morera theorem
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2021 ◽  
Vol 13 (3) ◽  
pp. 191-205
Author(s):  
Gulmirza Khudaiberganov ◽  
Jonibek Shokirovich Abdullayev
Keyword(s):  

Author(s):  
Vitalii S. Shpakivskyi ◽  
Tetyana S. Kuzmenko

We consider a class of so-called quaternionic G-monogenic mappings associatedwith m-dimensional (m 2 f2; 3; 4g) partial differential equations and propose a description of allmappings from this class by using four analytic functions of complex variable. For G-monogenicmappings we generalize some analogues of classical integral theorems of the holomorphic functiontheory of the complex variable (the surface and the curvilinear Cauchy integral theorems,the Cauchy integral formula, the Morera theorem), and Taylor’s and Laurent’s expansions.Moreover, we investigated the relation between G-monogenic and H-monogenic (differentiablein the sense of Hausdorff) quaternionic mappings.


Author(s):  
Khudayberganov Gulmirza Kh. ◽  
◽  
Otemuratov Bayram P. ◽  
Rakhmonov Uktam S. ◽  
◽  
...  
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2014 ◽  
Vol 22 (1) ◽  
pp. 221-235 ◽  
Author(s):  
S. A. Plaksa ◽  
R. P. Pukhtaievych

AbstractWe obtain a constructive description of monogenic functions taking values in a finite-dimensional semi-simple commutative algebra by means of holomorphic functions of the complex variable. We prove that the mentioned monogenic functions have the Gateaux derivatives of all orders. For monogenic functions we prove also analogues of classical integral theorems of the holomorphic function theory: the Cauchy integral theorems for surface and curvilinear integrals, the Morera theorem and the Cauchy integral formula.


Author(s):  
Gulmirza Kh. Khudayberganov ◽  
◽  
Zokirbek K. Matyakubov ◽  

1999 ◽  
Vol 40 (3) ◽  
pp. 506-514
Author(s):  
S. Kosbergenov ◽  
A. M. Kytmanov ◽  
S. G. Myslivets
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