Best Proximity Point Iteration for Nonexpensive Mapping in Banach Spaces
Journal of nonlinear sciences and its applications, Tome 7 (2014) no. 2, p. 126-130.

Voir la notice de l'article provenant de la source International Scientific Research Publications

In this paper we prove existence theorems of best proximity points in Banach spaces. Also an iterative approximation of the best proximity point of a nonexpensive mapping in Banach space is developed.
DOI : 10.22436/jnsa.007.02.06
Classification : 46A32, 46M05, 41A17.
Keywords: Best proximity pair, best proximity point, cyclic contractive map, P-property.

Haddadi, Mohammad Reza 1

1 Faculty of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran
@article{JNSA_2014_7_2_a5,
     author = {Haddadi, Mohammad Reza},
     title = {Best {Proximity} {Point} {Iteration} for {Nonexpensive} {Mapping} in {Banach} {Spaces}},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {126-130},
     publisher = {mathdoc},
     volume = {7},
     number = {2},
     year = {2014},
     doi = {10.22436/jnsa.007.02.06},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.007.02.06/}
}
TY  - JOUR
AU  - Haddadi, Mohammad Reza
TI  - Best Proximity Point Iteration for Nonexpensive Mapping in Banach Spaces
JO  - Journal of nonlinear sciences and its applications
PY  - 2014
SP  - 126
EP  - 130
VL  - 7
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.007.02.06/
DO  - 10.22436/jnsa.007.02.06
LA  - en
ID  - JNSA_2014_7_2_a5
ER  - 
%0 Journal Article
%A Haddadi, Mohammad Reza
%T Best Proximity Point Iteration for Nonexpensive Mapping in Banach Spaces
%J Journal of nonlinear sciences and its applications
%D 2014
%P 126-130
%V 7
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.007.02.06/
%R 10.22436/jnsa.007.02.06
%G en
%F JNSA_2014_7_2_a5
Haddadi, Mohammad Reza. Best Proximity Point Iteration for Nonexpensive Mapping in Banach Spaces. Journal of nonlinear sciences and its applications, Tome 7 (2014) no. 2, p. 126-130. doi : 10.22436/jnsa.007.02.06. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.007.02.06/

[1] Chauhan, S.; Pant, B. D. Fixed point theorems for compatible and subsequentially continuous mappings in Menger spaces, J. Nonlinear Sci. Appl., Volume 7 (2001), pp. 78-89

[2] Abkar, A.; Gabeleh, M. Best proximity points of non-self mappings, TOP, Volume 21 (2013), pp. 287-295

[3] Eldred, A. A.; Kirk, W. A.; Veeramani, P. Proximinal normal structure and relatively nonexpansive mappings, Studia Math, Volume 171 (2005), pp. 283-293

[4] Eldred, A. A.; Veeramani, P. Existence and convergence of best proximity points , J. Math. Anal. Appl., Volume 323 (2006), pp. 1001-1006

[5] Gabeleh, M. Proximal Weakly Contractive and Proximal Nonexpansive Non-self-Mappings in Metric and Banach Spaces , J. Optim. Theory Appl. , Volume 158 (2013), pp. 615-625

[6] Haddadi, M. R.; Moshtaghioun, S. M. Some Results on the Best Proximity Pair, Abstract and Applied Analysis, ID 158430, Volume 2011 (2011), pp. 1-9

[7] Nashine, H. Kumar; Kumam, P.; Vetro, C. Best proximity point theorems for rational proximal contractions, Fixed Point Theory and Applications, 2013:95 , 2013

[8] Purtasa, Yunus; Kiziltunc, Hukmi Weak and strong convergence of an explicit iteration process for an asymptotically quasi-i-nonexpansive mapping in Banach spaces , J. Nonlinear Sci. Appl., Volume 5 (2012), pp. 403-411

[9] Basha, S. Sadiq Best proximity points: global optimal approximate solution, J Global Optim. , doi:10.1007/s10898- 009-9521-0, 2010

[10] Basha, S. Sadiq Extensions of Banachs contraction principle, Numer Funct Anal Optim, Volume 31 (2010), pp. 569-576

[11] Sankar, Raj V.; P. Veeramani Best proximity pair theorems for relatively nonexpansive mappings, Appl Gen Topol, Volume 10(1) (2009), pp. 21-28

[12] Sankar, Raj V. A best proximity point theorem for weakly contractive non-self-mappings, Nonlinear Analysis, Volume 74 (2011), pp. 4804-4808

[13] Xu, H. K. An iterative approach to quadratic optimization, J. Optim. Theory Appl., Volume 116 (2003), pp. 659-678

Cité par Sources :