The first aim of this paper is to present $P_p$-statistical approximation theorem for max-product operators with the use of statistical convergence with respect to power series method which is incompatible with statistical convergence. The second aim is to obtain the $P_p$-statistical rate of this approximation. In the end of the paper, we construct special sequences of nonlinear operators which satisfy our results as an application.

In this paper, we introduce the harmonicity on the cotangent bundle equipped with vertical rescaled Cheeger-Gromoll metric which rescales the vertical part by a non-zero differentiable function $f$. We establish a necessary and sufficient condition under which a covector field is harmonic with respect to this metric. We also construct some examples of harmonic vector fields. Finally, we study the harmonicity of a map between a Riemannian manifold and a cotangent bundle of another Riemannian manifold and vice versa.

In this work, we obtain new versions of the Hermite-Hadamard Inequality via generalized fractional derivatives, which differentiates our work from previous known ones, which use integral operators. Several known results from the literature are particular cases of ours, demonstrating the breadth and generality of our conclusions.

Let $R$ be a commutative Noetherian ring and $I\subseteq J$ be ideals of $R$. Let $M$ and $N$ be finitely generated $R$-modules such that . In this paper, we study the supremum of non Artinian $I$-cofinite modules $H_I^i(M,N)$ over a commutative Noetherian ring where $i\ge 1$ and give a bound for ${\tilde{\text{q}}}_J(M,N)$ by using ${\tilde{\text{q}}}_I(M,N)$. We show that ${\tilde{\text{q}}}_J(M,N)\le {\tilde{\text{q}}}_I(M,N)+{\text{cd}}_J(M,N/IN)$.

Let ${\overline{a}}_{j,k}^m(n)$ denote the number of overpartitions of $n$ with two colors in which no parts are divisible by $m$ and only parts congruent to $j$ modulo $k$ may be overlined. In this work, we establish many infinite families of congruences modulo powers of $2$ for ${\overline{a}}_{1,3}^3(n)$, ${\overline{a}}_{1,4}^3(n)$ and congruences modulo powers of $2$ and $3$ for ${\overline{a}}_{1,4}^9(n)$.

In this paper, we study the spectrum of Hahn-Sturm-Liouville operators. In this context, it is shown that the regular symmetric Hahn-Sturm-Liouville operator is semi-bounded from below. Moreover, we give some conditions for the self-adjoint singular Hahn-Sturm-Liouville operator to have a discrete spectrum. The method of proof is based on the splittings technique. Finally, we investigate the continuous spectrum of this operator.

In this study, we dealt with the natural lift curves of the spherical indicatrices of a non-null curve according to Bishop frame. Furthermore, some interesting results about the original curve were obtained depending on the assumption that the natural lift curves should be the integral curve of the geodesic spray on the tangent bundle $T\left(S_1^2\right)$ and $T\left(H_0^2\right)$.