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Open AccessArticle

Caristi, Nadler and H + -Type Contractive Mappings and Their Fixed Points in θ-Metric Spaces

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Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur 440010, India
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Faculty of Sciences and Mathematics, University of Priština, Lole Ribara 29, Kosovska Mitrovica 38220, Serbia
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Nonlinear Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City 71000, Vietnam
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Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 71000, Vietnam
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(4), 504; https://doi.org/10.3390/sym11040504
Received: 19 March 2019 / Revised: 1 April 2019 / Accepted: 2 April 2019 / Published: 7 April 2019
A new proper generalization of metric called as θ -metric is introduced by Khojasteh et al. (Mathematical Problems in Engineering (2013) Article ID 504609). In this paper, first we prove the Caristi type fixed point theorem in an alternative and comparatively new way in the context of θ -metric. We also investigate two θ -metrics on CB ( X ) (family of nonempty closed and bounded subsets of a set X). Furthermore, using the obtained θ -metrics on CB ( X ) , we prove two new fixed point results for multi-functions which generalize the results of Nadler and Lim type in the context of such spaces. In order to illustrate the usability of our results, we equipped them with competent examples. View Full-Text
Keywords: θ-metric; θ-Hausdorff distance; multivalued mapping; fixed point θ-metric; θ-Hausdorff distance; multivalued mapping; fixed point
MDPI and ACS Style

Patle, P.; Vujaković, J.; Patel, D.; Radenović, S. Caristi, Nadler and H + -Type Contractive Mappings and Their Fixed Points in θ-Metric Spaces. Symmetry 2019, 11, 504.

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