In recent years, learning methods are desirable because of their reliability and efficiency in real-world problems. We propose a novel method to find infinitely many kernel combinations for learning problems with the help of infinite and semi-infinite optimization regarding all elements in kernel space. This will provide to study variations of combinations of kernels when considering heterogene...

In this paper, we study the second-order nonlinear singular Sturm-Liouville boundary value problems with Riemann-Stieltjes integral boundary conditions    −(p(t)u(t)) + q(t)u(t) = f(t, u(t)), 0 < t < 1, α1u(0)− β1u (0) = ∫ 1 0 u(τ)dα(τ), α2u(1) + β2u (1) = ∫ 1 0 u(τ)dβ(τ), where f(t, u) is allowed to be singular at t = 0, 1 and u = 0. Some new results for the existence of positive solu...

We consider forced second order differential equation with p-Laplacian and nonlinearities given by a Riemann-Stieltjes integrals in the form of ( p(t)φγ ( x′(t) ))′ + q0 (t)φγ (x(t)) + ∫ b 0 q (t, s)φα(s) (x(t)) dζ (s) = e(t), where φα (u) := |u| sgnu, γ, b ∈ (0,∞) , α ∈ C [0, b) is strictly increasing such that 0 ≤ α (0) < γ < α (b−), p, q0, e ∈ C ([t0,∞),R) with p (t) > 0 on [t0,∞), q ∈ C ([0...

In this paper the discrete Sobolev inner product 〈p, q〉 = ∫ p(x)q(x)dμ+ r ∑ i=0 Mi p (c)q(c) is considered, whereμ is a finite positive Borel measure supported on an infinite subset of the real line, c ∈ R and Mi 0, i = 0, 1, . . . , r. Connection formulas for the orthonormal polynomials associated with 〈., .〉 are obtained. As a consequence, for a wide class of measures μ, we give the Mehler–He...

In this paper, we investigate the existence of at least one solution to following higher order Riemann–Liouville fractional differential equation with Riemann–Stieltjes integral boundary condition resonance: − ( D 0 + α x ) t = f , 1 n < ≤ ∈ [ 0,1 ] ′ … 2 k ∫ d A $$ {\displaystyle \begin{array}{cc}\hfill -\left({D}_{0+}^{\alpha }x\right)(t)=& f\left(t,x(t),{D}_{0+}^{\alpha -1}x(t)\right),n-1<\a...