new best proximity point results in g-metric space

Authors

a ansari

karaj branch, islamic azad university a razani

n hussain

king abdulaziz university

abstract

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 exists an element $x$ satisfying the condition $d(x,tx)=inf {d(y,tx):yin k}$, where $d$ is a metric on $e$. recently, hussain et al. (abstract and applied analysis, vol. 2014, article id 837943) introduced proximal contractive mappings and established certain best proximity point results for these mappings in $g$-metric spaces. the aim of this paper is to introduce certain new classes of auxiliary functions and proximal contraction mappings and establish best proximity point theorems for such kind of mappings in $g$-metric spaces. as consequences of these results, we deduce certain new best proximity and fixed point results in $g$-metric spaces. moreover, we present certain examples to illustrate the usability of the obtained results.

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

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...

full text

Best Proximity Point for Cyclic Contraction in G −metric Space

In this paper, we introduce the results of best proximity point in G-metric spaces for the cyclic contraction mapping with an example that illustrates the usability of the obtained results. 2010 AMS Subject Classification: 41A65, 46B85, 47H25.

full text

Best proximity point theorems in 1/2−modular metric spaces

‎In this paper‎, ‎first we introduce the notion of $frac{1}{2}$-modular metric spaces and weak $(alpha,Theta)$-$omega$-contractions in this spaces and we establish some results of best proximity points‎. ‎Finally‎, ‎as consequences of these theorems‎, ‎we derive best proximity point theorems in modular metric spaces endowed with a graph and in partially ordered metric spaces‎. ‎We present an ex...

full text

Best Proximity Point Result for New Type of Contractions in Metric Spaces with a Graph

In this paper‎, ‎we introduce a new type of graph contraction using a special class of functions and give a best proximity point theorem for this contraction in complete metric spaces endowed with a graph under two different conditions‎. ‎We then support our main theorem by a non-trivial example and give some consequences of best proximity point of it for usual graphs.

full text

Best proximity point results for generalized contractions in metric spaces

*Correspondence: [email protected] 3Department of Mathematics, GDCW, Bosan Road, Multan, Pakistan Full list of author information is available at the end of the article Abstract In this paper, we first introduce a cyclic generalized contraction map in metric spaces and give an existence result for a best proximity point of such mappings in the setting of a uniformly convex Banach space. Then we...

full text

My Resources

Save resource for easier access later


Journal title:
journal of linear and topological algebra (jlta)

جلد ۶، شماره ۰۱، صفحات ۷۳-۸۹

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023