Related papers: A generalization of Tanaka's formula

We establish a new generalized Taylor's formula for power fractional derivatives with nonsingular and nonlocal kernels, which includes many known Taylor's formulas in the literature. Moreover, as a consequence, we obtain a general version…

Talagrand's fundamental result on the entropy numbers is slightly improved. Our proof uses different ideas based on results from greedy approximation.

This review article brings forth some recent results in the theory of the Riemann zeta-function $qzeta(s)$.

A new general and unified method of summation, which is both regular and consistent, is invented. It is based on the idea concerning a way of integers reordering. The resulting theory includes a number of explicit and closed form summation…

We report on observations we made on computational data that suggest a generalization of Maeda's conjecture regarding the number of Galois orbits of newforms of level $N = 1$, to higher levels. They also suggest a possible formula for this…

We survey recent developments on the Restriction conjecture.

We prove an analytic Bertini theorem, generalizing a previous result of Fujino and Matsumura.

We give a new proof of Tietze Theorem on the convergence of infinite semi-regular continued fractions.

We survey the classical results of the Dirichlet Approximation Theorem.

We continue the work started in Part I of this article, showing how the addition of noise can stabilize an otherwise unstable system. The analysis makes use of nearly optimal Lyapunov functions. In this continuation, we remove the main…

New cases of the multiplicity conjecture are considered.

We prove new results on the derivative of the Minkowski question mark function. Some of our theorems are non-improvable.

We prove a new q-analogue of Nicomachus's Theorem about the sum of cubes and some related results.

We announce numerous new results in the theory of orthogonal polynomials on the unit circle.

In this paper we prove a generalization of famous Larchr's theorem concerning good lattice points.

We prove the Aharoni Berger Conjecture

We prove a generalized Gauss-Kuzmin-L\'evy theorem for the $p$-numerated generalized Gauss transformation $$T_p(x)=\{\frac{p}{x}\}.$$ In addition, we give an estimate for the constant that appears in the theorem.

In this note we obtain a new convergence result for the Adomian decomposition method.

In this paper, we give a refinement of a theorem by Franks, which answers two questions raised by Kang.

We obtain similar types of conclusions as that of Br\"{u}ck [1] for two differential polynomials which in turn radically improve and generalize several existing results. Moreover, a number of examples have been exhibited to justify the…