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In this paper, we study the existence and nonexistence of entire solutions of finite and infinite order of certain nonlinear difference equations of the form $$\begin{aligned} f^{n}\left( z\right) +L\left( z,f\right) =p_{1}\left( z\right) e^{\alpha _{1}\left( z\right) }+p_{2}\left( z\right) e^{\alpha _{2}\left( z\right) }, \quad \text { }n\ge 3 \end{aligned}$$ where \(p_{i}\left( z\right) \), \(\alpha _{i}\left( z\right) \)\(\left( i=1,2\right) \) are polynomials and \(L\left( z,f\right) \) is a nonzero linear difference polynomial in f, we give also an affirmative answer to the conjecture posed by Zhang et al. (Adv Differ Equ 2015:150, 2015).

We study the heat conduction through a pipe filled with incompressible viscous fluid. The goal of this paper is to take into account the effects of the spipe’s dilatation due to the heating. In view of that, we assume that the longitudinal dilatation of the pipe is described by a linear heat expansion law. We prove the existence and uniqueness theorems for the corresponding boundary value problem. The main difficulty comes from the fact that the flow domain changes depending on the solution of the heat equation leading to a nonlinear coupled governing problem.

A submanifold M of an almost Hermitian manifold $$(\widetilde{M},g,J)$$ is called slant, if for each point $$p\in M$$ and $$0\ne X\in T_p M$$ , the angle between JX and $$T_p M$$ is constant (see Chen in Bull Aust Math Soc 41:135–147, 1990). Later, Carriazo (in: Proceedings of the ICRAMS 2000, Kharagpur, 2000) defined the notion of bi-slant immersions as an extension of slant immersions. In this paper, we study warped product bi-slant submanifolds in Kaehler manifolds and provide some examples of warped product bi-slant submanifolds in some complex Euclidean spaces. Our main theorem states that every warped product bi-slant submanifold in a Kaehler manifold is either a Riemannian product or a warped product hemi-slant submanifold.

In this paper, we consider a class of integral boundary value problems of fractional p-Laplacian equation, which involve both Riemann–Liouville fractional derivative and Caputo fractional derivative. By using the generalization of Leggett–Williams fixed point theorem, some new results on the existence of at least three positive solutions to the boundary value problems are obtained. Finally, some examples are presented to illustrate the extensive potential applications of our main results.

This paper considers the Degn–Harrison reaction–diffusion system subject to homogeneous Neumann boundary conditions in a smooth and bounded domain. Using the presence of contracting rectangles and the method of Lyapunov, we establish sufficient conditions for the global asymptotic stability of the unique constant steady state.

In this paper, we propose and derive several new explicit formulas of the generalized Bernoulli and Euler polynomials in terms of the generalized Stirling numbers of the second kind. A study of some families of the modified generalized Euler polynomials yields an interesting algorithm for calculating the generalized Euler polynomials.

First of all, in this paper, we prove the convergence of the nabla h-sum to the Riemann–Liouville integral in the space of continuous functions and in some weighted spaces of continuous functions. The connection with time scales convergence is discussed. Second, the efficiency of this approximation is shown through some Cauchy fractional problems with singularity at the initial value. The fractional Brusselator system is solved as a practical case.

In this paper, we study the existence of solutions for the following impulsive fractional boundary-value problem: $$\begin{aligned} {\left\{ \begin{array}{ll} - \frac{\mathrm{d}}{\mathrm{d}t} \Big (\frac{1}{2} {}_0D_t^{\alpha - 1} ({}_0^c D_t^\alpha u (t) ) - \frac{1}{2} {}_tD_T^{\alpha - 1} ({}_t^c D_T^\alpha u (t)) \Big ) = \lambda u (t) + f (t, u (t)), &{} t \ne t_j, \;\;\text {a.e.}\;\; t \in [0, T],\\ \Delta \Big (\frac{1}{2} {}_0D_t^{\alpha - 1} ({}_0^c D_t^\alpha u (t_j) ) - \frac{1}{2} {}_tD_T^{\alpha - 1} ({}_t^c D_T^\alpha u (t_j)) \Big ) = I_j (u (t_j)), &{} j = 1, 2, \ldots , n,\\ u (0) = u (T) = 0, \end{array}\right. } \end{aligned}$$ where \(\alpha \in (1/2, 1]\), \(0 = t_0< t_1< t_2< \cdots< t_n< t_{n +1} = T\), \(\lambda \) is a parameter and \(f :[0, T] \times {\mathbb {R}} \rightarrow {\mathbb {R}}\) and \(I_j : {\mathbb {R}} \rightarrow {\mathbb {R}}\), \(j = 1, \ldots , n\) are continuous functions and $$\begin{aligned}&\Delta \left( \frac{1}{2} {}_0D_t^{\alpha - 1} ({}_0^c D_t^\alpha u (t_j) ) - \frac{1}{2} {}_tD_T^{\alpha - 1} ({}_t^c D_T^\alpha u (t_j)) \right) \\&\quad = \frac{1}{2} {}_0D_t^{\alpha - 1} ({}_0^c D_t^\alpha u (t_j^+) ) - \frac{1}{2} {}_tD_T^{\alpha - 1} ({}_t^c D_T^\alpha u (t_j^+) \\&\qquad -\, \frac{1}{2} {}_0D_t^{\alpha - 1} ({}_0^c D_t^\alpha u (t_j^-) ) - \frac{1}{2} {}_tD_T^{\alpha - 1} ({}_t^c D_T^\alpha u (t_j^-) ,\\&\frac{1}{2} {}_0D_t^{\alpha - 1} ({}_0^c D_t^\alpha u (t_j^+) ) - \frac{1}{2} {}_tD_T^{\alpha - 1} ({}_t^c D_T^\alpha u (t_j^+)) \nonumber \\&\quad = \lim _{t \rightarrow t_j^+} \left( \frac{1}{2} {}_0D_t^{\alpha - 1} ({}_0^c D_t^\alpha u (t) ) - \frac{1}{2} {}_tD_T^{\alpha - 1} ({}_t^c D_T^\alpha u (t))\right) ,\\&\frac{1}{2} {}_0D_t^{\alpha - 1} ({}_0^c D_t^\alpha u (t_j^-) ) - \frac{1}{2} {}_tD_T^{\alpha - 1} ({}_t^c D_T^\alpha u (t_j^-)) \\&\quad = \lim _{t \rightarrow t_j^-} \left( \frac{1}{2} {}_0D_t^{\alpha - 1} ({}_0^c D_t^\alpha u (t) ) - \frac{1}{2} {}_tD_T^{\alpha - 1} ({}_t^c D_T^\alpha u (t))\right) . \end{aligned}$$ By using critical point theory and variational methods, we give some new criteria to guarantee that the impulsive problems have at least one solution and infinitely many solutions.

In this paper, we obtain fixed point theorems for operators defined on Cartesian product spaces under heterogeneous conditions upon the structure of the factor spaces and the operator components. The main results combine Banach–Perov contraction principle with topological fixed point theorems of Monch type in strong and weak topologies. The results make possible a tinted analysis of the operator systems. An application of the vectorial technique to evolution equations with nonlocal Cauchy conditions is included.

In this paper, we study the following quasilinear Schrodinger equation of the form $$\begin{aligned} -\Delta u+V(x)u-\Delta (u^{2})u= g(x,u),~~~ x\in \mathbb {R}^N \end{aligned}$$ where V and g are 1-periodic in $$x_{1},\ldots ,x_{N}$$ , and g is a superlinear but subcritical growth as $$|u|\rightarrow \infty $$ . We develop a more direct and simpler approach to prove the existence of ground state solutions.

We consider the nonlinear fourth-order semipositone boundary value problem $$\begin{aligned} u^{(4)}=f(t,u(t),u'(t)), \quad t \in (0,1), \end{aligned}$$ $$\begin{aligned} u(0)=u'(0)=u''(1)=u'''(1)=0, \end{aligned}$$ where \(f: [0,1] \times [0,\infty ) \times [0, \infty ) \rightarrow (-\infty , \infty )\) has the property \(f(t,x,y) \ge -g(t)\) for a nonnegative continuous function g(t). This paper improves the results of Ma (Hiroshima Math J 33:217–227, 2013) and Spraker (Differ Equ Appl 8:21–31, 2016).

In this paper, we present sufficient conditions involving limsup which guarantee the oscillation of all solutions of a differential equation with non-monotone deviating argument and non-negative coefficients. Corresponding differential equations of both delayed and advanced type are studied. Using algorithms on MATLAB software, examples are given to demonstrate the advantage of our results.

In this paper, we investigate the following critical fractional Schrodinger equation $$\begin{aligned} (-\Delta )^su+V(x)u=|u|^{2_s^*-2}u+\lambda K(x)f(u), \ x \in \mathbb {R}^N, \end{aligned}$$ where \(\lambda >0\), \(0 2s\) and \(2_s^*=\frac{2N}{N-2s}\). We prove that the equation has a positive solution for large \(\lambda \) by the variational method.

In this paper we discuss the existence and the global behavior of positive solutions of the following generalized Lane–Emden system of differential equations: $$\begin{aligned} -u''= & {} a(x)u^{\alpha }\,v^{r}\quad \text{ in } (0,1), \\ -v''= & {} b(x)u^{s}\,v^{\beta }\quad \, \text{ in } (0,1), \\ u'(0)= & {} v'(0)=0; \quad \, u(1)=v(1)=0, \end{aligned}$$ where \(r,\,s\in {\mathbb {R}}\), \(\alpha ,\,\beta 0\) and the nonnegative functions \(a,\,b\) satisfy some conditions related to the Karamata regular variation theory.

In this paper, we prove that unlike Hardy and weighted Bergman spaces of the upper half-plane, there are non-trivial analytic self-maps of the upper half-plane that induce compact composition operators on the Bloch space of the upper half-plane. Moreover, we also prove that like Hardy and weighted Bergman spaces of the upper half-plane, the growth space of the upper half-plane does not support compact composition operators.

The aim of this paper is to answer the question if there are three-dimensional real hypersurfaces in non-flat complex space forms whose covariant derivative with respect to the kth generalized Tanaka–Webster connection of a tensor field of type (1, 1) coincides with the Lie derivative of it either in direction of any vector field orthogonal to \(\xi \) or in direction of \(\xi \). The answer is given, in case the tensor field is the shape operator of a real hypersurface or the structure Jacobi operator of it.

In this paper, we propose a new proximal point algorithm for finding a common element of the set of fixed points of nonexpansive single-valued mappings, the set of fixed points of nonexpansive multi-valued mappings, and the set of minimizers of convex and lower semi-continuous functions. We obtain $$\Delta $$ -convergence and strong convergence of the proposed algorithm to a common element of the three sets in CAT(0) spaces. Furthermore, we apply our convergence results to obtain in a special space of CAT(0) spaces, so-called $$\mathbb {R}$$ -tree, under the gate condition. A numerical example to support our main results is also given.

In this paper, a class of $\log$-polyharmonic mappings $\mathcal{L}_p\mathcal{H}$ together with its subclass $\mathcal{L}_p\mathcal{H}(G)$ in the unit disk $\mathbb{D}=\{z: |z, 11 pages

In this paper we establish Parseval type identities and surprising new inequalities for Hilbert-Schmidt frames. Our results generalize and improve the remarkable results which have been obtained by Balan et al. and G{\u{a}}vru{\c{t}}a., Comment: 14 pages

In this paper, we present some results concerning the existence and uniqueness of S-asymptotically $$\omega $$ -periodic solutions for a class of nonlinear fractional differential equations with finite delay in Banach space X. These results are new even in the case of $$X=\mathbb {R}^n$$ . Moreover, we apply the above results to study the S-asymptotically $$\omega $$ -periodicity for the fractional-order diffusion equations and the fractional-order autonomous neural networks with delay.

In this paper, by extending the notions of harmonic transplantation and harmonic radius in the Heisenberg group, we give an upper bound for the first eigenvalue for the following Dirichlet problem: $$\begin{aligned} (P_{\Omega }) \left\{ \begin{array}{rllll} -\Delta _{\mathbb {H}^1} u &{} = &{} \lambda u &{}\quad \text{ in } &{} \Omega \\ u &{} = &{} 0 &{}\quad \text{ on } &{} \partial \Omega , \end{array} \right. \end{aligned}$$ where \( \Omega \) is a regular bounded domain of \( \mathbb {H}^1\) and \(\Delta _{\mathbb {H}^1}\) is the Kohn–Laplace operator. Using a result of Pansu which gives a relation between the volume of \(\Omega \) and the perimeter of its boundary, we prove that $$\begin{aligned} \lambda _{1}( \Omega ) \le C_{\Omega } \frac{ l_{11}^2 }{ \max _{ \xi \in \Omega } r_{\Omega }^2(\xi )} \end{aligned}$$ where \(l_{11} \) is the first strictly positive zero of the Bessel function of first kind and order 1, \( C_{\Omega } \) is a constant depending of \( \Omega \), and \(r_{\Omega }(\xi ) \) is the harmonic radius of \( \Omega \) at a point \(\xi \) of \(\Omega .\)

Let $$\sigma $$ be an automorphism of an arbitrary algebra. In this paper, we introduce the notions of inner and extremal $$\sigma $$ -biderivations and of proper $$\sigma $$ -commuting maps. We prove that (under certain assumptions) every $$\sigma $$ -biderivation of a triangular algebra is the sum of an extremal $$\sigma $$ -biderivation and an inner $$\sigma $$ -biderivation; and provide sufficient conditions on a triangular algebra for all of its $$\sigma $$ -biderivations (respectively, $$\sigma $$ -commuting maps) to be inner (respectively, proper). We introduce and describe a new class of automorphisms of triangular algebras. We provide many classes of triangular algebras whose automorphisms can be determined.

The aim of this paper is to study the uncertainty principles for the Dunkl wavelet transform, that set a limit to the possible concentration of a function in the time–frequency plane. Then, using for this transformation a class of concentration operators that are compact and self-adjoint, we show that their eigenfunctions are maximally time–frequency concentrated and we use its to obtain approximation inequalities for functions that are essentially concentrated in some region of the time–frequency plane.

The algorithm for the symbolic computation of the Aluthge transform of a polynomial matrix is derived in this paper. For this purpose, the well-known PSVD by PQRD algorithm is considered to avoid square roots of polynomials in the Aluthge transform matrix. The algorithm for the symbolic computation of the polar decomposition for polynomial matrices is developed as well. Furthermore, the Aluthge transform for rank-one matrices defined by cross-products of vectors is symbolically calculated and presented in a closed formula.

In this paper, $$\Delta $$ -convergence and metric convergence of proximal point algorithms of Mann and Halpern types to a zero of a monotone operator on a Hadamard space are established. Some applications in convex minimization and fixed point theory are also presented.

In this paper, we investigate a singular integral operator with polyanalytic Cauchy kernel. In particular, we will prove that the higher order Lipschitz classes (of order \(1+\alpha \)) behave invariant under the action of that operator.

In this paper, we provide some existence theorems for systems of equations involving condensing operators and as applications we discuss the problem of existence of solutions for systems of integral equations. Some examples are included to show the applicability of the main results.

[EN] In this paper a new version of the chain rule for calculat- ing the mean square derivative of a second-order stochastic process is proven. This random operational calculus rule is applied to construct a rigorous mean square solution of the random Chebyshev differential equation (r.C.d.e.) assuming mild moment hypotheses on the random variables that appear as coefficients and initial conditions of the cor- responding initial value problem. Such solution is represented through a mean square random power series. Moreover, reliable approximations for the mean and standard deviation functions to the solution stochastic process of the r.C.d.e. are given. Several examples, that illustrate the theoretical results, are included., This work was completed with the support of our TEX-pert.

In this paper, we study pseudo-Riemannian submanifolds of a pseudo-hyperbolic space \(\mathbb H^{m-1}_s (-1) \subset \mathbb E^m_{s+1}\) with 2-type pseudo-hyperbolic Gauss map. We give a characterization of proper pseudo-Riemannian hypersurfaces in \(\mathbb H^{n+1}_s (-1) \subset \mathbb E^{n+2}_{s+1}\) with non-zero constant mean curvature and 2-type pseudo-hyperbolic Gauss map. For \(n=2\), we prove classification theorems. In addition, we show that the hyperbolic Veronese surface is the only maximal surface fully lying in \(\mathbb H^4_2 (-1) \subset \mathbb H^{m-1}_2 (-1)\) with 2-type pseudo-hyperbolic Gauss map. Moreover, we prove that a flat totally umbilical pseudo-Riemannian hypersurface \(M^n_t\) of the pseudo-hyperbolic space \(\mathbb {H}^{n+1}_t(-1) \subset \mathbb E^{n+2}_{t+1}\) has biharmonic pseudo-hyperbolic Gauss map.

In this paper, we are concerned with the following nonlocal problem $$\begin{aligned} -\Delta u+u=q(x)\left( \int _{\mathbb {R}^N}\frac{q(y)|u(y)|^p}{|x-y|^{N-\alpha }}\mathrm{d}y\right) |u|^{p-2}u,\quad x\in \mathbb {R}^N, \end{aligned}$$ where \(N\ge 3, \alpha \in ((N-4)_+,N), 2\le p

In this paper, a new concept for a \(2\times 2\) block relation matrix is studied in a Banach space. We define a matrix linear relation and present some of its properties. It is shown that, under certain condition, we can investigate the Frobenius–Schur of relation matrices.

In this paper, by using a nonlinear alternative for a sum of compact upper semicontinuous and contractive multivalued operators, we establish sufficient conditions for the existence of solutions for perturbed fractional differential inclusions with nonlocal multi-point Erdelyi–Kober fractional integral boundary conditions. For the applicability of the main result, we include an example.

In this paper, we show an approximation in law of the complex Brownian motion by processes constructed from a stochastic process with independent increments. We give sufficient conditions to the characteristic function of the process with independent increments that ensure the existence of such an approximation. We apply these results to Levy processes. Finally we extend these results to the m-dimensional complex Brownian motion.

In this paper, some classes of local polynomial functions on abelian groups are characterized by the properties of their variety. For this characterization, we introduce a numerical quantity depending on the variety of the local polynomial only. Moreover, we show that the known characterization of polynomials among generalized polynomials can be simplified: a generalized polynomial is a polynomial if and only if its variety contains finitely many linearly independent additive functions.

Using the Laplace transform method, this paper deals with the Ulam stability of linear fractional differential equations with constant coefficients.

In this paper, we study a class of fractional-order cellular neural network containing delay. We prove the existence and uniqueness of the equilibrium solution followed by boundedness. Based on the theory of fractional calculus, we approximate the solution of the corresponding neural network model over the interval \([0,\infty )\) using discretization method with piecewise constant arguments and variation of constants formula for fractional differential equations. Furthermore, we conclude that the solution of the fractional-delayed system can be approximated for large t by the solution of the equation with piecewise constant arguments, if the corresponding linear system is exponentially stable. At the end, we give two numerical examples to validate our theoretical findings.

This paper presents a numerical method for solving nonlinear stochastic Ito Volterra integral equations driven by fractional Brownian motion with Hurst parameter \( H \in (0,1)\) via of hat functions. Using properties of the generalized hat basis functions and fractional Brownian motion, new stochastic operational matrix of integration is achieved and the nonlinear stochastic equation is transformed into nonlinear system of algebraic equations which by solving it, an approximation solution with high accuracy is obtained. In addition, error analysis of the method is investigated, and by some examples, efficiency and accuracy of the suggested method are shown.

The purpose of this paper is to study the pointwise pseudo-slant warped product submanifolds of a Kahler manifold $$\widetilde{M}$$ . We derive the conditions of integrability and totally geodesic foliation for the distributions allied to the characterization of a pointwise pseudo-slant submanifolds of $$\widetilde{M}$$ . The necessary and sufficient conditions for isometrically immersed pointwise pseudo-slant submanifolds of $$\widetilde{M}$$ to be a pointwise pseudo-slant warped product and a locally Riemannian product are obtained. Further, we classify pointwise pseudo-slant warped product submanifolds of $$\widetilde{M}$$ by developing the sharp inequalities in terms of second fundamental form and wrapping function.

In this paper, we expand the study of the multiplication operators on the Lipschitz space of a tree begun in Colonna and Easley (Integral Equ Oper Theory 68:391–411, 2010) by focusing on their adjoint acting on a certain separable subspace of the Lipschitz space whose dual is isometrically isomorphic to \(\mathbf L^1\). We then study the properties of two useful operators \(\nabla \) and \(\Delta \) and use them (along with the multiplicative symbol \(\psi \)) to define the Toeplitz operator \(T_\psi \) on the space \(\mathbf L^p\) for \(1\le p \le \infty \). We give conditions for its boundedness and study its point spectrum.

Let \( \mathcal {A} \) be an algebra. Under particular assumptions on \(\mathcal {A}\), in this paper we determine the explicit form of any map \( \psi \) on \( \mathcal {A} \) which satisfies \(\psi (A) \psi (P) + \eta \psi (P) \psi (A) = AP + \eta P A\) for each \(A \in \mathcal {A},\) some idempotent or projection \(P \in \mathcal {A}\) and some \(\eta \in \mathbb {C}.\)

In this paper, we define and study the continuous wavelet transform associated with the spherical mean operator, we prove Plancherel formula, inversion formula, etc. Next we establish an analogue of Heisenberg’s inequality for wavelet transform. Last, we study wavelet transform on subset of finite measures.

In this paper, functional equations related to derivations on semiprime rings and standard operator algebras are investigated. We prove the following result which is related to a classical result of Chernoff. Let X be a real or complex Banach space, let \({\mathcal {L}}(X)\) be the algebra of all bounded linear operators of X into itself and let \({\mathcal {A}}(X)\subset {\mathcal {L}}(X)\) be a standard operator algebra. Suppose there exist linear mappings \(D, G:{\mathcal {A}}(X)\rightarrow {\mathcal {L}}(X)\) satisfying the relations \(D(A^{2n+1})=D(A^{2n})A+A^{2n}G(A)\) and \(G(A^{2n+1})=G(A^{2n})A+A^{2n}D(A)\) for all \(A\in {\mathcal {A}}(X)\). Then there exists \(B\in {\mathcal {L}}(X)\) such that \(D(A)=G(A)=[A,B]\) for all \(A\in {\mathcal {A}}(X)\).

In this paper, we give analogues of local uncertainty inequality on \({\mathbb{R}^n}\) for stratified Laguerre hypergroup, connected with the spectral analysis of a given homogeneous sublaplacian L, also indicate how local uncertainty inequalities imply global uncertainty inequalities. It would be interesting to note that we deduce the local uncertainty inequalities for the radial functions on the Heisenberg group. Finally, we extend Heisenberg-Pauli-Weyl uncertainty inequality by ultracontractive properties of the semigroups generated by the differential operator and on the estimate on the heat kernel.

The main aim of this paper is to discuss the third Hankel determinants for three classes: \(S^*\) of starlike functions, \(\mathcal {K}\) of convex functions and \(\mathcal {R}\) of functions whose derivative has a positive real part. Moreover, the sharp results for twofold and threefold symmetric functions from these classes are obtained.