*Correspondence: [email protected] 1School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia Full list of author information is available at the end of the article Abstract The estimates for the second Hankel determinant a2a4 – a3 of the analytic function f (z) = z + a2z + a3z + · · · , for which either zf ′(z)/f (z) or 1 + zf ′′(z)/f ′(z) is subordinate to a certai...

We survey recent work on the use of Hankel matrices H(f,2) for real-valued graph parameters f and a binary sum-like operation 2 on labeled graphs such as the disjoint union and various gluing operations of pairs of laeled graphs. Special cases deal with real-valued word functions. We start with graph parameters definable in Monadic Second Order Logic MSOL and show how MSOL-definability can be r...

In the rst part 13] of the paper transformationsmappingToeplitz and Toeplitz-plus-Hankel matrices into generalizedCauchy matrices were studied. In this second part fast algorithms for LU-factorization and inversion of generalized Cauchy matrices are discussed. It is shown that the combinationof transformation pivoting techniques leads to algorithms for indeenite Toeplitz and Toeplitz-plus-Hanke...

In this study, by making the use of q-analogous hyperbolic tangent function and a Sălăgean q-differential operator, new class q-starlike functions is introduced. The prime contribution study covers derivation sharp coefficient bounds in open unit disk U, especially first three bounds, Fekete–Szego type functional, upper second- third-order Hankel determinant for to class. We also Zalcman genera...