Small Dynamical Heights for Quadratic Polynomials and Rational Functions

Small Dynamical Heights for Quadratic Polynomials and Rational Functions

Let φ ∈ Q(z) be a polynomial or rational function of degree 2. A special case of Morton and Silverman’s Dynamical Uniform Boundedness Conjecture states that the number of rational preperiodic points of φ is bounded above by an absolute constant. A related conjecture of Silverman states that the canonical height ĥφ(x) of a non-preperiodic rational point x is bounded below by a uniform multiple o...

Faber Polynomials for Rational Mapping Functions

Computer Algebra of Polynomials and Rational Functions

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Uniqueness of meromorphic functions ans Q-differential polynomials sharing small functions

‎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...

Bernstein's polynomials for convex functions and related results

In this paper we establish several polynomials similar to Bernstein's polynomials and several refinements of  Hermite-Hadamard inequality for convex functions.