in this paper, we consider a new class of analytic functions in the unit disk using polynomials of order alpha. we give some sufficient conditions for functions belonging to this class.

‎we mainly discuss the existence of meromorphic (entire) solutions of‎ ‎certain type of non-linear difference equation of the form‎: ‎$f(z)^m+p(z)f(z+c)^n=q(z)$‎, ‎which is a supplement of previous‎ ‎results in [k‎. ‎liu‎, ‎l. z‎. ‎yang and x‎. ‎l‎. ‎liu‎, ‎existence of entire solutions of nonlinear difference‎ ‎equations‎, ‎czechoslovak math. j. 61 (2011)‎, no. 2, ‎565--576‎, and x‎. ‎g‎. ‎qi‎...

‎The paper concerns interesting problems related to the field of Complex Analysis‎, ‎in particular, Nevanlinna theory of meromorphic‎ ‎functions‎. ‎We have studied certain uniqueness problem on differential polynomials of meromorphic functions sharing a‎ ‎small function‎. ‎Outside‎, ‎in this paper‎, ‎we also consider the uniqueness of $q-$ shift difference‎ - ‎differential polynomials‎ ‎of mero...

‎In this paper‎, ‎we investigate some results on natural metrics on the $mu$-normal functions and meromorphic $Q_p$-classes‎. ‎Also‎, ‎these classes are shown to be complete metric spaces with respect to the corresponding metrics‎. ‎Moreover‎, ‎compact composition operators $C_phi$ and Lipschitz continuous operators acting from $mu$-normal functions to the meromorphic $Q_p$-classes are characte...

the purpose of this article is to investigate the uniqueness of meromorphic functions sharing five small functions on annuli.

‎in this paper‎, ‎we investigate some results on natural metrics on the $mu$-normal functions and meromorphic $q_p$-classes‎. ‎also‎, ‎these classes are shown to be complete metric spaces with respect to the corresponding metrics‎. ‎moreover‎, ‎compact composition operators $c_phi$ and lipschitz continuous operators acting from $mu$-normal functions to the meromorphic $q_p$-classes are characte...

The purpose of this article is to investigate the uniqueness of meromorphic functions sharing five small functions on annuli.

in this article, we consider the uniqueness of the difference monomials $f^{n}(z)f(z+c)$. suppose that $f(z)$ and $g(z)$ are transcendental meromorphic functions with finite order and $e_k(1, f^{n}(z)f(z+c))=e_k(1, g^{n}(z)g(z+c))$. then we prove that if one of the following holds (i) $n geq 14$ and $kgeq 3$, (ii) $n geq 16$ and $k=2$, (iii) $n geq 22$ and $k=1$, then $f(z)equiv t_1g(z)$ or $f(...

in this paper, we defined two classes $s_{p}^{ast }(n,lambda ,a,b)$ and $ k_{p}(n,lambda ,a,b)$ of meromorphic $p-$valent functions associated with a new linear operator. we obtained convolution properties for functions in these classes.