Common fixed-point results in best approximation theory

نویسندگان

  • N. Hussain
  • A. R. Khan
چکیده

A common fixed-point generalization of the results of Dotson, Tarafdar, and Taylor is obtained which in turn extends a recent theorem by Jungck and Seasa to locally convex spaces. As applications of our work, we improve and unify well-known results on fixed points and common fixed points of beat approximation. @ 2003 Elsevier Science Ltd. All rights reserved. Keywords--common fixed point, Best approximation, Nonexpansive map, Weakly commuting maps, Locally convex space.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Common Fixed Points and Invariant Approximations for Cq-commuting Generalized nonexpansive mappings

Some common fixed point theorems for Cq-commuting generalized nonexpansive mappings have been proved in metric spaces. As applications, invariant approximation results are also obtained. The results proved in the paper extend and generalize several known results including those of M. Abbas and J.K. Kim [Bull. Korean Math. Soc. 44(2007) 537-545], I. Beg, N. Shahzad and M. Iqbal [Approx. Theory A...

متن کامل

New best proximity point results in G-metric space

Best approximation results provide an approximate solution to the fixed point equation $Tx=x$, when the non-self mapping $T$ has no fixed point. In particular, a well-known best approximation theorem, due to Fan cite{5}, asserts that if $K$ is a nonempty compact convex subset of a Hausdorff locally convex topological vector space $E$ and $T:Krightarrow E$ is a continuous mapping, then there exi...

متن کامل

Common Fixed Point and Approximation Results for Generalized Φ-contractions

We establish common fixed point theorems for weakly compatible generalized φcontractions. As applications, various common fixed point and best approximation results for Cq-commuting and compatible maps are derived. Our results unify, extend and complement various known results existing in the literature.

متن کامل

A Result in Best Approximation Theory for Family of Maps

Refer ences Al-Thagafi, M. A. , Common fixed points and best approximation, J. Approx Theory, 85, (1996), 318–323. Al-Thagafi, M. A. and Shahzad, N. , Noncommuting selfmaps and invariant approximations, Nonlinear Anal. , 64, (2006), 2778–2786. Al-Thagafi, M. A. and Shahzad, N. , Generalized I-nonexpansive selfmaps and invariant approximations, Acta Math Sinica, 24, (2008), 867–876. Beg, I. , Sh...

متن کامل

SOME NEW RESULTS ON REMOTEST POINTS IN NORMED SPACES

In this paper, using the best proximity theorems for an extensionof Brosowski's theorem. We obtain other results on farthest points. Finally, wedene the concept of e- farthest points. We shall prove interesting relationshipbetween the -best approximation and the e-farthest points in normed linearspaces (X; ||.||). If z in W is a e-farthest point from an x in X, then z is also a-best approximati...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Appl. Math. Lett.

دوره 16  شماره 

صفحات  -

تاریخ انتشار 2003