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In this paper, we present some fixed point theorems of Krasnosel’skii’s type in Banach spaces. The involved operators need not to be compact nor weakly continuous. The results are obtained and formulated with the use of the measures of weak noncompactness and a large classes of contractions (strict contractions, nonlinear contractions, as well as nonexpansive or pseudocontractive mappings). Throughout the paper, we use the hypothesis $$\mathsf {(H1)}$$ and $$\mathsf {(H2)}$$ , which are one of the main ingredients of the proofs. Finally, with the obtained fixed point results, we discuss the existence of solutions to a stationary transport equation with delayed neutrons.

In the present paper, we investigate the existence and regularity of weak solutions for $$\psi $$ -Hilfer fractional boundary value problem in $$\mathbb {C}^{\alpha ,\beta ;\psi }_{2}$$ and $$\mathcal {H}$$ (Hilbert space) spaces, using extension of the Lax–Milgram theorem. In this sense, to finalize the paper, we discuss the integration by parts for $$\psi $$ -Riemann–Liouville fractional integral and $$\psi $$ -Hilfer fractional derivative.

The goal of this paper is to prove the boundedness of fundamental integral operators of Harmonic Analysis in generalized weighted grand Lebesgue spaces $$L^{p),\varphi }_w$$ defined on domains in $${\mathbb {R}}^n$$ without assuming that the underlying measure $$\mu $$ is doubling. Operators under consideration involve maximal and Calderon–Zygmund operators, also commutators of singular integrals with BMO functions. Essential part of this paper is devoted to the weighted Sobolev-type inequalities in these spaces for fractional integrals with non-doubling measures satisfying the growth condition. We discuss the case when a weight function defines the absolute continuous measure of integration, or plays the role of multiplier in the definition of the norm. All these results are new even for the classical weighted grand Lebesgue spaces $$L^{p),\theta }_w$$ defined with respect to non-doubling measures. The results are obtained under the Muckenhoupt condition on weights. The results are obtained for weight functions satisfying Muckenhoupt $$A_p$$ conditions defined with respect to non-homogeneous spaces.

In this paper, we introduce a new class of curves that we call helical extension curve in Euclidean space. Then we investigate the differential geometric properties of the helical extension curves. The main result of the paper is that the helical extension curve of a helix is a plane curve. Moreover, we give several simple characterizations of helical extension curve of special curves such as spherical curve.

The aim of this paper is to study the existence of solutions for critical Schrodinger–Kirchhoff-type problems involving a nonlocal integro-differential operator with potential vanishing at infinity. As a particular case, we consider the following fractional problem: $$\begin{aligned}&M\left( \iint _{{\mathbb {R}}^{2N}}\frac{|u(x)-u(y)|^{p}}{|x-y|^{N+sp}}\mathrm{dxdy}+\int _{{\mathbb {R}}^N}V(x)|u(x)|^{p}\mathrm{{d}}x\right) ((-\Delta )_p^{s}u(x)+V(x)|u|^{p-2}u)\\&\quad =K(x)(\lambda f(x,u)+|u|^{p_s^{*}-2}u), \end{aligned}$$ where $$M:[0, \infty )\rightarrow [0, \infty )$$ is a continuous function, $$(-\Delta )_p^{s}$$ is the fractional p-Laplacian, $$00$$ is a real parameter. Using the mountain pass theorem, we obtain the existence of the above problem in suitable space W. For this, we first study the properties of the embedding from W into $$L_{K}^{\alpha }({\mathbb {R}}^N), \alpha \in [p, p_s^{*}].$$ Then, we obtain the differentiability of energy functional with some suitable conditions on f. To the best of our knowledge, this is the first existence results for degenerate Kirchhoff-type problems involving the fractional p-Laplacian with potential vanishing at infinity. Finally, we fill some gaps of papers of do O et al. (Commun Contemp Math 18: 150063, 2016) and Li et al. (Mediterr J Math 14: 80, 2017).

This paper is concerned with a Delsarte-type extremal problem. Denote by$${\mathcal {P}}(G)$$P(G)the set of positive definite continuous functions on a locally compact abelian groupG. We consider the function class, which was originally introduced by Gorbachev,$$\begin{aligned}&{\mathcal {G}}(W, Q)_G = \left\{ f \in {\mathcal {P}}(G) \cap L^1(G)~:\right. \\&\qquad \qquad \qquad \qquad \qquad \left. f(0) = 1, ~ {\text {supp}}{f_+} \subseteq W,~ {\text {supp}}{\widehat{f}} \subseteq Q \right\} \end{aligned}$$G(W,Q)G=f∈P(G)∩L1(G):f(0)=1,suppf+⊆W,suppf^⊆Qwhere$$W\subseteq G$$W⊆Gis closed and of finite Haar measure and$$Q\subseteq {\widehat{G}}$$Q⊆G^is compact. We also consider the related Delsarte-type problem of finding the extremal quantity$$\begin{aligned} {\mathcal {D}}(W,Q)_G = \sup \left\{ \int _{G} f(g) \mathrm{d}\lambda _G(g) ~ : ~ f \in {\mathcal {G}}(W,Q)_G\right\} . \end{aligned}$$D(W,Q)G=sup∫Gf(g)dλG(g):f∈G(W,Q)G.The main objective of the current paper is to prove the existence of an extremal function for the Delsarte-type extremal problem$${\mathcal {D}}(W,Q)_G$$D(W,Q)G. The existence of the extremal function has recently been established by Berdysheva and Révész in the most immediate case where$$G={\mathbb {R}}^d$$G=Rd. So, the novelty here is that we consider the problem in the general setting of locally compact abelian groups. In this way, our result provides a far reaching generalization of the former work of Berdysheva and Révész.

In the present paper, we define generalized skew semi-invariant submersion and give an example for such submersions. Necessary and sufficient conditions are given to obtain the integrability and totally geodesicness of the distributions, which are mentioned in the definition of generalized skew semi-invariant submersion. The geometry of the fibers is investigated. At the end of the paper, the generalized skew semi-invariant submersion is considered with parallel canonical structures and some results are obtained.

An elegant full characterization of reflexive line graphs of trees has proved to be quite difficult task. This paper tries to shed some more light on known results about such graphs by providing more numerical details regarding their structural composition. The paper also presents numerous results and ideas on the topic, as well as some observations with respect to the connection with Salem numbers.

In this paper, we study the Cauchy problem to a class of non-autonomous evolution equations of parabolic type with non-instantaneous impulses in Banach spaces, where the operators in linear part (possibly unbounded) depend on time t and generate an evolution family. New existence result of piecewise continuous mild solutions is established under more weaker conditions. At last, as a sample of application, the abstract result is applied to a class of non-autonomous partial differential equation of parabolic type with non-instantaneous impulses. The result obtained in this paper is a supplement to the existing literature and essentially extends some existing results in this area.

In this paper we provide an abstract aproach to the study of classes of multiple summing multilinear operators between Banach spaces. The main purpose is unify the study of several known classes and results, for example multiple $(p, q_1,\dots, q_n)$-summing operators, multiple mixing $(s, q, p)$-summing operators and multiple strong $(s, q, p)$-mixing summing operators. We also define new class of multiple summing multilinear operator that are particular cases of our construction and, therefore, satisfy the results proved in the paper., Comment: 19 pages

This paper continues the ongoing effort to study the structure of the set of nilpotent elements in noncommutative ring constructions. Let R be any ring, $${(S,\leq)}$$ a strictly (partially) ordered monoid and also $${\omega:S\rightarrow}$$ End(R) a monoid homomorphism. A skew generalized power series ring $${R[[{S,\omega\leq}}]]$$ consists of all functions from a monoid S to a coefficient ring R, whose support contains neither infinite descending chains nor infinite antichains, with pointwise addition, and with multiplication given by convolution twisted by an action $${\omega}$$ of the monoid S on the ring R. Our studies in this paper is strongly connected to the question of whether or not a skew generalized power series ring $${R[[{S,\omega\leq}}]]$$ over a nil coefficient ring R is nil, which is related to the famous question of Amitsur. However, we show that under mild “Armendariz-like” hypothesis on a coefficient ring R, we obtain stronger conditions on the coefficients of elements of a skew generalized power series ring $${R[[{S,\omega\leq}}]]$$ . We will also explore some annihilator conditions in the skew generalized power series ring setting, unifying and generalizing a number of known Armendariz-like and McCoy-like conditions in the special cases.

[EN] In this paper, we deal with uncertainty quantification for the random Legendre differential equation, with input coefficient A and initial conditions X-0 and X-1. In a previous study (Calbo et al. in Comput Math Appl 61(9):2782-2792, 2011), a mean square convergent power series solution on (-1/e, 1/e) was constructed, under the assumptions of mean fourth integrability of X-0 and X-1, independence, and at most exponential growth of the absolute moments of A. In this paper, we relax these conditions to construct an L-p solution (1, This work has been supported by the Spanish Ministerio de Economia y Competitividad Grant MTM2017-89664-P. Marc Jornet acknowledges the doctorate scholarship granted by Programa de Ayudas de Investigacion y Desarrollo (PAID), Universitat Politecnica de Valencia.

In this paper, we investigate an existence and uniqueness theorem of the solution to a class of nonlinear nabla fractional difference system with a time delay. More precisely, observing $$\nu (t-k)^{\overline{\nu -1}}\le {t^{\bar{\nu }}}$$ , we get the evaluation of $$\nabla _{a+k}^{-\nu } ||z(t-k)||$$ , which allows us to apply the generalized Gronwall’s inequality for the solutions of nonlinear nabla fractional difference system. The theorems we establish fill the gaps in some existing papers.

We relax the conditions $$\underset{1}{\nabla }F=0$$ and $$\underset{2}{\nabla }F=0$$ with respect to the non-symmetric linear connections $$\underset{1}{\nabla }$$ and $$\underset{2}{\nabla }$$ and an almost complex structure F of a generalized Kahler space. In such a way we introduce a wider class of generalized Kahler spaces which admits a holomorphically projective mapping. These generalized Kahler spaces are named generalized Kahler spaces in Eisenhart’s sense, since they are defined as a particular case of Eisenhart’s generalized Riemannian spaces. Curvature tensors of generalized Kahler spaces in Eisenhart’s sense have some interesting properties that have been pointed out in the present paper. Also, we consider equitorsion holomorphically projective mappings and examine some invariant geometric objects with respect to these mappings. Our results are deduced without restrictive conditions that were given in some of the previous papers.

In this paper, we develop a projection-type algorithm for set-valued variational inequalities on Hadamard manifolds. The proposed method is well defined whether the solution set of the problem is non-empty or not. Under pseudomonotonicity assumptions on the underlying vector field, our method is convergent to a solution of the given set-valued variational inequality. The results presented in this paper generalize and improve some known results introduced by Tang et al. (Optimization 64(5):1081–1096, 2015).

In this paper, we show that a generalized Sasakian space form of dimension >3 is either of constant sectional curvature, or a canal hypersurface in Euclidean or Minkowski spaces, or locally a certain type of twisted product of a real line and a flat almost Hermitian manifold, or locally a warped product of a real line and a generalized complex space form, or an $${\alpha}$$ -Sasakian space form, or it is of five dimension and admits an $${\alpha}$$ -Sasakian Einstein structure. In particular, a local classification for generalized Sasakian space forms of dimension >5 is obtained. A local classification of Riemannian manifolds of quasi constant sectional curvature of dimension >3 is also given in this paper.

In this paper, the authors prove that the solution blows up in a finite time for a larger class of initial data, namely positive initial energy. The results generalize and improve that of Giacomoni et al. (J Math Anal Appl 410:607–624, 2014). Furthermore, a lower bound estimate about blow-up time is also established. Finally, two examples are given in the paper to show the existence of the initial datum satisfying the conditions in the main theorem.

We introduce here the notion of conformal semi-Riemannian map between semi-Riemannian manifolds aiming to unify and generalize two geometric concepts. The first one is studied by Garcia-Rio and Kupeli (namely, semi-Riemannian map between semi-Riemannian manifolds). The second notion is defined by Aahin (namely, conformal Riemannian map between Riemannian manifolds) as an extension of the notion of Riemannian map introduced by Fischer. We support the main notion of this paper with several classes of examples, e.g. semi-Riemanninan submersions (see O'Neill's book and Falcitelli, Ianus and Pastore's book) and isometric immersions between semi-Riemannian manifolds. As a tool, we use the screen distributions (specific in semi-Riemannian geometry) of Duggal and Bejancu's book to obtain some characterizations and to give a semi-Riemannian version of Fischer's (resp. Aahin's) results, using the new map introduced here. We study the generalized eikonal equation and at the end relate the main notion of the paper with harmonicity.

This paper is devoted to introduce a numerical simulation with a theoretical study for flow of a Newtonian fluid over an impermeable stretching sheet which embedded in a porous medium with a power law surface velocity and variable thickness in the presence of thermal radiation. The flow is caused by a non-linear stretching of a sheet. Thermal conductivity of the fluid is assumed to vary linearly with temperature. The governing PDEs are transformed into a system of coupled non-linear ODEs which are using appropriate boundary conditions for various physical parameters. The proposed method is based on replacement of the unknown function by truncated series of well known shifted Legendre expansion of functions. An approximate formula of the integer derivative is introduced. Special attention is given to study the convergence analysis and derive an upper bound of the error of the presented approximate formula. The introduced method converts the proposed equation by means of collocation points to a system of algebraic equations with shifted Legendre coefficients. Thus, by solving this system of equations, the shifted Legendre coefficients are obtained. The effects of the porous parameter, the wall thickness parameter, the radiation parameter, thermal conductivity parameter and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin-friction and Nusselt numbers are presented. Comparison of obtained numerical results is made with previously published results in some special cases, and excellent agreement is noted. The results attained in this paper confirm the idea that proposed method is powerful mathematical tool and it can be applied to a large class of linear and nonlinear problems arising in different fields of science and engineering.

The present paper gives several subordination results involving a generalized Srivastava–Attiya operator (defined below). Among the results presented in this paper include also a sufficiency condition for the convexity of the convolution of certain functions and a sharp result relating to the convolution structure. We also mention various useful special cases of the main results including those which are related to the Zeta function.

In this paper, we introduce a subclass of analytic and bi-univalent functions in the open unit disk. Here, we give upper bound estimates for the second Hankel determinant of the functions that belong to this class. Some interesting applications and conclusions of the results obtained in this paper are also discussed.

Let $$(U(t))_ {t\ge 0}$$ be a strongly continuous semigroup of bounded linear operators on a Banach space X and B be a bounded operator on X. In this paper, we develop some aspects of the theory of semigroup for which U(t)B (respectively, BU(t), BU(t)B) is demicompact for some (respectively, every) $$t>0$$ . In addition, we study the demicompactness of similar, subspace and product semigroups. We also investigate the demicompactness of the resolvent. We close this paper by giving some conditions guaranteeing the demicompactness of a generator of a strongly continuous semigroup in a Hilbert space.

In this paper, we are interested in the following damped vibration system: where B is an antisymmetric $$N\times N$$ constant matrix, $$q:{\mathbb {R}}\longrightarrow {\mathbb {R}}$$ is a continuous function, $$L(t)\in C({\mathbb {R}},{\mathbb {R}}^{N^{2}})$$ is a symmetric matrix, and $$W(t,x)\in C^{1}({\mathbb {R}}\times {\mathbb {R}}^{N},{\mathbb {R}})$$ are neither autonomous nor periodic in t. The novelty of this paper is that, supposing that $$Q(t)=\int ^{t}_{0}q(s)\mathrm{d}s$$ is bounded from below and L(t) is coercive unnecessarily uniformly positively definite for all $$t\in {\mathbb {R}}$$ , we establish the existence of ground-state homoclinic solutions for (1) when the potential W(t, x) satisfies a kind of superquadratic conditions due to Ding and Luan for Schr $${\ddot{o}}$$ dinger equation. The main idea here lies in an application of a variant generalized weak linking theorem for strongly indefinite problem developed by Schechter and Zou. Some recent results in the literature are generalized and significantly improved.

The main purpose of the paper is the study of the total space of a holomorphic Lie algebroid E. The paper is structured in three parts. In the first section, we briefly introduce basic notions on holomorphic Lie algebroids. The local expressions are written and the complexified holomorphic bundle is introduced. The second section presents two approaches on the study of the geometry of the complex manifold E. The first part contains the study of the tangent bundle $$T_{\mathbb {C}}E=T'E\oplus T''E$$ and its link, via the tangent anchor map, with the complexified tangent bundle $$T_{\mathbb {C}}(T'M)=T'(T'M)\oplus T''(T'M)$$ . A holomorphic Lie algebroid structure is emphasized on $$T'E$$ . A special study is made for integral curves of a spray on $$T'E$$ . Theorem 2.8 gives the coefficients of a spray, called canonical, obtained from a complex Lagrangian on $$T'E$$ . In the second part of section two, we study the holomorphic prolongation $$\mathcal {T}'E$$ of the Lie algebroid E. In the third section, we study how a complex Lagrange (Finsler) structure on $$T'M$$ induces a Lagrangian structure on E. Three particular cases are analysed by the rank of the anchor map, the dimensions of manifold M, and those of the fibres. We obtain the correspondent on E of the Chern–Lagrange nonlinear connection from $$T'M$$ .

In this paper, we propose two classes of derivative-free Newton-like methods for solving system of nonlinear equations based on double Newton step. We also give the local convergence analysis of the iterative methods. In addition, some numerical results are also reported in the paper, which confirm the good theoretical properties of our approach.

In this paper, we present a new numerical method to solve fractional differential equations. Given a fractional derivative of arbitrary real order, we present an approximation formula for the fractional operator that involves integer-order derivatives only. With this, we can rewrite FDEs in terms of a classical one and then apply any known technique. With some examples, we show the accuracy of the method., Comment: This is a preprint of a paper whose final and definite form will be published in Mediterr. J. Math

This paper represents a continuation of Barboteu et al. (Analysis of a contact problem with unilateral constraint and slip-dependent friction, Math Mech Sol, 2015). There, a mathematical model which describes the frictional contact between an elastic body and a foundation was considered. The variational and numerical analysis of the problem was provided by considering a weak formulation in terms of displacements, the so-called primal variational formulation. The aim of the current paper is to study the problem using a weak formulation in terms of the stress, the so-called dual variational formulation. We start by presenting the model, the assumption on the data and some preliminary results. Then we state and prove an equivalence result, Theorem 4.1. We proceed with an existence and uniqueness results, Theorem 5.1. The proofs are based on arguments of monotonicity, convexity and lower semicontinuity.

In this paper, we investigate boundedness, polar decomposition and spectral decomposition of weighted conditional expectation type operators on \(L^2(\Sigma )\). Some examples are provided to illustrate concrete application of the main results of the paper.

The purpose of this paper is the presentation of an identity which is closely related to the sum relation involving multiple zeta star values with even arguments. Let $$E^{\star }(m,n,k)$$ be the sum of all multiple zeta star values of depth k and weight mn with arguments multiples of $$m\ge 2$$ . In this paper, we give two formulas for $$E^{\star }(2s,n,k)$$ for $$s=1,2,3$$ and in particular, by comparing the two we obtain a Bernoulli numbers identity. There are corresponding results included in a special kind of alternating multiple zeta values.

In this paper, we consider a Cauchy problem for nonlinear fractional differential equation with constant coefficient $$\lambda >0$$ of the type: $${^c}{D}^{\alpha }x(t)=\lambda x(t)+f(t,x(t))$$ with $$x(0)=x_{0}.$$ The aim of this paper is to investigate the existence and interval of existence of solutions, uniqueness, continuous dependence of solutions on initial conditions, estimates on solutions and continuous dependence on parameters and functions involved in the equations. Finally, one illustrative example is given to demonstrate the theoretical results.

In this paper, we prove that the density of the topology of uniform convergence d(C(X)) is equal to the density of the m-topology. For general topological spaces X, the density d(C(X)) is not known. In this paper we investigate the cardinal invariants of the m-topology on C(X), which is a classical topology. We prove that it behaves like a metric one in the sense that many cardinal invariants, including weight, cellularity and density, are equal for this topology. In fact, they are all equal to d(C(X)).

In this paper we introduce a general class of integral operators that fix exponential functions, containing several recent modified operators of Gauss–Weierstrass, or Picard or moment type operators. Pointwise convergence theorems are studied, using a Korovkin-type theorem and a Voronovskaja-type formula is obtained.

In symmetric cryptography, the round functions used as building blocks for iterated block ciphers are obtained as the composition of different layers acting as a sequence of bijective transformations providing global increasing complexity. The study of the conditions on such layers which make the group generated by the round functions of a block cipher a primitive group has been addressed in the past years, both in the case of Substitution Permutation Networks and Feistel Networks, giving to block cipher designers the recipe to avoid the imprimitivity attack, which exploits the invariance of some subspaces during the encryption. In the case of Lai–Massey schemes, where both Substitution Permutation Network and Feistel Network features are combined, the resistance against imprimitivity attacks has been a long-standing open problem. In this paper we consider a generalization of such a scheme and we prove its resistance against the imprimitivity attack. Our solution is obtained as a consequence of a more general result in which the problem of proving the primitivity of a generalized Lai–Massey scheme is reduced to the simpler one of proving the primitivity of the group generated by the round functions of a strictly related Substitution Permutation Network. We prove how this implies a reduction in the computational cost of invariant-subspace search.

In this paper, we give estimates for the essential norm of a weighted composition operator $$uC_\varphi $$ acting on the disk from general function spaces F(p, q, s) into Bloch-type spaces including $$\alpha $$ -Bloch spaces and logarithmic Bloch spaces.

Let f and g be two holomorphic curves of a ball $$\Delta (R)$$ into $${\mathbb {P}}^n({\mathbb {C}})$$ with finite growth index, and let $$H_1,\ldots ,H_{2n+2}$$ be $$2n+2$$ hyperplanes in general position. In this paper, our first purpose is to show that if f and g have the same inverse images for all $$H_i\ (1\le i\le 2n+2)$$ with multiplicities counted to level $$l_i$$ satisfying an explicitly estimate concerning $$c_f$$ and $$c_g$$ , then the map $$f\times g$$ into $${\mathbb {P}}^n({\mathbb {C}})\times {\mathbb {P}}^n({\mathbb {C}})$$ must be algebraically degenerated. Our second purpose is to prove that $$f=g$$ if they share $$2n+2$$ hyperplanes with some certain conditions (in particular, they share $$2n+2$$ hyperplanes with multiplicities counted to level $$n+1$$ ). Our results extend and improve the previous results for the case of holomorphic curve from $${\mathbb {C}}$$ on these directions.

This paper deals with the blow-up phenomenon of solutions to a reaction–diffusion equation with weighted nonlocal gradient absorption terms in a bounded domain. Based on the method of auxiliary function and the technique of modified differential inequality, we establish appropriate conditions on weight function and nonlinearities to guarantee the solution exists globally or blows up at finite time. Moreover, upper and lower bounds for blow-up time are derived under appropriate measure in higher dimensional spaces.

Many different types of fractional calculus have been defined, which may be categorised into broad classes according to their properties and behaviours. Two types that have been much studied in the literature are the Hadamard-type fractional calculus and tempered fractional calculus. This paper establishes a connection between these two definitions, writing one in terms of the other by making use of the theory of fractional calculus with respect to functions. By extending this connection in a natural way, a generalisation is developed which unifies several existing fractional operators: Riemann–Liouville, Caputo, classical Hadamard, Hadamard-type, tempered, and all these taken with respect to functions. The fundamental calculus of these generalised operators is established, including semigroup and reciprocal properties as well as application to some example functions. Function spaces are constructed in which the new operators are defined and bounded. Finally, some formulae are derived for fractional integration by parts with these operators.

The notions of r-Bell polynomials and their generalization, the r-Dowling polynomials are due to Mező and Cheon, Jung. Recently, Nyul and Rácz defined the r-Lah polynomials, which are close relatives of r-Bell polynomials. In the present paper, we introduce the Dowling type generalization of r-Lah polynomials, the r-Dowling–Lah polynomials. We give a comprehensive study of them using the results of the author and Nyul on r-Whitney–Lah numbers, which are the coefficients of these polynomials.

This paper is devoted to the study of the error estimates in the periodic homogenization of elliptic equations in divergence form with Dirichlet boundary conditions. We are interested in the application of a two-scale asymptotic expansions method. We present the error estimates of the third-order with and without boundary layers terms.

In this paper, an improved extrapolated collocation method with cubic B-spline as basis functions is presented. This method is applied to a class of self-adjoint singularly perturbed boundary value problems, with the equispaced discretization of the domain. As with the standard B-spline collocation method, the optimal order of convergence could not be achieved, so posteriori corrections are made in cubic B-spline interpolant and its higher-order derivatives. This results in the enhancement of order of convergence by several powers of step size ‘ $${\hat{h}}$$ ’. The proposed technique has $$O({\hat{h}}^{6})$$ convergence, which is established using Green’s function approach. A number of examples are solved numerically and the results are compared with the results available in the literature to illustrate the efficacy and reliability of the proposed numerical technique.

In this paper, we investigate the stability in the sense of Hyers–Ulam–Rassias for the two types of generalized fractional differential systems by the $$\rho $$ -Laplace transform method. Several examples are given to illustrate the theoretical results.

In this paper we classify commutative ring extensions with exactly two non Prufer domain intermediate rings. An initial step involves the description of the commutative ring extensions with only one non Prufer domain intermediate ring. Some generalizations to the context of rings with zero divisors are proved. We also answer a question which was left open in Jarboui and Aljubran (Ric Mat, https://doi.org/10.1007/s11587-020-00500-0 , 2020). More precisely, let $$S = K[y_1]]...[y_t]]$$ be a K-algebra (not necessarily finitely generated over the field K) having Krull dimension $$n \ge 1$$ . Let I be a nonzero proper ideal of S (not necessarily maximal in S) and D be a proper subring of K. We provide necessary and sufficient conditions in order that $$R = D + I$$ is a maximal non-integrally closed subring of S.

This paper discusses the abstract time-space fractional evolution equation with the Caputo derivative of order $$\alpha \in (0,1)$$ and fractional power operator $$-A^{\beta }$$ , $$\beta \in (0,1)$$ , where $$-A$$ generates a $$C_{0}$$ -semigroup on a Banach space. The compactness and exponential stability of the semigroup which is generated by fractional power operator $$-A^{\beta }$$ are investigated. With the aid of the properties of the semigroup, the existence and global asymptotic behavior of S-asymptotically periodic solutions are obtained by some fixed point theorems and related inequalities. An example to the time-space fractional diffusion equation with fractional Laplacian will be shown.

In this paper, we introduce a new conjugation $$C_{\xi }$$ on the weighted Hardy space $$H_{\rho }(\mathbb {D})$$ , where $$C_{\xi }$$ is given by (2.1) in Theorem 2.2. In particular, we prove that $$C_{\xi }$$ and $$C_{\mu ,\lambda }$$ are unitarily equivalent where $$C_{\mu ,\lambda }$$ is given in Ko and Lee (J Math Anal Appl 434:20–34, 2016). Using this, we investigate a complex symmetric Toeplitz operator $$T_{\varphi }$$ with respect to the conjugation $$C_{\xi }$$ on the weighted Hardy space $$H_{\rho }(\mathbb {D})$$ . Finally, we consider $$C_{\mu ,\lambda }$$ -invariant of Berezin transform.

In this paper, we introduce a new class of operators: absolute-(k, m) paranormal operators. We will show basic structural properties and some spectral properties of this class of operators. We will be studying the conditions under which composition operators and weighted composition operators on $$L^{2}(\mu )$$ spaces become absolute-(k, m)-paranormal operators and absolute- $$(k^{*},m)$$ -paranormal operators, in terms of Radon–Nikodym derivative $$h_{m}.$$ Some necessary and sufficient conditions for a composition operator $$C_{\phi }$$ on Fock Spaces to be an absolute-(1, m)-paranormal operators and absolute- $$(1^{*},m)$$ -paranormal operators have also been explored.

In this paper, we are concerned in establishing properties about the function $$\vartheta $$ and versions of the classical Keller–Osserman condition to prove existence of solutions to the Schrodinger quasilinear elliptic problem $$\begin{aligned} \left\{ \begin{array}{l} \displaystyle \mathrm{div}\left( \vartheta (u)\nabla u\right) -\frac{1}{2}\vartheta '(u)|\nabla u|^2=a(x)g(u)~ \text{ in }~ \Omega ,\\ u\ge 0\ \text{ in }~\Omega ,\ u(x){\mathop {\longrightarrow }\limits ^{d(x)\rightarrow 0}} \infty , \end{array} \right. \end{aligned}$$ where $$\Omega \subset {\mathbb {R}}^N$$ , with $$N\ge 3$$ , is a bounded domain, $$a:{\bar{\Omega }} \rightarrow [0,\infty )$$ and $$g:[0,\infty ) \rightarrow [0,\infty )$$ are suitable nonnegative continuous functions, $$\vartheta :{\mathbb {R}}\rightarrow (0,\infty )$$ is a $$C^1$$ -function satisfying appropriated hypotheses, and $$d(x)=\mathrm{dist}(x,\partial \Omega )$$ stands for the distance function to the boundary of $$\Omega $$ . By exploring a dual approach and the relationship among the properties of $$\vartheta $$ with its corresponding Keller–Osserman condition, we were able to show existence of solutions for this problem.

An iterative method generates a sequence associated with an equation, that, under appropriate conditions, converges to a solution of that equation. A perturbation of the equation produces also a perturbation of the sequence. In this paper, we study the Ulam stability (the behavior of the solutions of the perturbed equation with respect to the solutions of the exact equation) of an operatorial equation of the form $$x_{n+1}=T_nx_n+a_n$$ , where $$T_n:X \rightarrow X$$ , $$n \in \mathbb {N}$$ , are linear and bounded operators acting on a Banach space X. As applications we obtain some stability results for the case of Volterra, Fredholm and Gram–Schmidt operators. In this way, we improve and complement some results on this topic.

This paper is devoted to the following p-Kirchhoff type of problems: $$\begin{aligned} \left\{ \begin{array}{ll} -(a+b\int _{\Omega }|\nabla u|^{p}\,\text{ d }x)\Delta _{p} u=-\lambda |u|^{q-2}u+f(x,u),x\in \Omega \\ u=0,x\in \partial \Omega . \end{array} \right. \end{aligned}$$ Without assuming the standard subcritical polynomial growth condition ensuring the compactness of a bounded (P.S.) sequence, we show that the Dirichlet boundary value problem has at least a weak nontrivial solution by using Morse theory.

In this paper, we study the regularity of $$\log (\partial \phi )$$ when $$\phi $$ is the principal solution of the homogeneous Beltrami equation and the coefficient $$\mu $$ has compact support and is in the Sobolev space $$W^{1,p}_c({\mathbb {C}})$$ with $$1

A nonzero element a in a unital ring R is called unit fine if there is a unit u in R such that ua is fine (i.e. a sum of a unit and a nilpotent). A ring all whose elements are unit fine is called accordingly. This turns out to be a new class of simple rings, including the class of fine rings (and so the class of simple Artinian rings). The paper studies unit fine elements and rings. For rings such that 1 is a sum of two units, it is proved that matrix rings over unit fine rings, are unit fine.