Markin, Marat V.
Published in
Open Mathematics

Given the abstract evolution equation y′(t)=Ay(t),t≥0, $$\begin{array}{} \displaystyle y'(t)=Ay(t),\, t\ge 0, \end{array}$$ with scalar type spectral operator A in a complex Banach space, found are conditions necessary and sufficient for all weak solutions of the equation, which a priori need not be strongly differentiable, to be strongly Gevrey ul...

George, Reny Nabwey, Hossam A. Vujaković, Jelena Rajagopalan, R. Vinayagam, Selva
Published in
Open Mathematics

In this paper we introduce dislocated and dislocated quasi version of a cone b-metric space over a Banach algebra as well as weak semi α-admissible and α-identical pair of mappings and prove common fixed point theorems for a pair of α-identical and weak α-admissible mappings in the aforesaid spaces. Our results are supported with suitable examples ...

Gil’, Michael
Published in
Open Mathematics

For an integer p ≥ 1, let Γp be an approximative quasi-normed ideal of compact operators in a Banach space with a quasi-norm NΓp(.) and the property ∑k=1∞|λk(A)|p≤apNΓpp(A)(A∈Γp), $$\begin{array}{} \displaystyle \sum_{k=1}^{\infty} |\lambda_k(A)|^p\le a_p N_{{\it\Gamma}_p}^p(A) \;\;(A\in {\it\Gamma}_p), \end{array}$$ where λk(A) (k = 1, 2, …) are t...

Wang, Hengtai Chen, Huiwen Ouyang, Zigen Li, Fubin
Published in
Open Mathematics

In this paper, Lie symmetry analysis is performed for the equation derived from $(2+1)$-dimensional higher order Broer-Kaup equation. Meanwhile, the optimal system and similarity reductions based on the Lie group method are obtained. Furthermore, the conservation law is studied via the Ibragimov’s method.

Ling, Jiaoxiu Zhou, Zhan
Published in
Open Mathematics

In this paper, by using critical point theory, we obtain some sufficient conditions on the existence of infinitely many positive solutions of the discrete Dirichlet problem involving the mean curvature operator. We show that the suitable oscillating behavior of the nonlinear term near at the origin and at infinity will lead to the existence of a se...

Iranmanesh, Mahdiyeh Jafarpour, Morteza Cristea, Irina
Published in
Open Mathematics

The aim of this paper is to construct and study the properties of a certain graph associated with a non-central hypergroup, i.e. a hypergroup having non-commutative the associated fundamental group. The method of the construction of the graph is similar to that one proposed by Paul Erdős, when he defined a graph associated with a non-commutative gr...

Xu, Hong Yan Zheng, Xiu Min
Published in
Open Mathematics

The purpose of this manuscript is to study some properties on meromorphic solutions for several types of q-difference equations. Some exponents of convergence of zeros, poles and fixed points related to meromorphic solutions for some q-difference equations are obtained. Our theorems are some extension and improvements to those results given by Qi, ...

Cheng, Xiao Yun Wang, Mei Wang, Wei Wang, Jun Tao
Published in
Open Mathematics

The main goal of this paper is to introduce the notion of stabilizers in EQ-algebras and develop stabilizer theory in EQ-algebras. In the paper, we introduce (fuzzy) left and right stabilizers and investigate some related properties of them. Then, we discuss the relations among (fuzzy) stabilizers, (fuzzy) prefilters (filters) and (fuzzy) co-annihi...

Lee, Manseob
Published in
Open Mathematics

In this paper, we show that for generic C1, if a flow Xt has the shadowing property on a bi-Lyapunov stable homoclinic class, then it does not contain any singularity and it is hyperbolic.

Hou, Jian Zhao, Yong
Published in
Open Mathematics

Linear regression models are foundation of current statistical theory and have been a prominent object of study in statistical data analysis and inference. A special class of linear regression models is called the seemingly unrelated regression models (SURMs) which allow correlated observations between different regression equations. In this articl...