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001-es BibID:	BIBFORM120974
035-os BibID:	(Scopus)85190836158
Első szerző:	Boros Zoltán (matematikus)
Cím:	Strong geometric derivatives / Zoltán Boros, Péter Tóth
Dátum:	2024
ISSN:	0022-247X
Megjegyzések:	We consider the lower and upper limits of 2^n ( f(y+h/2^n) - f(y)) whenever n tends to infinity and y tends to a fixed element x of the domain I of f. We consider two families of functions determined by the properties of these limits. The first interesting property is when these lower and upper limits are finite and equal to each other for every real number h and every x in I. The second notable family is determined by the property that both limits are finite and increasing (in a specific sense) with respect to x for every positive number h. These properties are motivated by the families of continuously differentiable functions and convex functions, respectively. However, restrictions of additive mappings belong to these classes as well. Our decomposition theorems establish that these motivating examples generate the whole classes. Namely, every function belonging to the first family can be represented as the sum of a continuously differentiable function and an additive one, while every function taken from the second family turns out to be the sum of a convex function and an additive one. We apply our results in order to give a local and approximate characterization of affine functions and Wright-convex functions, respectively.
Tárgyszavak:	Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény külföldi lapban folyóiratcikk Generalized derivatives Strongly differentiable functions Convex functions Affine mappings Approximate solutions
Megjelenés:	Journal of Mathematical Analysis and Applications. - 538 : 1 (2024), p. 1-19. -
További szerzők:	Tóth Péter (1998-) (matematikus)
Pályázati támogatás:	K-134191 OTKA ÚNKP-22-3 Egyéb PhD Excellence Scholarship from the Count István Tisza Foundation for the University of Debrecen Egyéb
Internet cím:	Szerző által megadott URL DOI Intézményi repozitóriumban (DEA) tárolt változat
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