On fixed point theory for generalized contractions in cone metric spaces via scalarizing

In this paper, some fixed point theorems for generalized contractions in cone metric spaces are provided. The normal condition on the underling cone is omitted. Moreover, the equivalency between the ordered boundedness and topologically boundedness, without using normality on the cone, for a subset...

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Main Authors: Parastoo Zangenehmehr, Ali Farajzadeh, Seyed Mansour Vaezpour
Language:English
Published: Science Faculty of Chiang Mai University 2019
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Online Access:http://it.science.cmu.ac.th/ejournal/dl.php?journal_id=6259
http://cmuir.cmu.ac.th/jspui/handle/6653943832/66176
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Institution: Chiang Mai University
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spelling th-cmuir.6653943832-661762019-08-21T09:18:23Z On fixed point theory for generalized contractions in cone metric spaces via scalarizing Parastoo Zangenehmehr Ali Farajzadeh Seyed Mansour Vaezpour Cone metric spaces topologically bounded ordered bounded Hausdorf metric normal cone nonlinear scalarization function In this paper, some fixed point theorems for generalized contractions in cone metric spaces are provided. The normal condition on the underling cone is omitted. Moreover, the equivalency between the ordered boundedness and topologically boundedness, without using normality on the cone, for a subset of an ordered topological vector space is presented. The results of this article can be considered as the extension of [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc., 136(5) (2008), 1861-1869], [M. Kikkawa and T. Suzuki, Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal., 69(9) (2008), 2942-2949] and [A.P. Farajzadeh, A. Amini-Harandi, D. Baleanu, Fixed point theory for generalized contractions in cone metric spaces, Commun. Nonlinear. Sci. Numer. Simulat. 17(2)(2012) 708-712]. 2019-08-21T09:18:23Z 2019-08-21T09:18:23Z 2015 Chiang Mai Journal of Science 42, 4 (Oct 2015), 1038 - 1043 0125-2526 http://it.science.cmu.ac.th/ejournal/dl.php?journal_id=6259 http://cmuir.cmu.ac.th/jspui/handle/6653943832/66176 Eng Science Faculty of Chiang Mai University
institution Chiang Mai University
building Chiang Mai University Library
country Thailand
collection CMU Intellectual Repository
language English
topic Cone metric spaces
topologically bounded
ordered bounded
Hausdorf metric
normal cone
nonlinear scalarization function
spellingShingle Cone metric spaces
topologically bounded
ordered bounded
Hausdorf metric
normal cone
nonlinear scalarization function
Parastoo Zangenehmehr
Ali Farajzadeh
Seyed Mansour Vaezpour
On fixed point theory for generalized contractions in cone metric spaces via scalarizing
description In this paper, some fixed point theorems for generalized contractions in cone metric spaces are provided. The normal condition on the underling cone is omitted. Moreover, the equivalency between the ordered boundedness and topologically boundedness, without using normality on the cone, for a subset of an ordered topological vector space is presented. The results of this article can be considered as the extension of [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc., 136(5) (2008), 1861-1869], [M. Kikkawa and T. Suzuki, Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal., 69(9) (2008), 2942-2949] and [A.P. Farajzadeh, A. Amini-Harandi, D. Baleanu, Fixed point theory for generalized contractions in cone metric spaces, Commun. Nonlinear. Sci. Numer. Simulat. 17(2)(2012) 708-712].
author Parastoo Zangenehmehr
Ali Farajzadeh
Seyed Mansour Vaezpour
author_facet Parastoo Zangenehmehr
Ali Farajzadeh
Seyed Mansour Vaezpour
author_sort Parastoo Zangenehmehr
title On fixed point theory for generalized contractions in cone metric spaces via scalarizing
title_short On fixed point theory for generalized contractions in cone metric spaces via scalarizing
title_full On fixed point theory for generalized contractions in cone metric spaces via scalarizing
title_fullStr On fixed point theory for generalized contractions in cone metric spaces via scalarizing
title_full_unstemmed On fixed point theory for generalized contractions in cone metric spaces via scalarizing
title_sort on fixed point theory for generalized contractions in cone metric spaces via scalarizing
publisher Science Faculty of Chiang Mai University
publishDate 2019
url http://it.science.cmu.ac.th/ejournal/dl.php?journal_id=6259
http://cmuir.cmu.ac.th/jspui/handle/6653943832/66176
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