Although prox-regular functions in general are nonconvex, they possess properties that one would expect to find in convex or lowerC2  functions. The class of prox-regular functions covers all convex functions, lower C2  functions and strongly amenable functions. At first, these functions have been identified in finite dimension using proximal subdifferential. Then, the definition of prox-regula...

‎using several examples of positive definite functions‎, ‎some inequalities for the numerical radius of‎ ‎matrices are investigated‎. ‎also‎, ‎some open problems are stated‎.

cooperation among actors is an essential part of urban regeneration initiatives. the main idea of this paper is that, citizens with higher levels of quality of life have more abilities to take part in regeneration and so have more positive attitudes to these initiatives. all real estate owners and residents in all urban distressed areas in mashhad were the statistical population of this researc...

 ‎Using several examples of positive definite functions‎, ‎some inequalities for the numerical radius of‎ ‎matrices are investigated‎. ‎Also‎, ‎some open problems are stated‎.

We prove Pólya’s conjecture of 1943: For a real entire function of order greater than 2 with finitely many non-real zeros, the number of non-real zeros of the n-th derivative tends to infinity as n → ∞ . We use the saddle point method and potential theory, combined with the theory of analytic functions with positive imaginary part in the upper half-plane.