In this paper, by applying the new and improved form of Hölder’s integral inequality called Hölder—Íşcan three inequalities Hermite—Hadamard Hadamard type for (h, d)—convex functions have been established. Various special cases including classes instance, h—convex, s—convex function Breckner Godunova—Levin—Dragomir strong versions aforementioned types convex identified. Some applications to err...

The main purpose of this manuscript is to present some new estimations the Jensen gap in a discrete sense along with their applications. proposed for are provided help notion 6-convex functions. Some numerical experiments performed determine significance and correctness intended estimates. Several outcomes results discussed Hölder inequality power quasi-arithmetic means. Furthermore, applicatio...

We investigate the mixed local and nonlocal parabolic p-Laplace equation $$\begin{aligned} \partial _t u(x,t)-\Delta _p u(x,t)+\mathcal {L}u(x,t)=0, \end{aligned}$$ where $$\Delta _p$$ is usual operator $$\mathcal {L}$$ type operator. Based on combination of suitable Caccioppoli-type inequality Logarithmic Lemma with a De Giorgi–Nash–Moser iteration, we establish boundedness Hölder continuity w...

For s-convex functions, the Hermite–Hadamard inequality is already well-known in convex analysis. In this regard, work presents new inequalities associated with left-hand side of for s-convexity by utilizing a novel technique based on Green’s function. Also, Hölder, Young, and power-mean are used to obtain these inequalities. Finally, some applications special means real numbers provided. concl...

A two-class mixture model, where the density of one components is known, considered. We address issue nonparametric adaptive estimation unknown probability second component. propose a randomly weighted kernel estimator with fully data-driven bandwidth selection method, in spirit Goldenshluger and Lepski method. An oracle-type inequality for pointwise quadratic risk derived as well convergence r...

This paper is a natural continuation of Krylov (2020 and 2021) where strong Markov processes are constructed in time inhomogeneous setting with Borel measurable uniformly bounded nondegenerate diffusion drift $L_{d+1}(\mathbb {R}^{d+1})$ some properties their Green’s functions probability passing through narrow tubes investigated. On the basis this here we study further these such as Harnack in...