Yıldız, İsmetUyanık, NeslihanAlbayrak, HilalAy, Hilal2020-04-302020-04-302017978-0-7354-1560-70094-243Xhttps://doi.org/10.1063/1.5000614https://hdl.handle.net/20.500.12684/3917International Conference on Functional Analysis in Interdisciplinary Applications (FAIA) -- OCT 02-05, 2017 -- Astana, KAZAKHSTANWOS: 000417411800015The Weierstrass's associated function is not elliptic but it is of great use in developing the theory of elliptic function. The Zeta function is defined by the double series Sigma(m)'Sigma(m)''{1/z-W-mn + 1/W-mn + z/W-mn(2)}, where W-mn = 2m omega(1) + 2n omega(2) and m, n are integers, not simultaneously zero; the summation Sigma(m)'Sigma(m)''{1/z-W-mn + 1/W-mn + z/W-mn(2)} extends overall integers, not simultaneously. Which W-mn are Lattice points. Evidently W-mn are simple poles of zeta(z) and hence the function is meromorphic in W = {m omega(1) + n omega(2) : (m, n) not equal (0, 0), m, n is an element of Z, Im tau > 0}, D* = {z : vertical bar z vertical bar > 1, vertical bar Rez vertical bar < 1/2 and Im tau > 0, z is an element of C}. zeta(z) is uniformly convergent series of analytic functions, so the series can be differentiated term-by-term. zeta(z) is an odd function, hence the coefficients of the terms z(2k) is evidently zero when k is positive integers. Let A be the class of functions f (z) which are analytic and normalized with f (0) = 0 and f' (0) = 1. Let S be the subclass of A consisting of functions f (z) which are univalent in D. Let P class be univalent functions largely concerned with the family S of functions f analytic and univalent in the unit disk D, and satisfying the conditions f (0) = 0 and f'(0) = 1. One of the basic results of the theory is growth theorem, which asserts in part that for each f is an element of S. In particular, the functions f is an element of S are uniformly bounded on each compact subset of D. Thus the family S is locally bounded, and so by Montel's theorem it is a normal family. A relation was established between S class with function of Weierstrass which is analytic and monomorphic Closes-to-P class in unit disk.en10.1063/1.5000614info:eu-repo/semantics/closedAccessConference Object1880N/AN/A