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This paper is devoted to value distribution and uniqueness problems for difference polynomials of entire functions such as fⁿ(f-1)f(z+c). We also consider sharing value problems for f(z) and its shifts f(z+c), and improve some recent results of Heittokangas et al. [J. Math. Anal. Appl. 355 (2009), 352-363]. Finally, we obtain some results on the existence of entire solutions of a difference equation of the form
In this paper, we investigate the value distribution of meromorphic solutions of homogeneous and non-homogeneous complex linear differential-difference equations, and obtain the results on the relations between the order of the solutions and the convergence exponents of the zeros, poles, a-points and small function value points of the solutions, which show the relations in the case of non-homogeneous equations are sharper than the ones in the case of homogeneous equations.
A new approach to differentiation on a time scale is presented. We give a suitable generalization of the Vitali Lemma and apply it to prove that every increasing function f: → ℝ has a right derivative f₊’(x) for -almost all x ∈ . Moreover, .
The asymptotic and oscillatory behavior of solutions of Volterra summation equation and second order linear difference equation are studied.
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