in this paper, some results of singh, gopalakrishna and kulkarni (1970s) have been extended to higher order derivatives. it has been shown that, if $sumlimits_{a}theta(a, f)=2$ holds for a meromorphic function $f(z)$ of finite order, then for any positive integer $k,$ $t(r, f)sim t(r, f^{(k)}), rrightarrowinfty$ if $theta(infty, f)=1$ and $t(r, f)sim (k+1)t(r, f^{(k)}), rrightarrowinfty$ if $th...

In this paper, we study the uniqueness problems on meromorphic function and its k th order derivative. The results in this paper improve the results given by K. W. Yu (On entire and meromorphic functions that share small functions with their derivatives, J. Inequal. Pure Appl. Math. 4(1)(2003), Art. 21), L. P. Liu and Y. X. Gu (Uniqueness of meromorphic functions that share one small function w...

For r > 0, let Dr := {z ∈ C : |z| < r} and D := D1 be the open unit disk in the complex plane C. Let A denote the family of all functions f that are analytic in D with the normalization f(0) = 0 = f ′(0) − 1. Let S denote the class of functions in A that are univalent in D. A domain D in C is called starlike (with respect to the origin) if every line segment joining the origin to any other poin...

We consider the n × n matrix linear differential systems in the complex plane. We find necessary and sufficient conditions under which these systems have meromorphic fundamental solutions. Using the operator identity method we construct a set of systems which have meromorphic solutions. We prove that the well known operator with the sine kernel generates a class of meromorphic Painlevé type fun...

‎The objective of this paper is to obtain an upper bound to the second Hankel determinant $|a_{2}a_{4}-a_{3}^{2}|$‎ ‎for the function $f$‎, ‎belonging to the class of Gamma-starlike functions‎, ‎using Toeplitz determinants‎. ‎The result presented here include‎ ‎two known results as their special cases‎.  

In this paper, we introduced and investigated starlike and convex functions of order α with respect to 2(j,k)-symmetric conjugate points and coefficient inequality for function belonging to these classes are provided . Also we obtain some convolution condition for functions belonging to this class.

Some subclasses of analytic functions f(z) in the open unit disk U are introduced. In the present paper, Some interesting sufficient conditions, including coefficient inequalities related close-to-convex functions f(z) of order α with respect to a fixed starlike function g(z) and strongly starlike functions f(z) of order μ in U, are discussed. Several special cases and consequences of these coe...

In the paper we compare the relative Valiron defect with the relative Nevanlinna defect of a meromorphic function or a transcendental meromorphic function on the basis of sharing of values of them. Mathematics Subject Classification: 30D35, 30D30

It is clear that 0∈ h(Δ). Moreover, (i) if 0 ∈ h(Δ), then h is called spirallike (resp., starlike) with respect to an interior point; (ii) if 0 ∈ h(Δ), then h is called spirallike (resp., starlike) with respect to a boundary point. In this case, there is a boundary point (say, z = 1) such that h(1) := ∠ limz→1h(z)= 0 (see, e.g., [1, 6]); by symbol∠ lim, we denote the angular (nontangential) lim...

In the paper we deal with the uniqueness of meromorphic functions when two non-linear differential polynomials generated by two meromorphic functions share a small function.