Geodesic
Finite increments formula for mappings into inductive scales of spaces
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 8 (2001), pp. 419-439.

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Finite increments formula with closed convex estimate is transfered to the differentiable mappings into linear scales of locally convex spaces and homogeneously differentiable mappings into nonlinear scales. A weakened variant of the formula with functionally separable convex estimate is obtained for mappings into general inductive scales. Some generalizations and applications are considered. 
@article{JMAG_2001_8_a4,
     author = {I. V. Orlov},
     title = {Finite increments formula for mappings into inductive scales of spaces},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {419--439},
     publisher = {mathdoc},
     volume = {8},
     year = {2001},
     language = {ru},
     url = {https://geodesic-test.mathdoc.fr/item/JMAG_2001_8_a4/}
}
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I. V. Orlov. Finite increments formula for mappings into inductive scales of spaces. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 8 (2001), pp. 419-439. https://geodesic-test.mathdoc.fr/item/JMAG_2001_8_a4/