# Best approximation for nonconvex set in $q$-normed space

Archivum Mathematicum (2006)

- Volume: 042, Issue: 1, page 51-58
- ISSN: 0044-8753

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topNashine, Hemant Kumar. "Best approximation for nonconvex set in $q$-normed space." Archivum Mathematicum 042.1 (2006): 51-58. <http://eudml.org/doc/249793>.

@article{Nashine2006,

abstract = {Some existence results on best approximation are proved without starshaped subset and affine mapping in the set up of $q$-normed space. First, we consider the closed subset and then weakly compact subsets for said purpose. Our results improve the result of Mukherjee and Som (Mukherjee, R. N., Som, T., A note on an application of a fixed point theorem in approximation theory, Indian J. Pure Appl. Math. 16(3) (1985), 243–244.) and Jungck and Sessa (Jungck, G., Sessa, S., Fixed point theorems in best approximation theory, Math. Japonica 42(2) (1995), 249–252.) and some known results (Dotson,W. G., Jr., On fixed point of nonexpansive mappings in nonconvex sets, Proc. Amer. Math. Soc. 38(1) (1973), 155–156.), (Latif, A., A result on best approximation in p-normed spaces, Arch. Math. (Brno) 37 (2001), 71–75.), (Nashine,H. K., Common fixed point for best approximation for semi-convex structure, Bull. Kerala Math. Assoc. (communicated).) are obtained as consequence. To achieve our goal, we have introduced a property known as “Property(A)”.},

author = {Nashine, Hemant Kumar},

journal = {Archivum Mathematicum},

keywords = {Best approximation; demiclosed mapping; fixed point; $I$-nonexpansive mapping; $q$-normed space; best approximation; demiclosed mapping; fixed point},

language = {eng},

number = {1},

pages = {51-58},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Best approximation for nonconvex set in $q$-normed space},

url = {http://eudml.org/doc/249793},

volume = {042},

year = {2006},

}

TY - JOUR

AU - Nashine, Hemant Kumar

TI - Best approximation for nonconvex set in $q$-normed space

JO - Archivum Mathematicum

PY - 2006

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 042

IS - 1

SP - 51

EP - 58

AB - Some existence results on best approximation are proved without starshaped subset and affine mapping in the set up of $q$-normed space. First, we consider the closed subset and then weakly compact subsets for said purpose. Our results improve the result of Mukherjee and Som (Mukherjee, R. N., Som, T., A note on an application of a fixed point theorem in approximation theory, Indian J. Pure Appl. Math. 16(3) (1985), 243–244.) and Jungck and Sessa (Jungck, G., Sessa, S., Fixed point theorems in best approximation theory, Math. Japonica 42(2) (1995), 249–252.) and some known results (Dotson,W. G., Jr., On fixed point of nonexpansive mappings in nonconvex sets, Proc. Amer. Math. Soc. 38(1) (1973), 155–156.), (Latif, A., A result on best approximation in p-normed spaces, Arch. Math. (Brno) 37 (2001), 71–75.), (Nashine,H. K., Common fixed point for best approximation for semi-convex structure, Bull. Kerala Math. Assoc. (communicated).) are obtained as consequence. To achieve our goal, we have introduced a property known as “Property(A)”.

LA - eng

KW - Best approximation; demiclosed mapping; fixed point; $I$-nonexpansive mapping; $q$-normed space; best approximation; demiclosed mapping; fixed point

UR - http://eudml.org/doc/249793

ER -

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