Since the inception of the present members of the department conducted intensive research on topical problems of function theory and approximation, integral equations, numerical methods and their applications.

Research carried out in close contact with a number of mathematicians from different Russian scientific centers of the CIS countries, as well as from Bulgaria, Australia, Germany, Greece, USA, Italy, Egypt.

The results of the surveys, particularly in three Gabdulhaev's monographs and two review papers and 40 dissertations of his students, and refer to the following fields: approximation theory (the construction elements of the theory of approximation of functions in Holder spaces, Nikolsky, Zigmund, Sobolev, and their multidimensional analogues); general theory of approximate methods of functional analysis (a variant of the Kantorovich LN adapted to singular integral and integro-differential equations, the effective application of the proof of direct and projection methods for various classes of equations); theory of ill-posed problems (the decision of some kind of problems by a special selection of a pair of spaces desired elements and right sides); theory of extremal problems (the construction of finite-best approximation for the solution of operator equations and optimization of computational methods).

Currently, research at the Department maintained the following interrelated scientific areas:

Employees of Department carried out a number of research grants, Academy of Sciences of the Republic of Tatarstan and the Russian Foundation for Basic Research (RFBR).

**List of Current Projects Led By The Department**

Title | Head | Deadlines | Grants |
---|---|---|---|

Integral inequalities of geometric analysis | F.G. Avkhadiev | 2017-2019 | RFBR |

Extreme problems of complex analysis and the theory of noncommutative integration | F.G. Avkhadiev | 2017-2019 | The state budget |

Extremal problems of the theory of functions and their applications | F.G. Avkhadiev | 2018-2020 | RSF |