Abstract
We prove a theorem which states that the existence of an asymptotic limit off ¯z asz→z 0 implies ℝ-differentiability of a complex-valued functionf(z) atz 0.
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References
I. N. Vekua,Generalized Analytic Functions [in Russian], Nauka, Moscow (1988).
Yu. Yu. Trokhimchuk,Continuous Mappings and Monogeneity Conditions [in Russian], Fizmatgiz, Moscow (1963).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 329–337, April, 1994.
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Alikulov, É.O. New differentiability criteria for complex-valued functions. Ukr Math J 46, 343–351 (1994). https://doi.org/10.1007/BF01060404
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DOI: https://doi.org/10.1007/BF01060404