Fixed Point and Common Fixed Point Results of \(D_F\)-Contractions via Measure of Non-compactness with Applications

Asmat Ullah, Israr Ali Khan, Nayyar Mehmood

Abstract


In this paper, we study a new contraction mapping inspired by the concept of \(F\)-contraction, which was recently introduced by Wardowski [20]. We find common fixed points for a sequence of mappings by introducing \(D_F\)-contractive operators in Banach space using the concept of measure of
non-compactness. As an application, we prove some results on the existence of solutions for a system of an infinite fractional order differential equations in the space \(c\), where space \(c\) consists of real sequences having the finite limits.

Keywords


\(D_F\)-contraction; Fixed point; Common fixed points; Measure of non-compactness

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References


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DOI: http://dx.doi.org/10.26713%2Fcma.v9i1.926

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