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Approximation results for nonlinear integral operators in modular spaces and applications

Ilaria Mantellini, Gianluca Vinti (2003)

Annales Polonici Mathematici

We obtain modular convergence theorems in modular spaces for nets of operators of the form ( T w f ) ( s ) = H K w ( s - h w ( t ) , f ( h w ( t ) ) ) d μ H ( t ) , w > 0, s ∈ G, where G and H are topological groups and h w w > 0 is a family of homeomorphisms h w : H h w ( H ) G . Such operators contain, in particular, a nonlinear version of the generalized sampling operators, which have many applications in the theory of signal processing.

Asymptotic fuzzy contractive mappings in fuzzy metric spaces

Dhananjay Gopal, Juan Martínez-Moreno, Rosana Rodríguez-López (2024)

Kybernetika

Fixed point theory in fuzzy metric spaces has grown to become an intensive field of research. However, due to the complexity involved in the nature of fuzzy metrics, the authors need to develop innovative machinery to establish new fixed point theorems in such kind of spaces. In this paper, we propose the concepts of asymptotic fuzzy ψ -contractive and asymptotic fuzzy Meir-Keeler mappings, and describe some new machinery by which the corresponding fixed point theorems are proved. In this sense,...

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