Strong converse inequalities and quantitative Voronovskaya-type theorems for trigonometric Fej\'er sums

Quantitative-Voronovskaya and Grüss-Voronovskaya type theorems for Szász-Durrmeyer type operators blended with multiple Appell polynomials

In this paper, we establish a link between the Szász-Durrmeyer type operators and multiple Appell polynomials. We study a quantitative-Voronovskaya type theorem in terms of weighted modulus of smoothness using sixth order central moment and Grüss-Voronovskaya type theorem. We also establish a local approximation theorem by means of the Steklov means in terms of the first and the second order mo...

Explicit Evaluations and Reciprocity Theorems for Finite Trigonometric Sums

This evaluation can be found in standard tables of series, such as those of E. R. Hansen [44, p. 262, eq. (30.1.2)], L. B. W. Jolly [56, pp. 102–103, eq. (352)], and A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev [70, p. 646, eq. 6]. We do not know who first proved (1.1), but several proofs exist. If we replace the power 2 on the left side by an arbitrary positive even power, finding an e...

Strong converse theorems using Rényi entropies

On Two Strong Converse Theorems for Stationary Discrete Memoryless Channels

In 1973, Arimoto proved the strong converse theorem for the discrete memoryless channels stating that when transmission rate R is above channel capacity C, the error probability of decoding goes to one as the block length n of code word tends to infinity. He proved the theorem by deriving the exponent function of error probability of correct decoding that is positive if and only if R > C. Subse...

Strong convergence for variational inequalities and equilibrium problems and representations

We introduce an implicit method for nding a common element of the set of solutions of systems of equilibrium problems and the set of common xed points of a sequence of nonexpansive mappings and a representation of nonexpansive mappings. Then we prove the strong convergence of the proposed implicit schemes to the unique solution of a variational inequality, which is the optimality condition for ...