Common Best Proximity Points Theorems for H-Contractive Non-Self Mappings
Keywords:
common best proximity points, metric space, H-contractive conditionAbstract
Fixed point theory and contractive mappings are popular tools in solving a variety of problems such as control theory, economic theory, nonlinear analysis and global analysis.There are many works on different types of contractions to find a fixed point in metric spaces. Improving and extending some kind of those, in this paper, we introduce a new version of H-contradiction for four mappings in a metric space (X,d). Then, we prove the existence and uniqueness of a common best proximity point for four non-self mappings. An example is also given to support our main result. The related fixed point theorem are also proved.
References
K. Fan, Extensions of two xed point theorems of F.E. Browder, Math . Z . 112 , 234-240 (1969)
WA. Kirk, S. Reich, P. Veeramani, Proximinal retracts and best proximity pair theorems, Numer.Funct.Anal.Optim. 24 , 851-862 (2003)
MA. Alghamdi, N. Shahzad, F. Vetro, Best proximity points for some classes of proximal contractions, Abstr.Appl.Anal. 2013 , Article ID 713252 (2013)
M. Derafshpour, S. Rezapour, N. Shahzad, Best proximity points of cyclic -contractions in ordered metric spaces, Topol . Methods Nonlinear Anal . 37(1) , 193-202 (2011)
M. Gabeleh, Proximal weakly contractive and proximal nonexpansive non-self-mappings in metric and Banach spaces , J. Optim. Theory Appl. 158 , 615-625 (2013)
M. Gabeleh, N. Shahzad, Existence and convergence theorems of best proximity points, J.Appl.Math. 2013, Article ID 101439 (2013) . doi:10.1155/2013/101439
HK. Pathak, N. Shahzad, Convergence and existence results for best C-proximity points, Georgian Math.J. 19(2) , 301-316 (2012)
S. Sadiq Basha, N. Shahzad, Best proximity point theorems for generalized proximal contractions, Fixed Point Theory Appl . 2012 , 42 (2012)
T. Suzuki, M. Kikkawa, C. Vetro, The existence of best proximity points in metric spaces with the property UC, Nonlinear Anal . 71 , 2918-2926 (2009)
C. Vetro, Best proximity points : convergence and existence theorems for p-cyclic mappings, Nonlinear Anal . 73(7) , 2283-2291 (2010)
D. Wardowski, Fixed points of a new type of contractive mappings in complete metric space, Fixed Point Theory Appl, 2012. doi:10.1186/1687-1812-2012-94.
M. Omidvari, S.M. Vaezpour, R. Saadati, Best proximity point theorems for F- contractive non-self mappings, Miskolc mathematical notes, Vol. 15(2014), No. 2, pp. 615-623
