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.

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.

In this paper first we define the morphism between GEOMETRIC spaces in two different types. We construct two categories of U-GESP and L-GESP from GEOMETRIC spaces then investigate some properties of the two categories, for instance U-GESP is topological. The relation between hypergroups and GEOMETRIC spaces is studied. By constructing the category SNS-Hv of Hv-groups we answer the question that which construction of hyperstructures on the category of sets has free object in the sense of universal property. At the end we define the category of GEOMETRIC Hypergroups and we study its relation with the category of hypergroup.

In this paper, we study a three-parameter bivariate distribution obtained by taking GEOMETRIC minimum of Rayleigh distributions. Some important properties of this bivariate distribution have been investigated. It is observed that the maximum likelihood estimators of the parameters cannot be obtained in closed forms. We propose to use the EM algorithm to compute the maximum likelihood estimates of the parameters, and it is computationally quite tractable. Based on an extensive simulated study, the effectiveness of the proposed algorithm is confirmed. We also analyze one real data set for illustrative purposes. Finally, we conclude the paper.

This article comprises three parts. The first section deals with the evaluation of geometry & its relation to the parallelism among the main three fold worlds [intellectual world, absolute imagination world, & material world]. In this section, we considered Pythagoreans, Plato, Ibn Sina, Ekhvan alsafa, Abu Reyhan Biruni and Rene Guene view points about the symbolic position of geometry & its relation to the spiritual insights. In the thoughts of these figures, geometry describes the super natural realm & cosmic lives of the heavens by a philosophic language & by offering interior insights leads the soul to the real existence. In Ekhvan alsafa's view points, geometry splits into two Categories of sensible & rational & both are considered as a new way in recognition of the wisdom essence & the nature of the soul. The second section deals with GEOMETRIC position of the existence system in creating the order & unity of the world components. In this section the cosmic orderlines & parallelism of the symbolic appearance of god's justice in proportion to the inner merit &, in other words, the worth of every thing are explained. Third section is allocated to the relationship between geometry & monotheism insights & also some meanings of GEOMETRIC symbols. The presence of GEOMETRIC structure in the abstract styles of GEOMETRIC ornaments, Islamic, Khatayi or architectural forms & volumes is adopted from the holy principle of monotheism. The essence of monotheism in the field of visual imagination is manifested in the GEOMETRIC crystallized forms & by itself forms the essence of the Islamic art. At the end of this section we deal with the meanings of the main GEOMETRIC symbols: point, triangle, circle & square in the obtained view points.

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).