In this study, we obtain sharp bounds for the second Hermitian- Toeplitz determinants of a subclass of analytics functions in the open unit disk.

In this paper we consider the weighted Hardy space Hβ. This space which gives a generalization of some Hilbert spaces of analytic functions on the unit disk like, the Hardy space H , the weighted Bergman space Bν and the weighted Dirichlet space Dν, it plays a background to our contribution. Especially, we examine the extremal functions for the primitive operator Pf(z) := R [0,z] f(w)dw, where [0, z] = {tz, t ∈ [0, 1]}; and we deduce approximate inversion formulas for the operator P on the weighted Hardy space Hβ.

In this paper we have proven a result for a covered graph with at least one subgraph C4⨁e. We have also mentioned some observations and conditions for a graph containing C4⨁e. An algorithm along with the flowchart, that describes the impact of covering a specified C4⨁e with a common label is described by us.

In [6], Chen and Abdolyousefi studied the common spectral properties of operators AC and BD satisfying (AC)2A = ACDBA = DBACA = (DB)2A; (AC)2D = ACDBD = DBACD = (DB)2D. In this note, we continue studying the common local spectral properties of these operators. We show that AC and BD shared the single-valued extension property, the Bishop property (β), the property (βϵ), the decomposition property (δ), and decomposability. Furthermore, we investigate the closedness of the analytic core and the quasinilpotent part. We also examine the Dunford’s property (C) and the property (Q).

In this paper we will obtain some Bernstein-Kantorovich operators modified in Stancu sense which preserve exponential function eμx, where μ > 0. Concerning these operators we prove they verify Korovkin’s theorem conditions and also that they approximate functions from a weighted Lp space. Moreover, we will obtain a Voronovskaya theorem and some quantitative estimates of approximation using the first order modulus of continuity. Also, we will prove some estimates concerning the approximation of functions from a weighted Lp space using Peetre’s K-functional. Finally, we will obtain an estimate which involves the first order modulus of continuity and the second order modulus of smoothness by using the equivalence relation between these moduli and the corresponding K-functionals.

In this paper, we construct a new family of locally univalent and sensepreserving harmonic mappings Tc,q[f] by using quantum approach in the open unit disk D. We prove that the convolution of a harmonic convex mapping Tc,q[f] with a right half-plane mapping is q-convex in the direction of the real axis provided that the convolution is locally univalent and sense-preserving. Further, we show that the convolution of Tc,q[f] with a vertical strip mapping is also q-convex in the direction of the real axis. In particular, the results in this paper generalize or improve (in certain cases) the corresponding results obtained by recent researchers.

In this paper, a numerical study of a mixed nonlinear stochastic Schr¨odinger equation in the case of an additive white noise and with mixed concaveconvex, sub-super nonlinearities is developed. The influence of the stochastic part on the deterministic solutions such as stationary states and blow-up solutions is investigated. Numerical examples are provided with error estimates.

In this paper, we consider a class of nonhomogeneous fractional elliptic equations involving critical Hardy Sobolev exponents as follows {(−Δ)su − μ u |x|2s = |u|2∗ s−2u + λ u |x|2s−α + f(x), x ∈ Ω, u = 0 x ∈ ∂Ω, where Ω ⊂ RN is a bounded domain, 0 < s < 1, λ > 0 is a parameter. We prove the existence of multiple solutions using the variational methods and the Nehari manifold decomposition.

This paper focuses on three things. Firstly, we define a new type of implicit relations which covers a multitude of contractive conditions in one go. Secondly, we use this implicit relation to prove a new common fixed point theorem for four occasionally weakly biased maps of type (A) in a dislocated metric space. This theorem improves some results existing in the fixed point theory’s environment. Thirdly, we will provide an example to illustrate our main theorem and to expound the credibility and generality of our result.