The purpose of this paper is to give formulas and Recurrence relations for the Apostol-Euler numbers polynomials order with complex aid Euler operator partial derivatives generating function. Relations among these neqative integer order, beta-type rational functions, finite combinatorial sums, Stirling numbers, Lah are given. Finally, new classes modification exponential type splines constructed.

In this paper, we introduce a technique to find the cyclic path covering number of Euler graphs, by using the t-hypohamiltonian graphs. Also a special type of Euler graph in the name n-gon is also being introduced and a general result of cpcn of n-gon is also found. Finally an algorithm to find the cyclic path covering number of any Euler graph is being developed. AMS subject classification: 54...

We consider dynamic optimization problems for systems governed by differential inclusions. The main focus is on the structure of and interrelations between necessary optimality conditions stated in terms of Euler– Lagrange and Hamiltonian formalisms. The principal new results are: an extension of the recently discovered form of the Euler–Weierstrass condition to nonconvex valued differential in...

In this paper, by using the Euler-Maclaurin expansion for the Riemann-$zeta$ function, we establish an inequality of a weight coefficient. Using this inequality, we derive a new reverse Hilbert's type inequality. As an applications, an equivalent form is obtained.

In this paper we deal with pointwise approximation of solutions stochastic differential equations (SDEs) driven by an infinite dimensional Wiener process, additional jumps generated a Poisson random measure. Further investigations contain upper error bounds for the proposed truncated dimension randomized Euler scheme. We also establish matching (up to constants) and lower $\varepsilon$-complexi...