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Open AccessArticle

Double Controlled Metric Type Spaces and Some Fixed Point Results

1
Department of Mathematics and General Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia
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Department of Mathematics, College of Education in Jubail, Imam Abdulrahman Bin Faisal University, P.O. Box 12020, Jubail 31961, Saudi Arabia
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Department of Natural Sciences, Community College Al-Riyadh, King Saud University, Riyadh 4545, Saudi Arabia
*
Author to whom correspondence should be addressed.
Mathematics 2018, 6(12), 320; https://doi.org/10.3390/math6120320
Received: 12 November 2018 / Revised: 2 December 2018 / Accepted: 7 December 2018 / Published: 12 December 2018
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 ϕ -nonlinear type contractions in the setting of double controlled metric type spaces. View Full-Text
Keywords: fixed point; a double controlled metric type; extended b-metric space fixed point; a double controlled metric type; extended b-metric space
MDPI and ACS Style

Abdeljawad, T.; Mlaiki, N.; Aydi, H.; Souayah, N. Double Controlled Metric Type Spaces and Some Fixed Point Results. Mathematics 2018, 6, 320. https://doi.org/10.3390/math6120320

AMA Style

Abdeljawad T, Mlaiki N, Aydi H, Souayah N. Double Controlled Metric Type Spaces and Some Fixed Point Results. Mathematics. 2018; 6(12):320. https://doi.org/10.3390/math6120320

Chicago/Turabian Style

Abdeljawad, Thabet; Mlaiki, Nabil; Aydi, Hassen; Souayah, Nizar. 2018. "Double Controlled Metric Type Spaces and Some Fixed Point Results" Mathematics 6, no. 12: 320. https://doi.org/10.3390/math6120320

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