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The aim of this work is to provide the existence and uniqueness of a fixed point for a new SF -GF -contraction type. We show its properties, we also generalize and unify several results in the literature . Finally, we give some examples and applications to describe these results. Mathematics Subject Classification (2010). 34A08, 26A33,34K37.

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This manuscript aims to highlight the existence and uniqueness results for the following Schrödinger problem in the extended Colombeau algebra of generalized functions. 1 / ı ∂ / ∂ t u t , x − △ u t , x + v x u t , x = 0 , t ∈ R + , x ∈ R n , v x = δ x , u 0 , x = δ x , where δ is the Dirac distribution. The proofs of our main results are based on the Gronwall inequality and regularization method. We conclude our article by establishing the association concept of solutions.

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