Double Controlled Metric Type Spaces and Some Fixed Point Results

Thabet Abdeljawad, Nabil Mlaiki, Hassen Aydi and Nizar Souayah
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Thabet Abdeljawad: Department of Mathematics and General Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia
Nabil Mlaiki: Department of Mathematics and General Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia
Hassen Aydi: Department of Mathematics, College of Education in Jubail, Imam Abdulrahman Bin Faisal University, P.O. Box 12020, Jubail 31961, Saudi Arabia
Nizar Souayah: Department of Natural Sciences, Community College Al-Riyadh, King Saud University, Riyadh 4545, Saudi Arabia

Mathematics, 2018, vol. 6, issue 12, 1-10

Abstract: In this article, in the sequel of extending b -metric spaces, we modify controlled metric type spaces via two control functions α ( x , y ) and μ ( x , y ) on the right-hand side of the b - triangle inequality, that is, d ( x , y ) ≤ α ( x , z ) d ( x , z ) + μ ( z , y ) d ( z , y ) , for all x , y , z ∈ X . Some examples of a double controlled metric type space by two incomparable functions, which is not a controlled metric type by one of the given functions, are presented. We also provide some fixed point results involving Banach type, Kannan type and ? -nonlinear type contractions in the setting of double controlled metric type spaces.

Keywords: fixed point; a double controlled metric type; 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 (4)

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