Chuanxi Zhu

• Nanchang University

In this paper, we deal with the existence of nontrivial solutions for the following Kirchhoff-type equation where $0 < s < 1 < p < \infty$, $sp < N$, $\lambda > 0$ is a real parameter, $(-\Delta)_{p}^{s}$ is the fractional $p$-Laplacian operator, $V:\mathbb{R}^N\rightarrow\mathbb{R}^N$ is a potential function, $M$ is a Kirchhoff function, the nonl...

Quantifying the quantumness of ensembles is a vital and practical task in quantum information theory. In this paper, we quantify the quantumness of quantum ensembles based on a quantifier of the coherence of ensembles via generalized α-z-relative Rényi entropy. It is shown that this measure satisfies the intuitive and desirable properties which are...

This paper concerns the existence of sign-changing solutions for the following fractional Kirchhoff-type equation with critical and supercritical nonlinearities $$\begin{aligned} \left( a+b[u]^{2}\right) (-\Delta )^{\alpha }u+V(x)u=f(x,u)+\lambda |u| ^{r-2}u,\,\, \text {in}\,\,\mathbb {R}^3, \end{aligned}$$where \(a,b>0\) are constants, \(\alpha \i...

In this paper, we consider the following Kirchhoff equation −a+b∫R3|∇u|2dxΔu+V(x)u=f(u)+λ|u|p−2u,inR3,where a,b>0 are constants, λ>0 is a real parameter, p≥6 and V,f satisfy suitable conditions. By using a truncation argument, we prove that the existence of a sign-changing solution for this equation. Our results can be regarded as the complementary...

We study an approximate coincidence point and a common fixed point problem for a hybrid pair of mappings with constraints in Menger PM-spaces, and obtain some new results. We derive interesting consequences of the main results by using the properties of a Menger–Hausdorff metric, and analogous results based on graphs instead of partial orders can b...

In this paper, we propose some new coupled coincidence point and fixed point theorems for the mappings F and g. Our results are obtained by exploring the corresponding initial value problems for the mapping F and weakening the involved contractive conditions. As an application, we study the existence and uniqueness of solution to integro-differenti...

The aim of this paper is to propose a new φ-coupled fixed point theorem for a mixed monotone mapping in a metric space, which is taken no account of the continuity of the mapping. To this end, we introduce the notions of φ-coupled fixed point and modified F-control function. Our obtained results are applied to derive some φ-coupled fixed point theo...

Some new coupled coincidence point and coupled fixed point theorems are established in partially ordered metric-like spaces, which generalize many results in corresponding literatures. An example is given to support our main results. As an application, we discuss the existence of the solutions for a class of nonlinear integral equations.

In this paper, we introduce the concepts of cyclic \(\varphi \)-contractions in Menger PM-spaces and cyclic weak \(\phi \)-contractions in generalized Menger PM-spaces. Based on these concepts, some fixed point results for cyclic \(\varphi \)-contractions in Menger PM-spaces are obtained. Furthermore, some fixed point theorems for cyclic weak \(\ph...

In this paper, we introduce the concept of new generalized cyclic weak contraction mappings and prove a class of fixed point theorems for such mappings in partially ordered probabilistic metric spaces. In addition, we also establish a coupled fixed point for mixed monotone mappings under contractive conditions in partially ordered probabilistic met...

In this paper, we obtain some Suzuki-type fixed point theorems for generalized mappings in partial cone metric spaces over a solid cone. Our results unify and generalize various known comparable results in the literature. We also provide illustrative examples in support of our new results.

As a generalization of hesitant fuzzy sets (HFSs) and hesitant fuzzy linguistic term sets (HFLTSs), linguistic hesitant fuzzy sets (LHFSs) establish a proper interpretation of the hesitancy, inconsistency and uncertainty of experts in evaluating decision alternatives. In this paper, based on the cloud model, we discuss multiple attribute decision-m...

In this paper, we weaken the notion of ψ of Luong and Thuan, [V. N. Luong, N. X. Thuan, Nonlinear Anal., 74 (2011), 983{992] and prove some new coupled coincidences and coupled common fixed point theorems for mappings having a mixed g-monotone property in partially ordered complete probabilistic metric spaces. As an application, we discuss the exis...

In this paper, we prove some new common fixed point theorems for compatible and weakly compatible self-maps under ɸ-contractive conditions in Menger probabilistic G-metric spaces. Our results improve and generalize many comparable results in existing literature. Finally, an example is given as an application of our main results.

In this paper, we give the deIn this paper, we give the definitions of compatibility and weakly reciprocally continuity for sequence of random mappings Ti and a random self-mapping g. Further, using these definitions we establish quadruple random coincidence and quadruple random fixed point results by applying the concept of an α-series for sequenc...

In this paper, by using random fixed point index theory, some new boundary conditions based on strictly convex or strictly concave functions are established and some new theorems for the solutions of a class of random semi-closed 1-set-contractive operator equations A(ω, x) = μx are obtained, which extend and generalize some corresponding results o...

The conflict between the dynamics postulate (unitary evolution) and the measurement postulate (wave-packet collapse) of quantum mechanics has been reconciled by Zurek from an information transfer perspective [Phys. Rev. A 76 (2007) 052110], and has further been extended to a more general scenario [Phys. Rev. A 87 (2013) 052111]. In this paper, we r...

In this paper, we generalize the algebraic sum ⊕ of Fang. Based on this concept, we prove some common fixed point theorems for three pairs of self-mappings satisfying the common ( E . A ) property in Menger P G M -spaces. Finally, an example is given to exemplify our main results. MSC: 47H10, 46S10.

In this paper, the new concepts of \(\alpha \)-admissible mappings with respect to \(\eta \) in single-valued case and \(\alpha _{*}\)-admissible mappings with respect to \(\eta _{*}\) in set-valued case in Menger PM-spaces are introduced, and some new fixed point results for both single-valued and set-valued mappings under certain contractive cond...

This work is concerned with the approximate controllability of a nonlinear fractional impulsive evolution system under the assumption that the corresponding linear system is approximate controllable. Using the fractional calculus, the Krasnoselskii fixed point theorem, and the technique of controllability theory, some new sufficient conditions for...

In this work, we introduce a new φ-contractive mapping; following that, we obtain some multipled common fixed point theorems for a pair of mappings and A : X → X . The main results of this paper are generalization of the main results of Kutbi et al. (Fixed Point Theory Appl. 2015(1):32, 2015). As an illustration, we give an example to demonstrate t...

In this paper, we introduce the new concepts of multidimensional Menger probabilistic metric spaces and related fixed point for a pair of mappings T: and A: X → X . Utilizing the properties of the related triangular norm and the compatibility of A with T, some multidimensional common fixed point problems of hybrid probabilistic contractions with a...

The tension between unitarity and wave-packet collapse is an annoying problem in quantum mechanics, while a breakthrough was made by Zurek recently from the point of view of information transfer. In this paper, we reconsider Zurek's derivation in the setting of generalized probabilistic theories (GPT), and establish that actionable information abou...

In this paper, utilizing the concepts of weakly biased mappings and occasionally weakly biased mappings for a pair of self-mappings in Menger PM-spaces, some new common fixed point theorems under contractive conditions are obtained. Some examples are also given to exemplify our main results.

In this paper, we introduce the notions of multivalued f-weak contraction and generalized multivalued f-weak contraction on partial metric spaces. We obtain some coincidence and fixed point theorems. Our results extend and generalize some well known fixed point theorems on partial metric spaces.

In this paper, a new concept of the property G*-(E.A) in Menger PGM-spaces is introduced. Based on this, some common fixed point theorems under strict contractive conditions for mappings satisfying the property G*-(E.A) in Menger PGM-spaces and the corresponding results in G-metric spaces are obtained. Finally, an example is given to exemplify our...

We consider several hybrid probabilistic contractions with a gauge function φ. Without any continuity or monotonicity conditions for φ, we obtain some new common coupled fixed point theorems in Menger PGM-spaces. Finally, an example is given to illustrate our main results.

In this paper, we introduce the concepts of cyclic weakly (psi, phi)-contractive mappings and cyclic weakly (C, psi, phi)-contractive mappings, and prove some fixed point theorems for such two types of mappings in complete partially ordered Menger PM-spaces. Some new results are obtained, which extend and generalize some fixed point results in metr...

In this paper, we introduce the concepts of generalized probabilistically bounded set Ω ∗ and Menger-Hausdorff metric G ˜ ∗ in Menger probabilistic G-metric spaces, and prove that ( Ω ∗ , G ˜ ∗ , Δ ) is also a Menger probabilistic G-metric space. Utilizing these concepts, we establish some common fixed point theorems for three hybrid pairs of mappi...

In this work, some fixed point and common fixed point theorems are investigated in b-metric-like spaces. Some of our results generalize related results in the literature. Also, some examples and an application to integral equation are given to support our main results. MSC: 47H10, 54H25.

In this paper, some new fixed point theorems for semi-closed 1-setcontractive operators of functional type are obtained, which generalize the famous Petryshyn’s theorem and Altman’s theorem by replacing the norm with some classes of functionals. © 2015, Mathematical Society of the Rep. of China. All rights reserved.

In this paper, the new concepts of generalized Menger probabilistic metric spaces and tripled common fixed point for a pair of mappings T : X × X × X → X and A : X → X are introduced. Utilizing the properties of the pseudo-metric and the triangular norm, some tripled common fixed point problems of hybrid probabilistic contractions with a gauge func...

In this paper, we first introduce the concepts of generalized (ψ,f)λ-expansive mappings and generalized (ϕ,g,h)λ-weakly expansive mappings designed for three mappings. Then we establish some common fixed point results for such two new types of mappings in partial b-metric spaces. These results generalize and extend the main results of Karapınar et...

We introduce the concepts of (H,ψ,Φ)-contraction and probabilistic (α,φ)-contraction mappings in generalized probabilistic metric spaces and prove some fixed point theorems for such two types of mappings in generalized probabilistic metric spaces. Our results generalize and extend many comparable results in existing literature. Some examples are al...

In this paper, we introduce a new concept of generalized cyclic (κh,φL)S-weak contraction mappings and establish some coincidence point results for such mappings in complete partially ordered Menger PM-spaces. Our results generalize the main results of Nashine (Nonlinear Anal. 75:6160-6169, 2012) and Gopal et al. (Appl. Math. Comput. 233:955-967, 2...

In this paper, we introduce a new concept of quasi-b-metric-like spaces as a generalization of b-metric-like spaces and quasi-metric-like spaces. Some fixed point theorems are investigated in quasi-b-metric-like spaces. Moreover, an example is given to support one of our results. MSC: 47H10, 54H25.

Information flows in a network where individuals influence each other. In this paper, we study the influence maximization problem of finding a small subset of nodes in a social network that could maximize the spread of influence. We propose a novel information diffusion model CTMC-ICM, which introduces the theory of Continuous-Time Markov Chain (CT...

In this paper, we prove a common fixed point theorem for two pairs of non-self-mappings satisfying the generalized contraction condition of Ćirić type in cone metric spaces. Our result generalizes and extends some recent results related to non-self-mappings in the setting of cone metric spaces. MSC: 47H10, 54H25.

In this paper, we give a characterization of generalized quantum gates. We also show that many important operators are generalized quantum gates, moreover, some of these operators can be represented as the convex combination of only two unitary operators. Our results answer what kinds of operations a duality quantum computing admits. We point out t...

In this work, the concept of fractional calculus on time scales is developed to the study of fractional differential equations on time scales. By using the Banach contraction principle and the Schauder fixed-point theorem, some existence results for fractional differential equations on time scales are obtained. Finally, an example is given to illus...

In this note, the problem on the exponential stability in mean square moment of mild solution to impulsive neutral stochastic partial functional differential equations is considered by employing the inequality technique. Some sufficient conditions are established for the concerned problem, and some existing results are generalized and improved. Fin...

In this paper, some Banach spaces are introduced. Based on these spaces and the coincidence degree theory, a 2m-point boundary value problem for a coupled system of impulsive fractional differential equations at resonance is considered, and the new criterion on existence is obtained. Finally, an example is also given to illustrate the availability...

This article is concerned with the coupled system of fractional differential equations with nonlocal integral boundary conditions. The existence results are obtained by applying some standard fixed point theorems. Finally, an example is also provided to illustrate the availability of our main results.

Some common fixed point theorems for a family of non-self mappings defined on a closed subset of a metrically convex cone metric space (over the cone which is not necessarily normal) are obtained which generalize earlier results due to Imdad et al. and Janković et al. MSC: 47H10, 54H25.

In this work, we establish some fixed point theorems for weakly C-contractive mappings in partial metric spaces. Presented theorems extend and generalize some existence results in the literature. Also, an example is given to support our results. MSC: 47H10, 54H25.

The incompatibility of dynamics postulate (unitary evolution) and the measurement postulate (wave-packet collapse) of quantum mechanics has recently been solved by Zurek from an information transfer perspective. Luo gave his derivation by relaxing the repeatability postulate. In this paper, we reconsider Luo’s derivation in the setting of general p...

In this paper, a new concept of the common property (E.A) for two hybrid pairs of mappings is introduced in Menger PM-spaces. Utilizing this concept, some common fixed point theorems, which shed some new light on the study of fixed point results for hybrid pairs in Menger PM-spaces, are obtained under strict contractive conditions. The correspondin...

In this work, the existence criteria of extremal solutions of periodic boundary value problems for the first-order dynamic equations on time scales are given by using the method of lower and upper solutions coupled with the monotone iterative technique. Our results generalize and improve some existing results. Two examples are provided to show the...

This paper studies the problem of the robustly exponential stabilization for uncertain Markovian jump systems with mode-dependent time-varying state delays. The contribution of this paper is two-fold. Firstly, by constructing a modified Lyapunov functional and using free-weighting matrices technique, some delay-dependent robustly exponential stabil...

In this paper, we first define quantum Jensen-Shannon divergence (QJSD) between quantum states in infinite-dimensional case and discuss its properties. Then, using the probabilistic coupling technique, we further propose the notion of quantum Jensen-Shannon divergence (QJSD) between quantum ensembles. Some fundamental properties of this quantity ar...

This paper studies the problem of the robustly exponential stabilization for uncertain Markovian jump systems with mode-dependent time-varying state delays. The contribution of this paper is two-fold. Firstly, by constructing a modified Lyapunov functional and using free-weighting matrices technique, some delay-dependent robustly exponential stabil...

Some common fixed points theorems for two pairs of weakly compatible maps in fuzzy metricspaces both in the sense of Kramosil and Michalek and in the sense of George and Veeramani byusing common E.A. property are proved. These results generalize some known results in literature.

In this paper, we define expanding mappings in the setting of cone metric spaces analogous to expanding mappings in metric spaces. We also obtain some results for two mappings to the setting of cone metric spaces.

In this work, the Cauchy initial value problem is discussed for a class of fractional impulsive differential equations with delay, and the criteria on existence and uniqueness are obtained. Finally, an example is also provided to illustrate the effectiveness of our main results.

Over the last few years, online forums have gained massive popularity and have become one of the most influential web social media in our times. The forum document corpus can be seemed to be composed of various topics evolved over time, and every topics is reflected on a volume of keywords and social actors. In this paper, we attempt to study the i...

Some related fixed points theorems on two complete cone metric spaces are proved. These results generalize some known results in metric spaces.

In the paper, the topological degree for a compact continuous operator defined on an open subset of a Menger PN-space is generalized. The new concept of fixed-point index in Menger PN-spaces is introduced, themost important properties of the fixed-point index are established, and some other results are given.

Understanding the individual behavior has shown to be of paramount importance to the triumph of the telecommunication operators to retain customers, enhance their purchasing capacity, and predict the churn rate. Different behavior patterns can be observed for different groups of users. Hence, there is an interesting problem posted in telecommunicat...

We give a generalization of Hicks type contractions and Golet type contractions in intuitionistic fuzzy metric spaces. We prove some fixed point theorems for this new type contraction mappings on intuitionistic fuzzy metric spaces. These results generalize some known results in fuzzy metric spaces and probabilistic metric spaces.

In this paper, we prove some common fixed point theorems for any even number of compatible mappings in complete intuitionistic fuzzy metric spaces. Our main results extend and generalize some known results in fuzzy metric spaces and intuitionistic fuzzy metric spaces. KeywordsIntuitionistic fuzzy metric spaces-Common fixed point theorems-Compatibl...

In this paper, we mainly investigate the calculation problems of a random fixed point index and get some new results, part of which generalizes a previous result.

Complex network analysis has received increasing interest in recent years, which provides a remarkable tool to describe complex systems of interacting entities, particular for biological systems. In this paper, we propose a methodology for identifying the significant nodes of the networks, including core nodes, bridge nodes and high-influential nod...

We examine the inverse limits generated by inverse sequences on [0,1] with N-type bonding maps chosen from a four-parameter family of piecewise linear continuous functions. We analyze the continua generated by these sequences and obtain sufficient conditions for these sequences to give rise to indecomposable inverse limits.

We prove a common fixed point theorem for a sequence of mappings in cone metric spaces. This result offers a generalization of Huang and Zhang’s theorem in [L. D. Huang and X. Zhang, J. Math. Anal. Appl. 332, No. 2, 1468–1476 (2007; Zbl 1118.54022)]. An example to support our result is presented.

In this paper, we give a generalization of Hicks type contractions and Golet type contractions in intuitionistic fuzzy metric spaces. We prove some fixed point theorems for this new type contraction mappings on intuitionistic fuzzy metric spaces. These results generalize some known results in fuzzy metric spaces and probabilistic metric spaces.

In this paper, we prove some common fixed point theorems for any even number of compatible mappings in complete L-fuzzy metric spaces. Our main results extend and generalize some known results in fuzzy metric spaces, in-tuitionistic metric spaces and L-fuzzy metric spaces.

In this paper, we discuss some problems for nonlinear operators in the Menger PN space. Meanwhile, we prove existence theorems for the solution of an operator equation, and obtain some new results by means of the theory of topological degree for the Z-P-S space.

In the paper, the new concepts of bifurcation points and asymptotic bifurcation points of the compact continuous operator T are introduced in M-PN spaces. Some sufficient conditions for the existence of bifurcation points and asymptotic bifurcation points are obtained, and some theorems on the existence of intrinsic values are obtained. Meanwhile,...

In this work, we prove several important inequalities, and investigate the solution of an operator equation by means of the fixed point index in the theory of topological degree. For operator equations with different boundary conditions, the same conclusion is obtained. Meanwhile, the famous Rothe’s Theorem is generalized. Finally, an example is gi...

In this paper, we prove an important inequality and investigate some new calculating problems of random fixed point index, and generalize famous theorem by means of the theory of random fixed point index.

In this paper, the notion of ∊-strictly efficient solution for vector optimization with set-valued maps is introduced. Under the assumption of the ic-cone-convexlikeness for set-valued maps, the scalarization theorem, ∊-Lagrangian multiplier theorem, ∊-saddle point theorems and ∊-duality assertions are established for ∊-strictly efficient solution.

The characteristics of concave function and convex function are considered, the random solution existence of random 1-set contractive operator equations whose boundary conditions are governed by concave function, convex function or monotone function is investigated. The conclusions expand the famous Altman theorem and those in Zhu's and Li's.

In this paper, we investigate some nonlinear operator problems and the theory of topological degree. Meanwhile, we obtain some new fixed point theorems in the M-PN space.

In this work, the fixed point theorems of Krasnoselskii and Petryshyn are generalized to inner product spaces. An example is given to show the applications of the theorem.

The set-valued optimisation problem with constraints is considered in the sense of super efficiency in locally convex linear topological spaces. Under the assumption of nearly cone-subconvexlikeness, by applying the separation theorem for convex sets, Kuhn-Tucker and Lagrange necessary conditions for the set-valued optimisation problem to attain it...

We investigate random solutions of a class of random nonlinear integral equations and nonlinear differential equations. On infinite-dimensional Banach space, we give a counter-example and obtain some new results.