Controlled Metric Type Spaces and the Related Contraction Principle

Nabil Mlaiki, Hassen Aydi, Nizar Souayah and Thabet Abdeljawad
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Nabil Mlaiki: Department of Mathematics and General Sciences, Prince Sultan University, P. O. Box 66833, 11586 Riyadh, Saudi Arabia
Hassen Aydi: Department of Mathematics, College of Education in Jubail, Imam Abdulrahman Bin Faisal University, P. O. 12020, Industrial Jubail 31961, Saudi Arabia
Nizar Souayah: Department of Natural Sciences, Community College Al-Riyadh, King Saud University, Riyadh 11451, Saudi Arabia
Thabet Abdeljawad: Department of Mathematics and General Sciences, Prince Sultan University, P. O. Box 66833, 11586 Riyadh, Saudi Arabia

Mathematics, 2018, vol. 6, issue 10, 1-7

Abstract: In this article, we introduce a new extension of b -metric spaces, called controlled metric type spaces, by employing a control function α ( x , y ) of the right-hand side of the b -triangle inequality. Namely, the triangle inequality in the new defined extension will have the form, d ( x , y ) ≤ α ( x , z ) d ( x , z ) + α ( z , y ) d ( z , y ) , for all x , y , z ∈ X . Examples of controlled metric type spaces that are not extended b -metric spaces in the sense of Kamran et al. are given to show that our extension is different. A Banach contraction principle on controlled metric type spaces and an example are given to illustrate the usefulness of the structure of the new extension.

Keywords: fixed point; controlled metric type space; extended b-metric space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations: View citations in EconPapers (9)

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