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The paper describes a Bochner-type study for holomorphic horizontal vector fields defined on a holomorphic Finsler algebroid E. We obtain in this setting a vanishing theorem for horizontal fields with compact support on E.

In this paper, we introduce a new class of fractal approximants as a fixed points of the Read–Bajraktarevic operator defined on a suitable function space. In the development of our fractal approximants, we used the suitable bounded linear operators defined on the space $${\mathcal {C}}(I)$$ of continuous functions and $$\alpha $$ -fractal functions. The convergence of the proposed fractal approximants towards the continuous function f does not need any condition on the scaling vector. Owing to this reason, the proposed fractal approximants approximate the function f without losing their fractality. We establish constrained approximation by a new class of fractal polynomials. In particular, our constrained fractal polynomials preserve positivity and fractality of the original function simultaneously whenever the original function is positive and irregular. Calculus of the proposed fractal approximants is studied using suitable bounded linear operators defined on the space $${\mathcal {C}}^r(I)$$ of all real-valued functions on the compact interval I that are r-times differentiable with continuous r-th derivative. We identify the IFS parameters so that our $$\alpha $$ -fractal functions preserve fundamental shape properties such as monotonicity and convexity in addition to the smoothness of f in the given compact interval.

There is a mistake in the last subsection (5.3 Totally geodesic null hypersurfaces in Robertson–Walker spaces) of the paper [1]

The paper is devoted to the existence, uniqueness and asymptotic behaviors of mild solution to neutral impulsive stochastic integro-differential equations driven by fractional Brownian motion with $$H\in (\frac{1}{2},1)$$ by the theory of resolvent operator and contraction mapping principle. An example is provided to demonstrate the results of the proposed results.

In this paper, we consider the split null point problem and the fixed point problem for multivalued mappings in Hilbert spaces. We introduce a Halpern-type algorithm for solving the problem for maximal monotone operators and demicontractive multivalued mappings, and establish a strong convergence result under some suitable conditions. Also, we apply our problem of main result to other split problems, that is, the split feasibility problem, the split equilibrium problem, and the split minimization problem. Finally, a numerical result for supporting our main result is also supplied.

In this paper, we consider the nonsymmetric algebraic Riccati equation whose four coefficient matrices form an M-matrix K. When K is a regular M-matrix, the Riccati equation is known to have a minimal nonnegative solution. We present two new numerical methods which can be applied directly in the case where K is a regular M-matrix. Furthermore, we find that the alternately linearized implicit iteration method is also feasible. In addition, we study the monotone convergence property of the proposed methods. Numerical experiments show that the above three numerical iteration methods are feasible and effective for solving the nonsymmetric algebraic Riccati equation.

In this paper, we consider a linear Cauchy viscoelastic problem with an external source term. We find the critical weaker conditions on the source \({f(x,t)}\) needed to show that, for any compactly supported initial data and for an exponentially decaying relaxation function, the decay of the first energy of solution is polynomial.

The aim of this paper is to consider operator-valued functions that can be approximated in the strong and weak operator topology by simple functions. We relate these notions with the classical formulations of measurability and provide conditions for their coincidence. A number of examples and counterexamples are exhibited.

In this paper, we will develop a four-stage high algebraic order symmetric two-step method with vanished phase-lag and its first up to the fourth derivative. For the proposed method, we will study the following: the phase-lag analysis of the new method; the development of the new method; the local truncation error analysis which is based on the radial Schrodinger equation; the stability and the interval of periodicity analysis which is based on a scalar test equation with frequency different than the frequency of the scalar test equation used for the phase-lag analysis; the error estimation procedure which is based on the algebraic order; and the numerical results from our numerical tests for the examination of the efficiency of the new obtained method. The numerical tests are based on the numerical solution of the Schrodinger equation.

In this paper, we study the limit of the iterates of a large class of linear bounded operators preserving constants. We obtain in addition the limit of the iterates of algebraic version of the trigonometric Jackson integrals. The proofs are based on spectral theory of linear operators.

In Ben Slimane (Mediterr J Math, 13(4):1513–1533 (2016)), the second author proved that, generically in the Baire category sense, pairs of functions in $${B_{t_{1}}^{s_{1},\infty}(\mathbb{R}^m) \times B_{t_{2}}^{s_{2},\infty}(\mathbb{R}^m) }$$ , for $${s_{1} > \frac{m}{t_{1}}}$$ and $${s_{2} > \frac{m}{t_{2}}}$$ , satisfy a mixed multifractal formalism based on wavelet leaders. In this paper, we extend this validity on $${(B_{t_{1}}^{s_{1},\infty}(\mathbb{R}^m) \cap C^{\gamma_{1}}(\mathbb{R}^m)) \times (B_{t_{2}}^{s_{2},\infty}(\mathbb{R}^m) \cap C^{\gamma_{2}}(\mathbb{R}^m)}$$ , for $${0 < \gamma_{1} < s_{1} < \frac{m}{t_{1}}}$$ and $${0 < \gamma_{2} < s_{2} < \frac{m}{t_{2}}}$$ . The main change is that the wavelet coefficients of the saturating function which generates the residual $${G_\delta}$$ set are not everywhere large enough and do not coincide everywhere with the wavelet leaders. Nevertheless, the computation of the wavelet leaders is done everywhere and allows to deduce both mixed spectra and mixed scaling function.

In this paper, we introduce a numerical method for solving time-fractional order telegraph equation. The method depends basically on an expansion of approximated solution in a series of Sinc function and shifted Legendre polynomials. The fractional derivative is expressed in the Caputo definition of fractional derivatives. The expansion coefficients are then determined by reducing the time-fractional order telegraph equation with its boundary and initial conditions to a system of algebraic equations for these coefficients. This system can be solved numerically using the Newton’s iteration method. Several numerical examples are introduced to demonstrate the reliability and effectiveness of the introduced method.

Let \({{\mathcal B}(H)}\) be the algebra of all bounded linear operators on an infinite-dimensional complex Hilbert space \({H}\). In this paper, we get a complete classification of surjective linear maps on \({{\mathcal B}(H)}\) that preserve quadratic operators in both directions. An analogue result in the setting of finite-dimensional Banach spaces is given.

In this paper, we investigate the fractional p-Kirchhoff-type equation $$\begin{array}{ll} M\left(\int\int\limits_{\mathbb{R}^{2N}}\frac{|u(x)-u(y)|^p}{|x-y|^{N+ps}}{\rm d}x{\rm d}y\right)(-\Delta)_p^su+V(x)|u|^{p-2}u+b(x)|u|^{q-2}u\\ \quad = \lambda a(x)|u|^{m-2}u, \; x\in\mathbb{R}^N,\end{array}$$ where $${\lambda}$$ is a real parameter, $${(-\Delta)_p^s }$$ is the fractional p-Laplacian operator with $${0 < s < 1 < p}$$ and $${ps < N}$$ , $${V(x), a(x), b(x): \mathbb{R}^N\to (0,\infty)}$$ are three positive weights, and M is a continuous and positive function. The case $${1 < q < m < p_s^*}$$ is considered. Using variational methods, we prove the existence, nonexistence, and multiplicity of solutions for the above equation depending on $${\lambda, m,q}$$ and according to the weight functions a(x) and b(x). Our results extend the previous works of Pucci et al. [23] and of Xiang et al. [29].

This paper is concerned with the existence of solutions to the following singular elliptic boundary value problem involving \({p}\)-Laplace operator $$-{\rm div}(|\nabla u|^{p-2} \nabla u)=\frac{h}{u^\gamma} \text{in } \Omega, \quad u > 0\text{ in } \Omega,\quad u=0 \text{ on } \partial\Omega.$$ Here, \({\Omega\subset \mathbb{R}^N(N\geq3)}\) is a bounded domain with smooth boundary, and \({h}\) is a positive \({L^1}\) function on \({\Omega}\). A “compatibility condition” on the couple \({(h(x),\gamma)}\) is given for the problem to have at least one solution. More precisely, it is shown that the problem admits at least one solution if and only if there exists a \({u_0\in W_0^{1,p}(\Omega)}\) such that \({\int_\Omega hu_0^{1-\gamma} \mathrm{d}x < \infty}\). This generalizes a previous result obtained by Sun and Zhang (Calc Var Partial Differ Equ 49:909–922, 2014) who considered the case \({p=2}\).

Analytical solution of the two-dimensional integral equations are usually difficult. In many cases, approximate solutions are required. In this paper, we study the approximate solution for two-dimensional Fredholm integral equations of the first kind by two-dimensional wavelet. First, definition and the properties of one-dimensional Franklin wavelet must be presented. Next, integral equations converted via regularization method into the second kind, then, using the idea of wavelet Galerkin method, we will find an approximate solution. Finally, the convergence and efficiency of this method will be discussed with some examples which indicate the ability and accuracy of the method.

In this paper, we consider boundary value problems for impulsive fractional differential equations containing left and right Riemann–Liouville fractional integral operators. Variational structure for these problems are established in a proper fractional derivative space, which can be regarded as a novelty item. Some sufficient conditions for the existence of solutions to this boundary value problem for nonlinear impulsive fractional differential equations are established by applying critical point theorems and some skills of inequalities. Finally, two examples are presented to show the feasibility and effectiveness of our results.

In this paper, by constructing a cone K 1 × K 2 in the Cartesian product space C[0, 1] × C[0, 1], and using spectral analysis of the relevant linear operator for the corresponding differential system, some properties of the first eigenvalue corresponding to the relevant linear operator are obtained, and the fixed-point index of nonlinear operator in the K 1 × K 2 is calculated explicitly and the existence of at least one positive solution or two positive solutions of the singular differential system with integral boundary conditions is established.

In this paper, we consider a nonhomogeneous singular elliptic equation involving a critical Caffarelli–Kohn–Nirenberg exponent. Using Ekeland’s Variational Principle, the Mountain Pass Lemma and the Nehari manifold, we establish the existence of at least two solutions.

In this paper, we introduce and study a new fractional operator and its implications in terms of the Ruscheweyh derivative operator, the Salagean operator and a certain fractional differintegral operator. Some geometric properties of the analytic functions involving this operator are derived. We also consider some applications and derive certain corollaries of our main results. Some useful consequences and relationship of certain results with known results are also pointed out.

In this paper we study the invariant metrizability and projective metrizability problems for the special case of the geodesic spray associated to the canonical connection of a Lie group. We prove that such canonical spray is projectively Finsler metrizable if and only if it is Riemann metrizable. This result means that this structure is rigid in the sense that considering left-invariant metrics, the potentially much larger class of projective Finsler metrizable canonical sprays, corresponding to Lie groups, coincides with the class of Riemann metrizable canonical sprays. Generalisation of these results for geodesic orbit spaces are given., final version, accepted by MJOM

Our aim in this paper was to study the well-posedness and the dissipativity of higher-order anisotropic phase-field systems. More precisely, we prove the existence and uniqueness of solutions and the existence of the global attractor.

In this paper, we apply quartic B-splines properly to study a new approximation method for numerical solutions and numerical derivatives for a class of non-linear fifth-order boundary value problems. Their analytic solutions and any-order derivatives are well approximated with $${O(h^{6})}$$ errors. Numerical tests are performed and numerical results show that our new method is very practical and effective.

This paper deals with existence and uniqueness of solutions for several boundary value problems of fractional differential equations with p-Laplacian operator using fixed-point theorems in cone and coincidence degree theory. The main results enrich and extend some existing literatures. Some examples are given to illustrate our main results.

In this paper, we consider equitorsion third type almost geodesic mappings of non-symmetric affine connection spaces. Applying different computational methods, we find invariants of these mappings obtained from curvature tensors of a corresponding non-symmetric affine connection space. Weyl projective tensor of a symmetric affine connection space is generalized in this way for the case of a third type almost geodesic mapping.

A Mann-type iterative scheme which converges strongly to a fixed point of a multi-valued nonexpansive non-self mapping T is constructed in a real Hilbert space H. We also constructed a Mann-type sequence which converges to a fixed point of a multi-valued quasi-nonexpansive non-self mapping under appropriate conditions. In addition, an Ishikawa-type iterative scheme which approximates the fixed points of multi-valued Lipschitz pseudocontractive non-self mappings is constructed in Banach spaces. The results obtained in this paper improve and extend the known results in the literature.

This paper is devoted to study a class of fractional equations with critical exponent, concave nonlinearity and sign-changing weight functions. By means of variational methods, the multiplicity of the positive solutions to this problem is obtained.

In this paper, we prove an analog of Younis’s result [Int J Math Math Sci 9(2): 301–312 1986, Theorem 5.2] on the image under the Fourier–Helgason transform of a set of functions satisfying the Dini–Lipschitz functions in \({L^{p} (1 < p \leq 2)}\) for functions on noncompact rank 1 Riemannian symmetric spaces.

In this paper, we demonstrate under some general assumptions, that a generator of any uniformly bounded composition operator, mapping spaces of bounded variation (Waterman) functions into other spaces of this type, must be an affine function in the functional variable.

In this paper, we study B-Fredholm spectral properties of an invertible closed linear operator in relation with the B-Fredholm spectral properties of its bounded inverse. Precisely, for such operator, we characterize its B-Fredholm spectrum and other related spectra in terms of the corresponding spectra of its bounded inverse. As an application, we show that every normal operator with nonempty resolvent set, in particular self-adjoint Schrodinger operators, satisfies generalized Weyl’s theorem.

Let X, Y be compact Hausdorff spaces and A, B be subspaces of C(X) and C(Y), respectively, containing the constant functions such that B is point separating and the evaluation functionals are linearly independent on B. In this paper, we give the general form of a surjective, not assumed to be linear, diameter preserving map \({T:A \longrightarrow B}\) for the case where A is dense in C(X). Fixing a point \({x_1\in X}\), we show that there exist a subset \({Y_0}\) of Y, a scalar \({\beta\in \mathbb{T}}\), a bijective continuous map \({\Psi: Y_0 \longrightarrow X}\) and a constant function \({\alpha: Y_0 \longrightarrow \{-1,1\}}\) such that $$\begin{aligned}T_{1} f(y) - T_{1} f(y_{1}) = & \beta ({\rm Re} (f(\Psi(y)) - f(\Psi(y_{1}))) \\ & + \alpha(y) i {\rm Im} (f(\Psi(y)) - f(\Psi(y_{1}))))\end{aligned}$$ for all \({f\in A}\) and \({y\in Y_0}\), where \({T_1=T-T0}\) and \({\Psi(y_1)=x_1}\). In particular, either $$T_1(f)(y)=\beta f(\Psi(y))+L(f) \qquad (f\in A,y\in Y_0),$$ or $$T_1(f)(y)=\beta \overline{f(\Psi(y))}+L(f) \qquad (f\in A, y\in Y_0),$$ holds for some functional L on A, which is linear (resp. real-linear) whenever T is so.

In this paper, we illustrate the Hermite–Hadamard inequality for convex and strongly convex functions defined on hemispheres. A version of Ostrowski’s type inequality for Lipschitz functions is also given.

[EN] Semilocal convergence for an iteration of order five for solving nonlinear equations in Banach spaces is established under second-order Fr,chet derivative satisfying the Lipschitz condition. It is done by deriving a number of recurrence relations. A theorem for the existence-uniqueness along with the estimation of error bounds of the solution is established. Its R-order is shown to be equal to five. Both efficiency and computational efficiency indices are given. A variety of examples are worked out to show its applicability. In comparison to existing methods having similar R-orders, improved results in terms of computational efficiency index and error bounds are found using our methodology., The authors thank the referees for their valuable comments which have improved the presentation of the paper. The authors thankfully acknowledge the financial assistance provided by Council of Scientific and Industrial Research (CSIR), New Delhi, India.

This paper deals with the summability of conjugate Laplace series. In particular, the Abel summability is proved and an integral representation of the relevant sum is given.

The fractal interpolation function (FIF) is a special type of continuous function on a compact subset of $${\mathbb{R}}$$ interpolating a given data set. They have been proved to be a very important tool in the study of irregular curves arising from financial series, electrocardiograms and bioelectric recording in general as an alternative to the classical methods. It is well known that Jacobi polynomials form an orthonormal system in $${\mathcal{L}^{2}(-1,1)}$$ with respect to the weight function $${\rho^{(r,s)}(x)=(1-x)^{r} (1+x)^{s}}$$ , $${r > -1}$$ and $${s > -1}$$ . In this paper, a fractal Jacobi system which is fractal analogous of Jacobi polynomials is defined. The Weierstrass type theorem providing an approximation for square integrable function in terms of $${\alpha}$$ -fractal Jacobi sum is derived. A fractal basis for the space of weighted square integrable functions $${\mathcal{L}_{\rho}^{2}(-1,1)}$$ is found. The Fourier–Jacobi expansion corresponding to an affine FIF (AFIF) interpolating certain data set is considered and its convergence in uniform norm and weighted-mean square norm is established. The closeness of the original function to the Fourier–Jacobi expansion of the AFIF is proved for certain scale vector. Finally, the Fourier–Jacobi expansion corresponding to a non-affine smooth FIF interpolating certain data set is considered and its convergence in uniform norm and weighted-mean square norm is investigated as well.

In this note, we deal with semilinear integro-differential equations subject to homogeneous Dirichlet boundary conditions given on the boundaries of the sections. Even if the differentiation will be taken only in some directions, it is not possible to see the main problem parameterized by the other coordinates because of the non-local terms which also obliged the problem to be degenerate. We establish the existence of solutions by employing the singular perturbations method as a natural tool. The perturbed problems are classical, non-local, semilinear elliptic problems and the limits of the subsequences of their solutions, in weighted Sobolev type spaces, are solutions of the main problem. Some improvement, concerning the existence of the solutions and the convergence results depending on the weights, will be established. The paper also gives an idea about the study of the anisotropic singular perturbations in the framework of weighted spaces.

In this paper, we study bifurcation of positive solutions for a nonlocal problem in a bounded domain. Using the degree argument and variational method, we obtain two results about bifurcation of positive solutions.

Physical parameters in dimensionless form in the governing equations of real-life phenomena naturally occur. How to control them by determining their range of validity is in general a big issue. In this paper, a mathematical approach is presented to identify the correct range of physical parameters adopting the recently popular analytic approximate Adomian decomposition method (ADM). Having found the approximate analytical Adomian series solution up to a specified truncation order, the squared residual error formula is employed to work out the threshold and the existence domain of certain physical parameters satisfying a preassigned tolerance. If the current procedure is not closely pursued, the presented results with the ADM may not be up to the desired level of accuracy (the worst is the divergent physically meaningless solutions), or much more ADM series terms need to be computed to satisfy certain accuracy. Examples reveal the necessity of the present approach to make sure that the results embark the correct range of physical parameters in the study of a physical problem containing several dominating parameters.

Perov used the concept of vector valued metric space and obtained a Banach type fixed point theorem on such a complete generalized metric space. In this article, we study fixed point results for the new extensions of sequence of Ciric generalized contractions on cone metric space, and we give some generalized versions of the fixed point theorem of Perov. The theory is illustrated with some examples. It is worth mentioning that the main result in this paper could not be derived from Ciric’s result by the scalarization method, and hence indeed improves many recent results in cone metric spaces.

In this paper, we study the structure of $${\Delta_{m}(T)}$$ defined by the following: $${\Delta_m(T):=\sum_{j=0}^{m}(-1)^{m-j} \begin{pmatrix} m \cr j \end{pmatrix}{T^{\ast}}^{j}C{T}^{m-j}C}$$ . In particular, we prove that if $${m}$$ is even, then $${\Delta_m(T)}$$ is complex symmetric with the conjugation $${C}$$ , and if $${m}$$ is odd, then $${\Delta_m(T)}$$ is skew complex symmetric with the conjugation $${C}$$ . Moreover, we investigate the conditions for ( $${m+1}$$ )-complex symmetric operators to be $${m}$$ -complex symmetric operators and characterize the spectrum of $${\Delta_m(T)}$$ . Finally, we show that if $${T\in{\mathcal L({\mathcal H})}}$$ is Hermitian or $${\Delta_1(T)}$$ is $${p}$$ -hyponormal, then $${\Delta_2(T)=0}$$ implies $${\Delta_1(T)=0}$$ .

In this paper, our aim is to establish optimal upper estimates for the first positive eigenvalue of a Jacobi type operator, which is a suitable extension of the linearized operators of the higher order mean curvatures of a closed hypersurface immersed either in spherical or in hyperbolical spaces.

In this paper, we show that weak Hopf (co)quasigroups can be characterized by a Galois-type condition. Taking into account that this notion generalizes the ones of Hopf (co)quasigroup and weak Hopf algebra, we obtain as a consequence the first fundamental theorem for Hopf (co)quasigroups and a characterization of weak Hopf algebras in terms of bijectivity of a Galois-type morphism (also called fusion morphism).

In this paper, we study the existence of infinitely many homoclinic solutions of the perturbed second-order Hamiltonian system $$-\ddot{u}(t)+L(t)u=W_u(t,u(t))+G_u(t,u(t)),$$ where $${L(t)}$$ and $${W(t,u)}$$ are neither autonomous nor periodic in $${t}$$ . Under the assumptions that $${W(t,u)}$$ is indefinite in sign and only locally superquadratic as $${|u|\to +\infty}$$ and $${G(t,u)}$$ is not even in $${u}$$ , we prove the existence of infinitely many homoclinic solutions in spite of the lack of the symmetry of this problem by Bolle’s perturbation method in critical point theory. Our results generalize some known results and are even new in the symmetric case.

Recently Cvetkovic and Rakocevic (Appl Math Comput 235:712-722, 2014) obtained some fixed point results of quasi-contraction of Perov type in the setup of cone metric spaces. We prove a coincidence and common fixed point results of two pairs of mappings satisfying generalized Ciric contractive condition in cone metric space without appealing to the normality condition of the cone and without exploiting the notion of continuity of any map involved therein. We also obtain common fixed point results of Hardy–Roger’s type mappings. We present some remarks and examples to show that our results provide extension as well as substantial generalizations and improvements of several well known results in the existing comparable literature. It is worth mentioning that the main result in this paper could not be derived from Ciric’s result by the scalarization method, and hence indeed improves many recent results in cone metric spaces.

In the present paper, we consider the fractional p-Laplacian equation $$(-\Delta)_{p}^{s}u + V(x)|u|^{p-2}u = f(x, u),\quad \forall \in R^{N},$$ (1.1) where \({p \geq 2, N \geq 2}\), \({0 < s < 1}\), \({V \in C(R^N, R)}\) and \({f \in C(R^N \times R, R)}\) are allowed to be sign-changing. In such a double sign-changing case, a new result on the existence of nontrivial solutions for Eq. (1.1) is obtained via variational methods, which is even new for p = 2.

In this paper, using variational methods and critical point theory, we study the existence of ground-state solutions for the following nonlinear Schrodinger–Maxwell equations $$\left\{\begin{array}{l@{\quad}l} -\triangle u + V(x)u + \phi u = f(x, u), & {\rm in}\, \mathbb{R}^{3},\\ -\triangle\phi = 4\pi u^{2}, & {\rm in} \, \mathbb{R}^{3},\end{array}\right. $$ (NSM) where f is asymptotically cubic, V 1-periodic in each of \({x_1, x_2, x_3}\) and \({\underline{V}:= {\rm inf}_{x\in\mathbb{R}^3}V(x) > 0}\). Under some more assumptions on V and f, we develop a direct and simple method to find ground-state solutions for \({(\mathrm{NSM})}\). The main idea is to find a minimizing (PS) sequence for the energy functional outside the Nehari manifold \({\mathcal{N}}\) using the diagonal method. This seems to be the first result for \({(\mathrm{NSM})}\) satisfying the assumptions (V) and (N).

In this paper, we prove several Harnack estimates for positive solutions to the heat-type equations with respect to time-dependent Riemannian metric evolving by the geometric flow. In particular, we obtain Li–Yau type estimates and Perelman type differential Harnack inequalities and as an application, we demonstrate how these results can be obtained under various geometric flows.

Our aim in this paper is to deal with the boundedness of the Hardy–Littlewood maximal operator on non-homogeneous central Musielak–Orlicz–Morrey spaces. Further, we give Sobolev’s inequality for generalized Riesz potentials.

In this paper, we estimate the rate of convergence on function of bounded variation for a Kantorovich variant of a generalization of Szasz operators involving Brenke-type polynomials by means of some methods and techniques of probability theory.

In this paper, we discuss existence results for the nonlinear boundary value problem (1.1)–(1.2) on \({L^{1}}\)-spaces. This problem was already considered in Latrach and Zeghal (J Appl Math Comp 219:1163–1172, 2012) under the hypothesis that the velocity space has finite measure. This condition was used to establish a compactness result necessary to use fixed point theorems. In this work we show that this hypothesis is not necessary and it can be relaxed. Our analysis uses a new measure of weak noncompactness adapted to the problem, the concept of Dunford–Pettis operators and a new version of Darbo’s fixed point theorem.