DOI: 10.24193/fpt-ro.2024.2.05

Authors: Marija Cvetković

Abstract: F-contraction has been a widely investigated problem in the Fixed Point Theory during the last decade. There are different results regarding generalizations and modifications of F-contraction in various settings, along with the results concerning application of those concepts, mostly in the area of differential and difference equations, fractional calculus, etc. In this paper, it will be shown that there are abundant requests regarding the definition of F-contraction. In this way, the wider class of F contraction is formed and, for this new type of contraction, called simple F-contraction or sF-contraction, we prove the existence and uniqueness of the fixed point on a complete metric space. Similar results are derived for the modified concept of F-Suzuki contraction.

Key Words and Phrases: F-contraction, weak F-contraction, simple F-contraction.

2010 Mathematics Subject Classification: 47H10, 54H25.

Published on-line: June 15th, 2024.

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