1 citations · 6 across the 29 of their papers we have counts for
33 papers
Contractive difference-of-convex algorithms
Songnian He, Qiao-Li Dong, Michael Th. Rassias
The difference-of-convex algorithm (DCA) and its variants are the most popular methods to solve the difference-of-convex optimization problem. Each iteration of them is reduced to…
The behaviour of a certain additive function in large intervals between consecutive primes
Michael Th. Rassias
We investigate the behaviour of a certain additive function depending on prime divisors of specific integers lying in large gaps between consecutive primes. The result is obtained…
Recent results on large gaps between primes
Michael Th. Rassias
One of the themes of this paper is recent results on large gaps between primes. The first of these results has been achieved in the paper [12] by Ford, Green, Konyagin and Tao. It…
Stochastic forward-backward-half forward splitting algorithm with variance reduction
Liqian Qin, Yaxuan Zhang, Qiao-Li Dong +1
In this paper, we present a stochastic forward-backward-half forward splitting algorithm with variance reduction for solving the structured monotone inclusion problem composed of a…
Prime Avoidance Property of -th Powers of Piatetski-Shapiro Primes
Helmut Maier, Michael Th. Rassias
In previous papers the authors established the prime avoidance property of -th powers of prime numbers and of prime numbers within Beatty sequences. In this paper the authors co…
The ternary Goldbach problem with a prime with a missing digit and primes of special types
Helmut Maier, Michael Th. Rassias
Let Let , be fixed. Let also $a_0\in\{…
Double exponential lower bounds for possible solutions in the Second Case of the Fermat Last Theorem
Preda Mihăilescu, Michael T. Rassias
In a recent paper, the first author provided some lower bounds to solutions of the equations of Fermat and Catalan, based on local power series developments at the ramified prime o…
On the maximum of cotangent sums related to the Riemann Hypothesis in rational numbers in short intervals
Helmut Maier, Michael Th. Rassias
Cotangent sums play a significant role in the Nyman-Beurling criterion for the Riemann Hypothesis. Here we investigate the maximum of the values of these cotangent sums over variou…
New Trends in General Variational Inequalities
M. A. Noor, K. I. Noor, M. Th. Rassias
It is well known that general variational inequalities provide us with a unified, natural, novel and simple framework to study a wide class of unrelated problems, which arise in pu…
The ternary Goldbach problem with two Piatetski-Shapiro primes and a prime with a missing digit
Helmut Maier, Michael Th. Rassias
Let Let , be fixed. Let also .\\ We prove…
Cotangent sums related to the Riemann Hypothesis for various shifts of the argument
Helmut Maier, Michael Th. Rassias
One of the approaches to the Riemann Hypothesis is the Nyman-Beurling criterion. Cotangent sums play a significant role. Here we investigate the values of these cotangent sums for…
Explicit estimates of sums related to the Nyman-Beurling criterion for the Riemann Hypothesis
Helmut Maier, Michael Th. Rassias
We give an estimate for sums appearing in the Nyman-Beurling criterion for the Riemann Hypothesis. These sums contain the Möbius function and are related to the imaginary part of t…
The error for the second moment of cotangent sums related to the Riemann Hypothesis
Helmut Maier, Michael Th. Rassias
In various papers the authors have derived asymptotics for moments of certain cotangent sums related to the Riemann Hypothesis. S. Bettin has given an upper bound for the error ter…
Estimates of sums related to the Nyman-Beurling criterion for the Riemann Hypothesis
Helmut Maier, Michael Th. Rassias
We give an estimate for sums appearing in the Nyman-Beurling criterion for the Riemann Hypothesis containing the Möbius function. The estimate is remarkably sharp in comparison to…
A criterion related to the Riemann Hypothesis
Helmut Maier, Michael Th. Rassias
A crucial role in the Nyman-Beurling-Báez-Duarte approach to the Riemann Hypothesis is played by the distance \[ d_N^2:=\inf_{A_N}\frac{1}{2π}\int_{-\infty}^\infty\left|1-ζA_N\left…
From a cotangent sum to a generalized totient function
Michael Th. Rassias
In this paper we investigate a certain category of cotangent sums and more specifically the sum $$\sum_{m=1}^{b-1}\cot\left(\frac{πm}{b}\right)\sin^{3}\left(2πm\frac{a}{b}\right)\:…
Asymptotics for moments of certain cotangent sums for arbitrary exponents
Helmut Maier, Michael Th. Rassias
In this paper we extend a result on the asymptotics of moments of certain cotangent sums associated to the Estermann and Riemann zeta functions established in a previous paper for…
Asymptotics for moments of certain cotangent sums
Helmut Maier, Michael Th. Rassias
In this paper we improve a result on the order of magnitude of certain cotangent sums associated to the Estermann and the Riemann zeta functions.
The ternary Goldbach problem with a prime and two isolated primes
Helmut Maier, Michael Th. Rassias
In the present paper we prove that under the assumption of the GRH (Generalized Riemann Hypothesis) each sufficiently large odd integer can be expressed as the sum of a prime and t…
A Half-Discrete Hardy-Hilbert-Type Inequality with a Best Possible Constant Factor Related to the Hurwitz Zeta Function
Michael Th. Rassias, Bicheng Yan
Using methods of weight functions, techniques of real analysis as well as the Hermite-Hadamard inequality, a half-discrete Hardy-Hilbert-type inequality with multi-parameters and a…
A cotangent sum related to zeros of the Estermann zeta function
Michael Th. Rassias
We consider a cotangent sum related to Estermann's Zeta function. We provide an elementary and self-contained improvement of the error term in an asymptotic formula proved by V. I.…
On the stability of the linear functional equation in a single variable on complete metric groups
Soon-Mo Jung, Dorian Popa, Michael Th. Rassias
In this paper we obtain a result on Hyers-Ulam stability of the linear functional equation in a single variable on a complete metric group.
A Hilbert-Type Integral Inequality in the Whole Plane Related to the Hypergeometric Function and the Beta Function
Michael Th. Rassias, Bicheng Yang
A new Hilbert-type integral inequality in the whole plane with the non-homogeneous kernel and parameters is given. The constant factor related to the hypergeometric function and th…
Parameterized Yang-Hilbert-Type Integral Inequalities and Their Operator Expressions
Bicheng Yang, Michael Th. Rassias
Applying methods of Real Analysis and Functional Analysis, we build two weight functions with parameters and provide two kinds of parameterized Yang-Hilbert-type integral inequalit…