Common best proximity points for $(\psi-\phi)$-generalized weak proximal contraction type mappings
الموضوعات :
K. K. M. Sarma
1
(Department of Mathematics, Andhra University, India)
G. Yohannes
2
(Department of Mathematics, Wolkite University, Ethiopia)
الکلمات المفتاحية: Best proximity point, common best proximity points, lower semi continuous functions, (ψ − ϕ)-generalized proximal contraction,
ملخص المقالة :
In this paper, we introduce a pair of generalized proximal contraction mappings and prove theexistence of a unique best proximity point for such mappings in a complete metric space. Weprovide examples to illustrate our result. Our result extends some of the results in the literature.
[1] S. Basha Sadiq, N. Shahzad, R. Jeyaraj, Common best proximity points, Global optimization of multi-objective functions, Appl. Math. Lett. 24 (6) (2011), 883-886.
[2] K. Fan, Extensions of two fixed point theorems of F.E. Browder, Mathematische zeitschrift 112 (1969), 234-240.
[3] M. Gabeleh, Best proximity point theorems via proximal non-self mappings, J. Optim. Theory Appl. 164 (2) (2015), 565-576.
[4] M. Jleli, B. Samet, Best proximity points for (α − ψ)-proximal contractive type mappings and applications, Bulletin des Sciences Mathematiques. 137 (8) (2013), 977-995.
[5] W. A. Kirk, S. Reich, P. Veeramani, Proximinal retracts and best proximity pair theorems, Numer. Funct. Anal. Optim. 24 (2003), 851-862.
[6] J. B. Prolla, Fixed-point theorems for set-valued mappings and existence of best approximants,Numerical Funct. Anal. Optimiz. 5 (4) (1982-1983), 449-455.
[7] S. Reich, Approximate selections, best approximations, fixed points, and invariant sets, Journal of Math. Anal. Appl. 62 (1) (1978), 104-113.
[8] V. M. Sehgal, S. P. Singh, A generalization to multi functions of Fans best approximation theorem, Proc. Amer. Math. Soc. 102 (3) (1988), 534-537.
[9] B. Samet, Some results on best proximity points, J. of Optimization Theory and Appl. 159 (1) (2013), 281-291.
[10] S. L. Singh, R. Kamal, M. De la Sen, R. Chugh, A fixed point theorem for generalized weak contractions, Filomat. 29 (7) (2015), 1481-1490.
[11] K. K. M. Sarma, G. Yohannes, Best proximity points for generalized (α−η−ψ)-Geraghty proximal contraction mappings, Mathematica Moravica. 21 (2) (2017), 85-102.
