<abstract>
<p>In this manuscript, we introduce the notion of ℜ$ \alpha $-$ \theta $-contractions and prove some fixed-point theorems in the sense of ℜ-complete metric spaces. These results generalize existing ones in the literature. Also, we provide some illustrative non-trivial examples and applications to a non-linear fractional differential equation.</p>
</abstract>
In this paper, we introduce the concept of orthogonal convex structure contraction mapping and prove some fixed point theorems on orthogonal ♭-metric spaces. We adopt an example to highlight the utility of our main result. Finally, we apply our result to examine the existence and uniqueness of the solution for the spring-mass system via an integral equation with a numerical example.
We characterize skew-symmetric operators on a reproducing kernel Hilbert space in terms of their Berezin symbols. The solution of some operator equations with skew-symmetric operators is studied in terms of Berezin symbols. We also studied essentially unitary operators via Berezin symbols.
<abstract><p>In this manuscript, we introduce a three dimension metric type spaces so called $ J $-metric spaces. We prove the existence and uniqueness of a fixed point for self mappings in such spaces with different types of contractions. We use our result to prove the existence and uniqueness of a solution of the following fractional differential equations such as</p>
<p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \mathcal{(P)}:\left\{ \begin{array}{ccl} D^{\lambda}x(t) & = & f(t,x(t)) = Fx(t) \;{\rm{ if }}\; t\in I_0 = (0,T] \\ x(0) & = & x(T) = r \\ \end{array} \right\} . $\end{document} </tex-math></disp-formula></p>
<p>Moreover, we present other applications to systems of linear equations and Fredholm type integral equation.</p></abstract>
Abstract. We consider Berezin symbols and Hankel operators on the Hardy space H 2 (D) over the unit disc D = {z ∈ C : |z| < 1} and give their some applications. Namely, we estimate in terms of Hankel operators and Berezin symbols the distances from a given operator to the algebra of all analytic Toeplitz operators and to the set of all Toeplitz operators on H 2 (D). We use Hankel operator also to prove some lower estimate for the so-called Berezin number of bounded linear operators on H 2 . Some other related questions are also discussed.Mathematics subject classification (2010): 47A05, 47B10.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.