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This paper is devoted to the proof of an equilibrium existence theorem in incomplete markets, concerning the one-period economy with a finite number states of the world. The proof of the main theorem relies on the Brouwer Fixed Point Theorem. The assumption of incomplete markets is crucial for the proof of the main theorem, since the pricing functionals’-space is not one-dimensional. Usually, in General Equilibrium Theory of Incomplete Markets, the utility functions of the consumers -investors are supposed to be smooth-regular. In the present paper, we assume that the utility functions are continuous and the risk-less asset is extremely desirable. This class of utility functions assures that the demand vector is well-defined and unique, as well. The interest of economists about the effect of perturbation of pricing functionals on the existence of equilibrium is satisfied by the reference on the pricing functionals’ dimension. The equilibrium allocation uniqueness is not deduced by the Brouwer Fixed Point Theorem. We also notice that the existence of equilibrium may be deduced in the corresponding multi-period model by using the corresponding event-tree.

In Ruscheweyh and Salinas (Math Z 263:607–617, 2009) and Ruscheweyh et al. (Isreal J Math 171:285–304, 2009) the researchers introduced universally convex,universally starlike and universally prestarlike functions in the slit domain $$ {\mathbb {C}}\backslash [1,\infty {)}.$$ These papers extended the corresponding notions from the unit disc to other discs and half-planes containing the origin. In this paper, we consider universally prestarlike generalized functions of order $$\alpha $$ with $$\alpha \le 1$$ and we obtain upper bounds of the second Hankel determinant $$|a_{2}a_{4}-a_{3}^{2}|$$ for such functions related with exponential function.

The purpose of this paper is to introduce the Picard–Ishikawa hybrid iterative process. This new iterative process can be seen as a hybrid of Picard and Ishikawa iterative processes. It is our purpose in this paper to show that this new hybrid iterative process converges faster than all of Picard, Krasnoselskii, Mann, Ishikawa, Noor, Picard–Mann and Picard–Krasnoselskii iterative processes in the sense of Berinde (Iterative Approximation of Fixed Points. Efemeride, Baia Mare, 2002). We establish data dependence and stability results for our newly developed iterative process. Moreover, we apply our newly developed iterative process in finding the solution of delay differential equations.

In this paper, we first prove existence of fixed points for Berinde nonexpansive multivalued mappings on Banach spaces. Moreover, we obtain convergence theorems for common fixed point of Berinde and quasi-nonexpansive mappings. The main results obtained in this paper extened and generalize some of the well-known results in the literature.

Many problems in science and engineering involve nonlinear PDEs which are posed on the real line ( $${\mathbb {R}}$$ ). Particular examples include a number of important nonlinear wave equations. A rigorous numerical analysis of such problems is especially challenging due to the spatial discretization of the nonlinear operators involved in the models. Classically, such problems have been treated using Fourier pseudo-spectral methods by truncating the spatial domain and imposing periodic boundary conditions. Unfortunately, in many cases this approach may not be appropriate to adequately capture the dynamics of the problem on the spatial domain. In this paper, we consider a Chebyshev-type pseudo-spectral method based on the algebraically mapped Chebyshev basis defined in $${\mathbb {R}}$$ . The approximation properties of this basis are naturally described on the scale of weighted Bessel potential spaces and lead to optimal error estimates for the method. Based on these estimates an efficient spectral scheme for solving the nonlinear Korteweg-de Vries equation globally in $${\mathbb {R}}$$ is proposed. The numerical simulations presented in the paper confirm our theoretical results.

The aim of this paper is to study a new generalized system of nonlinear variational inclusions involving $$H(\cdot ,\cdot )$$ -co-accretive mapping in Banach spaces. Using the concept of resolvent operator associated to $$H(\cdot ,\cdot )$$ -co-accretive mapping, we prove the existence for this generalized system of nonlinear variational inclusions. We show the convergence and stability of this new system of variational inclusion using the proposed perturbed iterative algorithm. The results presented in this paper generalize, improve and unify the previously known results in this area. An example is also given.

In this paper, we propose two hybrid subgradient extragradient methods for solving common solutions of variational inequalities problems (CSVIP). The first is a parallel algorithm which can be performed simultaneously while the second is a cyclic algorithm which is computed sequentially on each subproblem in the family. The novelty of this paper is that we have designed the algorithms to develop possible practical numerical methods when the number of subproblems is large. The algorithms can be considered as improvements of some previously known results for CSVIPs. Numerical experiments are also performed to illustrate the efficiency of the proposed algorithms.

In this paper, we consider a finite difference fully discretization for the $$ 1-D $$ wave equation with a boundary feedback and we analyze the exponential decay of the energy of solutions. First, we prove that a uniform boundary observability has a positive answer for a conservative system when the mesh size tends to zero using Fourier series technique. Then, we prove that the decay rate of the energy is uniform with respect to the mesh size. Finally, we describe some numerical experiments developed in Matlab to illustrate the results proved in this paper.

In this paper, we introduce some classes of non-commutative residuated lattices, give theirs characterization by filters and study the relations among them. This work generalizes some results relative to BL-algebras (Turunen and Sessa, Mult Valued Logic 6:1–21, 2001; Motamed and Borumand, Neural Comp Appl 20:461–475, 2011), MTL-algebra (Haveshki, Fuzzy Sets Syst, 247:135–137, 2014), pseudo-BL-algebras (Georgescu and Leustean, J Aust Math Soc, 73:127–153, 2002) or residuated lattices (Busneag and Piciu, Soft Comput, 16:1639–1655, 2012; Kadji et al. Int J Math Math Sci, 28940:12 2014, Ma and Hu, Fuzzy Sets Syst, 247:92–107 2014). At the end of this paper, we draw diagrams summarizing the relationships between different types of filters and classes of pseudo-residuated lattices.

In this paper we develop an a posteriori error analysis of a nonconforming mixed finite element method for the coupling of fluid flow with porous media flow. The approach utilizes the same nonconforming Crouzeix–Raviart element discretization on the entire domain (Rui and Zhang, Comput Methods Appl Mech Eng 198:2692–2699, 2009). The a posteriori error estimate is based on a suitable evaluation on the residual of the finite element solution. It is proven that the a posteriori error estimate provided in this paper is both reliable and efficient.

In this paper, we introduce the notion of $$\chi $$ -pure exact sequence. An exact sequence $$0\longrightarrow A\longrightarrow B\longrightarrow C\longrightarrow 0$$ is said to be $$\chi $$ -pure-exact if $$0\longrightarrow A\bigotimes M\longrightarrow B\bigotimes M\longrightarrow C\bigotimes M\longrightarrow 0$$ is again an exact sequence, where A, B, C are right R-modules and $$M\simeq R/I$$ is a left R-module for $$I\in \chi $$ , where $$\chi $$ denotes the collection of left ideals of R. In this paper, we establish several equivalent conditions for a pure exact sequence to be $$\chi $$ -pure exact. We further define a $$\chi $$ -pure injective module and study the topological aspects of this module and introduce a condition under which a $$\chi $$ -pure injective module coincides with an algebraically compact module.

Let R be a commutative ring with identity and M be an R-module. Let Z(R) be the set of zero-divisors of R and Z(M) be the set of annihilators over M in R. The total graph of idealization, \(T\left( \Gamma (R(+)M)\right) \) was defined as the graph with all elements of the ring \(R(+)M =\lbrace (r,m)\mid r \in R, m \in M\rbrace \) as vertices where any two distinct vertices \((x,m), (y,n) \in R(+)M\) are adjacent if and only if \((x,m) + (y,n) \in Z(R(+)M)\), the set of zero-divisors of \(R(+)M\). In this paper we define the line graph of total graph of idealization, denoted by \(L\left( T(\Gamma (R(+)M))\right) \) as the graph with all the edges of \(T\left( \Gamma (R(+)M)\right) \) as vertices and any two distinct vertices are adjacent if and only if their corresponding edges share a common vertex in the graph \(T\left( \Gamma (R(+)M)\right) \). In this paper we discuss the diameter, girth and clique number of the graph \(L\left( T(\Gamma (R(+)M))\right) \). We also find condition for the graph \(L\left( T(\Gamma (R(+)M))\right) \) to be connected when \(Z(R(+)M)\) is not an ideal of the \(R(+)M\).

This paper is concerned with Sobolev-type inequalities and upper bound for the fundamental solution to the heat-type equation defined on compact manifold whose metric evolves by the generalized geometric flow. It turns out that the pointwise estimates obtained in this paper depend on the constants in the uniform Sobolev inequalities for the flow or the best constants in the euclidean Sobolev embedding. We give various illustrations to show that our results are valid in many contexts of geometric flow, where we may not need explicit curvature constraint. Moreover, our approach here also demonstrates equivalence of Sobolev inequalities, log-Sobolev inequalities, ultracontractive estimates and heat kernel upper bounds.

This paper deals with a class of algebraic hyperstructures called ternary semihypergroups, which are a generalization of ternary semigroups. Our main purpose of this paper is to introduce and study the notions of quasi-hyperideal and bi-hyperideal in ternary semihypergroups. The structure of ternary semihypergroups through the quasi- and bi-hyperideals is studied and some characterizations are given. Also, we introduce the notion of generalized bi-hyperideals. Several kinds of them are investigated.

In this paper, we discuss the existence of a solution of extended general quasi variational inequalities using projection technique. Using the technique of Noor, we suggest and analyze a new class of three-step iterative schemes for solving extended general quasi variational inequalities. Under some certain conditions on operators, we also discuss the convergence of the proposed iterative scheme. Results proved in this paper continue to hold for previously known and new classes of quasi variational inequalities. Ideas and techniques of this paper may stimulate further research in this field. The implementation and comparison of the proposed new algorithms is an interesting problem for further research.

In this paper, we introduce the notion of power ternary semiring as a generalization of power semirings introduced by Sen and Bhuniya (Semigr Forum 82:131–140, 2011). The main aim of this paper is twofold. The first one is to study some properties of power ternary semirings with the help of corresponding properties of ternary semigroups. The another important aspect is—if \(S_1\) and \(S_2\) are isomorphic ternary semigroups, then the corresponding power ternary semirings \(P(S_1)\) and \(P(S_2)\) are obviously isomorphic. It is quiet natural to ask whether the converse is true, i.e. is it true that for any ternary semigroups \(S_1\) and \(S_2\) it holds: \(P(S_1)\cong P(S_2)\) implies that \(S_1\cong S_2\)? In this paper, we try to answer this question partially.

The purpose of this paper is to introduce a new hybrid extragradient iterative algorithm for finding a common element of the set of points satisfying the Equilibrium problem, variational inequality and fixed point problems of a strict pseudocontraction mapping in Hilbert spaces. Consequently, we obtain the strong convergence of an iterative algorithm generated by the hybrid extragradient projection method. The results presented in this paper generalize, improve and extend some well-known results in the literature.

Does the world still need another index of poverty? The main goal of this paper is to define a new kind of poverty indicator able to measure the multidimensionality of poverty, in individuals or societies, and to provide a comprehensive graphical representation. The traditional poverty line is not valid when dealing with several dimensions, so the new method computes a poverty hyperplane replacing the role that the poverty line had in classic studies. This hyperplane can be intrinsically determined from the agents or exogenously fixed. Then a variety of dimensions of poverty are included in one single indicator, whose major properties are shown in the paper to support its use to a wide range of scientific research fields. Finally, as an example, the indicator is applied to the measurement of poverty in African countries.

In this paper, we generalize the Banach contraction principle by proving common fixed point theorems for mappings satisfying Presic type conditions in 2-Banach spaces. The common fixed point is approximated by the \(k\)-Picard type and \(k\)-Mann type iteration schemes in product spaces. The results in this paper extend the results of Presic in the framework of a 2-Banach space. An example is provided which illustrate the results.

In this paper, we consider a new system of generalized nonlinear variational inclusions involving \(A\)-maximal \(m\)-relaxed \(\eta \)-accretive [so-called, \((A,\eta )\)-accretive (Lan et al. in Comput Math Appl 51:1529–1538 2006)] mappings in \(q\)-uniformly smooth Banach spaces. By using the resolvent operator technique associated with \(A\)-maximal \(m\)-relaxed \(\eta \)-accretive mappings, we prove the existence of a unique solution of the aforementioned system. We use nearly uniformly Lipschitzian mappings \(S_i\)\((i=1,2,\ldots ,p)\) to define a self mapping \(\mathcal Q =(S_1,S_2,\ldots ,S_p)\). Then by using resolvent operator technique associated with \(A\)-maximal \(m\)-relaxed \(\eta \)-accretive mappings, we shall construct a \(p\)-step iterative algorithm with mixed errors for finding an element of the set of the fixed points of \(\mathcal Q \) which is also a unique solution of the aforesaid system. We also establish the convergence of the iterative sequence generated by the proposed algorithm under some suitable conditions. The results presented in this paper extend and improve several known results in the literature.

In this paper, we investigate meromorphic functions that share a small function with one of its linear differential polynomials and prove several theorems which generalize and improve the main results given by J. L. Zhang and L. Z. Yang. Some examples are provided to show that the results in this paper are sharp.

In a recent paper, El-Shahed and Gaber (Appl Math Comput 217, pp 9165–9172, 2011) have introduced and studied the two-dimensional q-differential transform method. We observe that, in their work some results giving the q-differential transform of product of two functions are erroneous. In the present paper, we first provide their corrected forms as Theorem 1 and Corollary 1. We then apply this method to solve two q-differential equations.

In this paper, we use bounded linear operators and the convexity in Banach space, introduce a new generalized operator quasi-contractive condition, prove a new fixed point theorem in cone metric space. The conclusion in this paper unify, improve and generalize many contractive-type and quasi-contractive-type fixed point theorems in metric spaces and cone metric spaces. A example is given, which explains that the operator versions contractive condition is real generalization of scalar versions contractive condition.

A simple technique for calculation of numerical integration errors for physically meaningful functions is presented. In this paper, first the function classes are introduced that relate a function studied directly to a particular physical problem. The matrix elements defining a particular class of functions are then directly incorporated into the error formula. The proposed technique relies on the extension of the concept of the Taylor series. Since the standard Taylor series can be used for calculating the errors for smooth functions, in this paper the behaviour of the error in the immediate vicinity of discontinuity is considered only. The extended Taylor series is obtained by performing the Taylor series expansion on both sides of the discontinuity, using a matrix to describe the behaviour of the function at the discontinuity position and finally summing up all terms proportional to the function value and of all its derivatives. For illustration, several basic classes of physically meaningful functions are introduced and the extended Taylor series is derived. The series is then used to calculate the local error of the numerical integration. The numerical results obtained confirm the accuracy of the derived formulae.

The first and second status connectivity indices of a connected graph G are defined as $$S_{1}(G) = \sum _{uv \in E(G)}[\sigma _G(u)+ \sigma _G(v)]$$ and $$S_{2}(G) = \sum _{uv \in E(G)}\sigma _G(u)\sigma _G(v)$$ respectively, where E(G) is the edge set of G and $$\sigma _G(u)$$ is the sum of distances between the vertex u and all other vertices of G. In this paper we compute the status connectivity indices of line graphs of trees. Further we give the bounds for these indices of line graphs of connected graphs.

In this paper, a new generalization of semi-linear uniform spaces is introduced for the first time. This generalization will dispense with the chain condition imposed on a semi-linear uniform space which is given in Tallafha and Khalil (Eur J Pure Appl Math 2:231–238, 2009). We will show that several facts and results have been verified without that strong condition. Finally, we use the concept of ultrafilter and Cauchy filter to study the concept of precompact in this generalization of semi-linear uniform spaces.

This paper aims to study the theory of variation diminishing convolution kernel in the fractional Hankel-type transform domain. Moreover, necessary and sufficient conditions are established for the function $$G^\theta $$ to be the variation diminishing convolution kernel.

In this paper, we address the additivity of $n$-multiplicative isomorphisms and $n$-multiplicative derivations on Gamma rings. We proved that, if $\M$ is a $\Gamma$-ring satisfying the some conditions, then any $n$-multiplicative isomorphism $\left(\varphi, \phi\right)$ of $\M$ onto an arbitrary gamma ring is additive., Comment: 10 pages

In this paper, we prove coincidence point results for $$\psi $$ -contractions in non-Archimedean fuzzy metric spaces by utilizing some relation-theoretic metric analogues of usual metrical notions. With a view to substantiate the utility of these findings, we solve the system of Fredholm integral equations as an application. In this way, these findings generalize and improve some prominent recent results obtained in Mihet (Fuzzy Sets Syst 159(6):739–744, 2008), Altun and Mihet (Fixed Point Theory Appl 2010:782680, 2010) and Alam Imdad (Filomat 31(14):4421–4439, 2017) and several others in non-Archimedean fuzzy metric spaces equipped with an amorphous binary relation.

The aim of this paper is to study the concept of ideals. Especially, prime (semiprime) ideals of $$\varGamma $$ -nearness hemiring are introduced and are given some properties of such ideals.

In this paper, we first introduce a generalized K-algebra (briefly, gK-algebra) $$(P, \cdot , \odot , e, ^{-1})$$ which is constructed on a non-symmetric polygroup $$(P, \cdot , e, ^{-1})$$ , by adjoining binary hyperoperation $$\odot $$ defined by $$x \odot y = x \cdot y^{-1}$$ , for all $$x, y \in P$$ . Then, we show that every gK-algebra associated to a canonical hypergroup is a hyper B-algebra with constant e. Finally, we define generalized gK-subalgebras, (prime) generalized gK-ideals, homomorphisms of $$(P, \cdot , \odot , e, ^{-1})$$ and quotient generalized gK-algebras.

In this paper, we generalize the concept of interval valued $$(\in ,\in \vee q_{\widetilde{k}})$$ -fuzzy left (right) filters in ordered semigroups introducing and studying the notion of an interval valued $$(\in ,\in \vee q_{\widetilde{ k}}^{_{\widetilde{\delta }}})$$ -fuzzy left (right) filter. Several properties and characterizations are investigated and obtained on ordered semigroups by an interval valued $$ (\in ,\in \vee q_{\widetilde{k}}^{_{\widetilde{\delta }}})$$ -fuzzy left (right) filter. Characterizations of interval valued fuzzy left (resp. right) filters and interval valued $$(\in ,\in \vee q_{\widetilde{k} }^{_{\widetilde{\delta }}})$$ -fuzzy left (resp. right) filters are considered by using implication operators and the notion of implication-based interval valued fuzzy left (resp. right) filters.

In this paper we study some applications of second order differential subordination, superordination and sandwich-type results for certain admissible classes of meromorphically multivalent functions associated with the Liu-Srivastava operator.

In this paper, we have established some new integral identities connected with the left-hand side of Hermite–Hadamard inequality. By using this identity, we have obtained some new bounds for functions whose derivatives in absolute values are s-convex.

In this paper, using $$q-$$ difference operator, we define a class of harmonic univalent functions and obtain various properties for it.

In this paper, we introduce a class of mappings called the weak KKH-Caristi type expansion in b-metric and ordered b-metric spaces by generalizing the Caristi-type contractions. Also, we present some fixed point results on this class of mappings. Some examples are also given to support and illustrate our results.

The only hitherto known Kurosh–Amitsur prime radical of near-rings is the equiprime radical which is also ideal-hereditary in the variety of zero-symmetric near-rings. In this paper an other prime radical is introduced in near-rings which is Kurosh-Amitsur but it fails to be ideal-hereditary.

This paper is devoted to examine a special case of Walker metric on a 4-dimensional manifold, and some of its curvature properties are studied, e.g., conditions for a Walker metric to be Einstein or locally conformally flat. Finally, a necessary and sufficient condition for a function c(x, y, z, t) of Walker metric of 4-dimensional manifold to have vector field X on M to be a Killing vector field, is constructed.

In this paper, we investigate and introduce new two subclasses of analytic functions by using q-Catas operator and definition of subordination. Furthermore, we obtain coefficient estimate theorems. Also, we present new results for subordination factor sequence.

In this paper, we obtain a integral involving the general class of polynomials (Srivastava polynomials) and Special functions which are the adequately general in nature and are capable of yielding a large number of simpler and useful results merely by specializing the parameters. For the sake of illustration, some corollaries are also recorded here as special case of our main result.

In earlier studies different methods of same convergence order are campared using numerical examples. The drawback of this approach is that, we do not know: if the results of those comparisons are true if the examples change; the largest radii of convergence; error estimates on distance between the iterate and solution, and uniqueness results that are computable. In this paper we campare the ball convergence of two-step iterative methods for solving the equation $$G(x)=0$$ using only the first derivative and a common set of criteria. Numerical experiments are used to test the convergence criteria and further validate the theoretical results. Our technique can be used to make comparisons between other methods of the same order.

The goal of this paper is to introduce and give some constructions and study properties of Hom-left-symmetric color dialgebras and Hom-tridendriform color algebras. Next, we study their connection with Hom-associative color algebra, Hom-post-Lie color algebra and Hom-Poisson color dialgebras. Finally, we generalize Yau's twisting to a class of color Hom-algebras and used endomorphisms or elements of centroids to produce other color Hom-algebras from given one., Comment: corrected affiliation of the second author, improved references and exposition

The aim of this paper is to give a generalization of the concept of commutativity degree of a finite group G (denoted by d(G)), to the concept of commutativity degree of a group algebra F[G], where G is a finite group and F is a finite field. We prove that two isoclinic groups for which the order of their centers are equal have the same commutativity degree. Finally, we give some lower and upper bounds for the commutativity degree of group algebra F[G] in terms of the order of G, the order of F and d(G).

In this paper, we prove that the $$(\omega +1)$$ -projective $$\Sigma $$ -modules are direct sums of countably generated modules each of which has length at most $$(\omega +1)$$ . We also give an example that this is not true for all other $$(\omega +k)$$ -projectives with $$2\le k< \omega $$ . Certain related assertions are established as well. These results are then used to discuss the class of highly essentially finitely indecomposable modules.

In this paper, we establish the existence and uniqueness of solutions to nonlocal initial value problem for differential equations with Hilfer–Katugampola type fractional derivative, also, the stability of this class of problem. The arguments are based upon the Banach contraction principle, and Schaefer’s fixed point theorem. An example is included to show the applicability of our results.

In this paper, the concept of co-ordinated (log, (s, m))-preinvex functions is introduced. Some new fractional Hermite–Hadamard type inequalities based on new integral identity are established.

Let R be a commutative ring with identity. The unit graph of R, denoted by G(R), has its set of vertices equal to the set of all elements of R and two distinct vertices x and y are adjacent if and only if $$x+y$$ is a unit of R. In this paper, perfect unit graphs of Artinian rings are investigated.

In 2017, Parvaneh et al. (J Math Anal 8(1):183–201, 2017) further extended rectangular metric space by introduced partial rectangular b-metric space and utilized the same to prove some fixed point results. Almost at the same time, Roshan et al. (Nonlinear Anal Model Control 21(5):614–634, 2016) generalized Geraghty fixed point results by proving some fixed point results in b-rectangular metric space. In this paper, we prove some ordered-theoretic fixed point results for Geraghty-weak contraction in ordered partial rectangular b-metric space. Our results extend and improve many existing results in literature. We also furnish an example which exhibits the utility of our results.

Let $$\mathbb {D}$$ be a simple connected digraph with n vertices and m arcs and let $$W(\mathbb {D})=(\mathbb {D},\omega )$$ be the weighted digraph corresponding to $$\mathbb {D}$$ , where the weights are taken from the set of non-zero real numbers. In this paper, we define the skew Laplacian matrix $$SL(W(\mathbb {D}))$$ and skew Laplacian energy $$SLE(W(\mathbb {D}))$$ of a weighted digraph $$W(\mathbb {D})$$ , which is defined as the sum of the absolute values of the skew Laplacian eigenvalues, that is, $$SLE(W(\mathbb {D}))=\sum _{i=1}^{n}|\rho _i|$$ , where $$\rho _1,\rho _2, \ldots ,\rho _n$$ are the skew Laplacian eigenvalues of $$W(\mathbb {D})$$ . We show the existence of the real skew Laplacian eigenvalues of a weighted digraph when the weighted digraph has an independent set such that all the vertices in the independent set have the same out-neighbors and in-neighbors. We obtain a Koolen type upper bound for $$SLE(W(\mathbb {D}))$$ . Further, for a connected weighted digraph $$W(\mathbb {D})$$ , we obtain bounds for $$SLE(W(\mathbb {D}))$$ , in terms of different digraph parameters associated with the digraph structure $$\mathbb {D}$$ . We characterize the extremal weighted digraphs attaining these bounds.

Making use of the $$q-$$ difference operator $$ L_{p,q}\left( a,c\right) $$ , we introduce a new two subclasses of $$p-$$ valent analytic functions in the open unit disk. The main objective of the present paper is to investigate the various important properties and characteristics of each of these subclasses. Furthermore, several properties involving neighborhoods and modified Hadamard products of functions in these subclasses are obtained.