Browsing by Author "Mukheimer, A."
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Article Citation Count: Abdeljawad, T...et al. (2012). Banach contraction principle for cyclical mappings on partial metric spaces. Fixed Point Theory And Applications, 154, 1-7. http://dx.doi.org/10.1186/1687-1812-2012-154Banach contraction principle for cyclical mappings on partial metric spaces(Springer International Publishing, 2012) Abdeljawad, Thabet; Alzabut, Jehad; Mukheimer, A.; Zaidan, Y.We prove that the Banacah contraction principle proved by Matthews in 1994 on 0-complete partial metric spaces can be extended to cyclical mappings. However, the generalized contraction principle proved by (Ilic et al. in Appl. Math. Lett. 24:1326-1330, 2011) on complete partial metric spaces can not be extended for cyclical mappings. Some examples are given to illustrate our results. Moreover, our results generalize some of the results obtained by (Kirk et al. in Fixed Point Theory 4(1):79-89, 2003). An Edelstein type theorem is also extended when one of the sets in the cyclic decomposition is 0-compact.Article Citation Count: Abdeljawad, T...et al. (2013). Best proximity points for cyclical contraction mappings with 0-boundedly compact decompositions. Journal of Computational Analysis and Application, 15(4), 678-685.Best proximity points for cyclical contraction mappings with 0-boundedly compact decompositions(Eudoxus Press, 2013) Abdeljawad, Thabet; Alzabut, Jehad; Mukheimer, A.; Zaidan, Y.The existence of best proximity points for cyclical type contraction mappings is proved in the category of partial metric spaces. The concept of 0-boundedly compact is introduced and used in the cyclical decomposition. Some possible generalizations to the main results are discussed. Further, illustrative examples are given to demonstrate the effectiveness of our results
