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On Generalized Hardy–Rogers Type α-Admissible Mappings in Cone b-Metric Spaces over Banach Algebras

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Department of Mathematics and General Courses, Prince Sultan University Riyadh, Riyadh 11586, Saudi Arabia
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Department of Medical Research, China Medical University Hospital China Medical University, Taichung 40402, Taiwan
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Department of M-Commerce and Multimedia Applications, Asia University, Taichung 41354, Taiwan
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Nonlinear Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam
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Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
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King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
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Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Beograd 35, Serbia
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Author to whom correspondence should be addressed.
Symmetry 2020, 12(1), 81; https://doi.org/10.3390/sym12010081
Received: 4 December 2019 / Revised: 22 December 2019 / Accepted: 24 December 2019 / Published: 2 January 2020
We introduce the notion of α -admissibility of mappings on cone b-metric spaces using Banach algebra with coefficient s, and establish a result of the Hardy-Rogers theorem in these spaces. Furthermore, using symmetry, we derive many recent results as corollaries. As an application we prove certain fixed point results in partially ordered cone b-metric space using Banach algebra. Also, we use our results to derive and prove some real world problems to show the usability of our obtained results. Moreover, it is worth noticing that fixed point theorems for monotone operators in partially ordered metric spaces are widely investigated and have found various applications in differential, integral and matrix equations. View Full-Text
Keywords: fixed points; cone b-metric space (CnMs); Banach algebra fixed points; cone b-metric space (CnMs); Banach algebra
MDPI and ACS Style

Shatanawi, W.; D. Mitrović, Z.; Hussain, N.; Radenović, S. On Generalized Hardy–Rogers Type α-Admissible Mappings in Cone b-Metric Spaces over Banach Algebras. Symmetry 2020, 12, 81.

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