Abstract We study a minimisation problem in L p and ∞ for certain cost functionals, where the class of admissible mappings is constrained by Navier–Stokes equations. Problems this type are motivated variational data assimilation atmospheric flows arising weather forecasting. Herein we establish existence PDE-constrained minimisers all , also that converge to as → ∞. further show solve an Euler–...

In this paper, we introduce δǫα∗ – a minimal coverage, real-time robotic search algorithm that yields a moderately aggressive search path with minimal backtracking. Search performance is bounded by a placing a combinatorial bound, ǫ and δ, on the maximum deviation from the theoretical shortest path and the probability at which further deviations can occur. Additionally, we formally define the n...

In this paper, we introduce the notions of fuzzy $alpha$-Geraghty contraction type mapping and fuzzy $beta$-$varphi$-contractive mapping and establish some interesting results on the existence and uniqueness of fixed points for these two types of mappings in the setting of fuzzy metric spaces and non-Archimedean fuzzy metric spaces. The main results of our work generalize and extend some known ...

In this article, we first give a modified Schwarz–Pompeiu formula in general sector ring with angle \(\vartheta =\frac{\pi }{\alpha },\ \alpha \ge 1/2\) by proper conformal mappings, and obtain the solution of Schwarz problem for Cauchy–Riemann equation explicit forms. Furthermore, construct some integral operators discuss their properties detail. Finally, virtue these operators, problems an in...

For quasianalytic Denjoy–Carleman differentiable function classes C where the weight sequence Q = (Qk) is log-convex, stable under derivations, of moderate growth and also an L-intersection (see (1.6)), we prove the following: The category of C-mappings is cartesian closed in the sense that C(E,C(F,G)) ∼= C(E × F,G) for convenient vector spaces. Applications to manifolds of mappings are given: ...

In this paper, we obtain a unique common fixed point results by using Suzuki - $(\mathcal{Z}_{\psi}(\alpha,\beta))$ type rational contractive mappings in metric spaces. Also give an example which supports our main theorem.

A continuous complex-valued function F in a domain $$D\subseteq \mathbf {C}$$ is poly-analytic of order $$\alpha $$ if it satisfies $$\partial ^{\alpha }F/\partial \overline{z}^{\alpha }=0$$ . One can show that has the form $$F(z)=\sum _{k=0}^{\alpha -1}\overline{z}^{k}A_{k}(z)$$ , where each $$A_k$$ an analytic function. In this paper, we prove existence Landau constant for functions and ...