Common best proximity points for $(\psi-\phi)$-generalized weak proximal contraction type mappings

Journal of Linear and Topological Algebra

مقاله 4، دوره 06، شماره 04، اسفند 2017، صفحه 289-300   

نوع مقاله: Special Issue on Fixed Point Theory

نویسندگان

K. K. M. Sarma^{* 1}؛ G. Yohannes²

¹Department of Mathematics, Andhra University, India

²Department of Mathematics, Wolkite University, Ethiopia

چکیده

In this paper, we introduce a pair of generalized proximal contraction mappings and prove the existence of a unique best proximity point for such mappings in a complete metric space. We provide examples to illustrate our result. Our result extends some of the results in the literature.

کلیدواژه‌ها

Best proximity point؛ common best proximity points؛ (ψ − ϕ)-generalized proximal contraction؛ lower semi continuous functions

مراجع

[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.