au mineralization within the Takhte-soleyman district. Firstly, in current study, all of the criteria and sub-criteria which are gained from exploratory data (geochemistry, remote sensing, geology and tectonic) are weighted by using AHP and thereafter are transformed into [0-1] range based on the FUZZY logic. All fuzzified layers according to the calculated weights were synthesized and prospectivity modeling of Au mineralization based on the FUZZY-AHP technique was generated. In this study, it was used another FUZZY method based on the FUZZY operators (OR and GAMMA) that called “ FUZZY-GAMMA” to generate the map of promising areas of Au mineralization in the study area. Finally, in order to evaluate the ability of the applied methods in delineating reliable promising areas, locations of Au occurrences in the study area were used. Consequently, the results demonstrate the more acceptable outcomes for FUZZY-AHP model by comparison with FUZZY-GAMMA model.

In this paper we introduce geometric CONTRACTION map and give a new condition for the existence and uniqueness of best proximity point of geometric CONTRACTIONs. We also consider the convergence of iterates to proximity points in metric spaces.

Endpoint results are presented for multi{valued cyclic CONTRACTION mappings on complete metric spaces (X; d). Our results extend previous results given by Nadler (1969), Da er{Kaneko (1995), Harandi (2010), Moradi and Kojasteh (2012) and Karapinar (2011).