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This paper is concerned with the uncertain multiattribute decision-making (UMADM) of which the attribute value is triangular fuzzy number. Firstly, the max-relative similarity degree and min-relative similarity degree of alternative decision-making objects are given based on the relative similarity degree of triangular fuzzy number, the advantage relation theories to comparative relative similarity degree of triangular fuzzy number are proposed, and some good properties, relations, and conclusions are derived. Secondly, in order to determine the attribute weight vector, a triangular fuzzy number-based decision-making object relative similarity programming model is established with the help of maximizing possibility degree algorithm rules in the cooperative game theory. Subsequently, by aggregating the comparison overall relative similarity degree values of all decision-making objects, we could pick over and sort the set of alternative objects and gather a new model algorithm for the relative similarity programming of triangular fuzzy number-based multiple attribute decision-making alternatives. Finally, an example is given to illustrate the feasibility and practicability of the model algorithm presented in this paper.

In this paper, we consider, discuss, complement, improve, generalize, and enrich some fixed point results obtained forβ−ψ1−ψ2−contractive conditions in ordered b-metric-like spaces. By using our new approach for the proof that one Picard’s sequence isbbl−Cauchy in the context of b-metric-like spaces, we get much shorter proofs than the ones mentioned in the recent papers. Also, by the use of our method, we complement and enrich some common fixed point results forβq,ϕs,ψ−contraction mappings. Our approach in this paper generalizes and modifies several comparable results in the existing literature.

This paper focuses on a singular boundary value (SBV) problem of nonlinear fractional differential (NFD) equation defined as follows: D 0 + β υ τ + f τ , υ τ = 0 , τ ∈ 0,1 , υ 0 = υ ′ 0 = υ ″ 0 = υ ″ 1 = 0 , where 3 < β ≤ 4 , D 0 + β is the standard Riemann–Liouville fractional (RLF) derivative. The nonlinear function f τ , υ τ might be singular on the spatial and temporal variables. This paper proves that a positive solution to the SBV problem exists and is unique, taking advantage of Green’s function through a fixed-point (FP) theory on cones and mixed monotone operators.

The aim of this paper is to present another family of fractional symmetric α - η -contractions and build up some new results for such contraction in the context of ℱ -metric space. The author derives some results for Suzuki-type contractions and orbitally T -complete and orbitally continuous mappings in ℱ -metric spaces. The inspiration of this paper is to observe the solution of fractional-order differential equation with one of the boundary conditions using fixed-point technique in ℱ -metric space.

The main objective of this paper is to obtain the fractional integral operator inequalities which provide bounds of the sum of these operators at an arbitrary point. These inequalities are derived for s-exponentially convex functions. Furthermore, a Hadamard inequality is obtained for fractional integrals by using exponentially symmetric functions. The results of this paper contain several such consequences for known fractional integrals and functions which are convex, exponentially convex, and s-convex.

A topological invariant is a numerical parameter associated with molecular graph and plays an imperative role in the study and analysis of quantitative structure activity/property relationships (QSAR/QSPR). The correlation between the entire π-electron energy and the structure of a molecular graph was explored and understood by the first Zagreb index. Recently, Liu et al. (2019) calculated the first general Zagreb index of the F-sum graphs. In the same paper, they also proposed the open problem to compute the general Randić index RαΓ=∑uv∈EΓdΓu×dΓvα of the F-sum graphs, where α∈R and dΓu denote the valency of the vertex u in the molecular graph Γ. Aim of this paper is to compute the lower and upper bounds of the general Randić index for the F-sum graphs when α∈N. We present numerous examples to support and check the reliability as well as validity of our bounds. Furthermore, the results acquired are the generalization of the results offered by Deng et al. (2016), who studied the general Randić index for exactly α=1.

This paper aims at determining the measure of Q under necessary and sufficient conditions. The measure is an equivalent measure for identifying the given P such that the process with respect to P is the deflator locally martingale. The martingale and locally martingale measures will coincide for the deflator process discrete time. We define s-viable, s-price system, and no locally free lunch in ordered Banach algebra and identify that the s-price system C,π is s-viable if and only a character functional ψC≤π exists. We further demonstrate that no locally free lunch is a necessary and sufficient condition for the equivalent martingale measure Q to exist for the deflator process and the subcharacter ϕ∈Γ such that φC=π. This paper proves the existence of more than one condition and that all conditions are equivalent.

In this paper, we consider a gradient-driven mathematical model of antiangiogenesis in tumor growth. In the model, the movement of endothelial cells is governed by diffusion of themselves and chemotaxis in response to gradients of tumor angiogenic factors and angiostatin. The concentration of tumor angiogenic factors and angiostatin is assumed to diffuse and decay. The resulting system consists of three parabolic partial differential equations. In the present paper, we study the global existence and boundedness of classical solutions of the system under homogeneous Neumann boundary conditions.

The goal of this paper is to derive some new variants of Simpson’s inequality using the class ofn-polynomial convex functions of higher order. To obtain the main results of the paper, we first derive a new generalized fractional integral identity utilizing the concepts of Katugampola fractional integrals. This new fractional integral identity will serve as an auxiliary result in the development of the main results of this paper.

Collatz Conjecture (3x+1 problem) states any natural number x will return to 1 after 3⁎x+1 computation (when x is odd) and x/2 computation (when x is even). In this paper, we propose a new approach for possibly proving Collatz Conjecture (CC). We propose Reduced Collatz Conjecture (RCC)—any natural number x will return to an integer that is less than x. We prove that RCC is equivalent to CC. For proving RCC, we propose exploring laws of Reduced Collatz Dynamics (RCD), i.e., from a starting integer to the first integer less than the starting integer. RCC can also be stated as follows: RCD of any natural number exists. We prove that RCD is the components of original Collatz dynamics (from a starting integer to 1); i.e., RCD is more primitive and presents better properties. We prove that RCD presents unified structure in terms of (3⁎x+1)/2 and x/2, because 3⁎x+1 is always followed by x/2. The number of forthcoming (3⁎x+1)/2 computations can be determined directly by inputting x. We propose an induction method for proving RCC. We also discover that some starting integers present RCD with short lengths no more than 7. Hence, partial natural numbers are proved to guarantee RCC in this paper, e.g., 0 module 2; 1 module 4; 3 module 16; 11 or 23 module 32; 7, 15, or 59 module 128. The future work for proving CC can follow this direction, to prove that RCD of left portion of natural numbers exists.

A class of nonlinear convection-diffusion equation is studied in this paper. The partial differential equation is converted into nonlinear ordinary differential equation by introducing a similarity transformation. The asymptotic analytical solutions are obtained by using double-parameter transformation perturbation expansion method (DPTPEM). The influences of convection functional coefficientk(z)and power law indexnon the heat transport characteristics are discussed and shown graphically. The comparison with the numerical results is presented and it is found to be in excellent agreement. The method and technique used in this paper have the significance in studying other engineering problems.

In this paper, we propose a parameter perturbation homotopy continuation method for solving fixed point problems on more general nonconvex sets with both inequality and equality constraints. By adopting appropriate techniques, we make the initial points not certainly in the set consisting of the equality constraints. This point can improve the computational efficiency greatly when the equality constraints are complex. In addition, we also weaken the assumptions of the previous results in the literature so that the method proposed in this paper can be applied to solve fixed point problems in more general nonconvex sets. Under suitable conditions, we obtain the global convergence of this homotopy continuation method. Moreover, we provide several numerical examples to illustrate the results of this paper.

The main outcome of this paper is to introduce the notion of orthogonal gauge spaces and to present some related fixed-point results. As an application of our results, we obtain existence theorems for integral equations.

Frame theory has a great revolution in recent years. This theory has been extended from the Hilbert spaces to Hilbert C ∗ -modules. In this paper, we consider the stability of continuous operator frame and continuous K -operator frames in Hilbert C ∗ -modules under perturbation, and we establish some properties.

Topological indices (TIs) transform a molecular graph into a number. The TIs are a vital tool for quantitative structure activity relationship (QSAR) and quantity structure property relationship (QSPR). In this paper, we constructed two classes of Benes network: horizontal cylindrical Benes network HCB r and vertical cylindrical Benes network obtained by identification of vertices of first rows with last row and first column with last column of Benes network, respectively. We derive analytical close formulas for general Randić connectivity index, general Zagreb, first and the second Zagreb (and multiplicative Zagreb), general sum connectivity, atom-bond connectivity ( VCB r ), and geometric arithmetic ABC index of the two classes of Benes networks. Also, the fourth version of GA and the fifth version of ABC indices are computed for these classes of networks.

Our aim in this paper is to study the asymptotic global stability of the positive solutions for a class of first-order nonlinear difference equations with a remarkable feature: the initial conditions are intrinsic and not explicitly given. Global stability results are obtained in a particular case and then for a general class of first-order difference equations. We also provide the results of some numerical experiments obtained by the mini software package FIXPOINT to illustrate asymptotic global stability as well as the rate of convergence. To the best of our knowledge, our approach is the first one in the literature on the stability of difference equations without explicit initial conditions and might generate an interesting new direction of further studies.

In this paper, Jensen and Hardy inequalities, including Pólya–Knopp type inequalities for superquadratic functions, are extended using Riemann–Liouville delta fractional integrals. Furthermore, some inequalities are proved by using special kernels. Particular cases of obtained inequalities give us the results on time scales calculus, fractional calculus, discrete fractional calculus, and quantum fractional calculus.

In this paper, we consider the split feasibility problem in Banach spaces. By applying the shrinking projection method, we propose an iterative method for solving this problem. It is shown that the algorithm under two different choices of the stepsizes is strongly convergent to a solution of the problem.

The boundedness, compactness, and the essential norm of weighted composition operators from derivative Hardy spaces into n -th weighted-type spaces are investigated in this paper.

In this paper, an interesting third-order linear recurrence formula is presented by using elementary and analytic methods. This formula is concerned with the calculating problem of the hybrid power mean of a certain two-term exponential sums and the cubic Gauss sums. As an application of this result, some exact computational formulas for one kind hybrid power mean of trigonometric sums are obtained.

In this paper, we introduce and study woven frames in quaternionic Hilbert spaces. We also give some properties of woven frames and give some conditions on family of frames under which it is woven in quaternionic Hilbert spaces. Also, a characterization of weaving frames in terms of a surjective-bounded right linear operator is given.

The harmonic index of a graph G ( H G ) is defined as the sum of the weights 2 / d u + d v for all edges u v of G , where d u is the degree of a vertex u in G . In this paper, we show that H G ≥ D G + 5 / 3 − n / 2 and H G ≥ 1 / 2 + 2 / 3 n − 2 D G , where G is a quasi-tree graph of order n and diameter D G . Indeed, we show that both lower bounds are tight and identify all quasi-tree graphs reaching these two lower bounds.

In this paper, we present two versions of the Hadamard inequality forα,mconvex functions via Caputo fractional derivatives. Several related results are analyzed for convex andm-convex functions along with their refinements and generalizations. The error bounds of the Hadamard inequalities are established by applying some known identities.

In this paper, we prove a fixed point theorem in complex partial b -metric space under new contraction mapping. The proved results generalize and extend some of the well-known results in the literature. We also give some applications of our main results.

Let G be a simple graph of order n . The matrix ℒ G = D G − A G is called the Laplacian matrix of G , where D G and A G denote the diagonal matrix of vertex degrees and the adjacency matrix of G , respectively. Let l 1 G , l n − 1 G be the largest eigenvalue, the second smallest eigenvalue of ℒ G respectively, and λ 1 G be the largest eigenvalue of A G . In this paper, we will present sharp upper and lower bounds for l 1 G and l n − 1 G . Moreover, we investigate the relation between l 1 G and λ 1 G .

This paper is devoted to study the null controllability properties of a population dynamics model with age structuring and nonlocal boundary conditions. More precisely, we consider a four-stage model with a second derivative with respect to the age variable. The null controllability is related to the extinction of eggs, larvae, and female population. Thus, we estimate a time T to bring eggs, larvae, and female subpopulation density to zero. Our method combines fixed point theorem and Carleman estimate. We end this work with numerical illustrations.

In this paper, we concern with the split feasibility problem (SFP) in real Hilbert space whenever the sets involved are nonempty, closed, and convex. By mixing W -mapping with the viscosity, we introduce a new iterative algorithm for solving the split feasibility problem, and we prove that our proposed algorithm is convergent strongly to a solution of the split feasibility problem.

In this paper, we study the nonlinear coupled system of equations with fractional integral boundary conditions involving the Caputo fractional derivative of orders θ 1 and θ 2 and Riemann–Liouville derivative of orders ϱ 1 and ϱ 2 with the p -Laplacian operator, where n − 1 < θ 1 , θ 2 , ϱ 1 , ϱ 2 ≤ n , and n ≥ 3 . With the help of two Green’s functions G ϱ 1 w , ℑ , G ϱ 2 w , ℑ , the considered coupled system is changed to an integral system. Since topological degree theory is more applicable in nonlinear dynamical problems, the existence and uniqueness of the suggested coupled system are treated using this technique, and we find appropriate conditions for positive solutions to the proposed problem. Moreover, necessary conditions are highlighted for the Hyer–Ulam stability of the solution for the specified fractional differential problems. To confirm the theoretical analysis, we provide an example at the end.

In this paper, we introduce a new class of mappings and investigate their fixed point property. In the first direction, we prove a fixed point theorem for general higher-order contraction mappings in a given metric space and finally prove an approximate fixed point property for general higher-order nonexpansive mappings in a Banach space.

In this paper, we first introduce a new graph Γ N over an extension N of semigroups and after that we study and characterize the spectral properties such as the diameter, girth, maximum and minimum degrees, domination number, chromatic number, clique number, degree sequence, irregularity index, and also perfectness for Γ N . Moreover, we state and prove some important known Zagreb indices on this new graph.

In this paper, we consider divisor problems related to Hecke eigenvalues in three dimensions. We establish upper bounds and asymptotic formulas for these problems on average.

This paper is devoted to presenting an averaging principle for stochastic pantograph equations. Under suitable non-Lipschitz conditions, the solutions to stochastic pantograph equations can be approximated by solutions to averaged stochastic systems in the mean-square sense and probability. At last, an example is given to demonstrate the feasibility of obtained results. Moreover, our results have generalized significantly some previous ones.

In this work, we establish new fixed point theorems for generalized Pata–Suzuki type contraction via α -admissible mapping in metric spaces and to prove some fixed point results for such mappings. Moreover, we give an example to illustrate our main result. Consequently, the results presented in this paper generalize and improve the corresponding results of the literature.

In this paper, we construct a class of special homogeneous Moran sets: m k -quasi-homogeneous perfect sets, and obtain the Hausdorff dimension of the sets under some conditions. We also prove that the upper box dimension and the packing dimension of the sets can get the maximum value of the homogeneous Moran sets under the condition sup k ≥ 1 m k < ∞ and estimate the upper box dimension of the sets in two cases.

In this paper, we study the boundary value problem of a fractional q -difference equation with nonlocal integral boundary conditions on the half-line. Using the properties of the Green function and monotone iterative method, the extremal solutions are obtained. Finally, an example is presented to illustrate our main results.

Let Γ = V , E be a graph. If all the eigenvalues of the adjacency matrix of the graph Γ are integers, then we say that Γ is an integral graph. A graph Γ is determined by its spectrum if every graph cospectral to it is in fact isomorphic to it. In this paper, we investigate some algebraic properties of the Cayley graph Γ = Cay ℤ n , S , where n = p m ( p is a prime integer and m ∈ ℕ ) and S = a ∈ ℤ n | a , n = 1 . First, we show that Γ is an integral graph. Also, we determine the automorphism group of Γ . Moreover, we show that Γ and K v ▽ Γ are determined by their spectrum.

In this paper, new refinements and improvements of Mitrinović–Cusa’s and related inequalities are presented. First, we give new polynomial bounds for sinc(x) and cos(x) functions using the interpolation and approximation method. Based on the obtained results of the above two functions, we establish new bounds for Mitrinović–Cusa’s, Wilker’s, Huygens’, Wu–Srivastava’s, and Neuman–Sándor’s inequalities. The analysis results show that our bounds are tighter than the previous methods.

Graph theory has provided a very useful tool, called topological index, which is a number from the graph M with the property that every graph N isomorphic to M value of a topological index must be same for both M and N. Topological index is a descriptor in graph theory which is used to quantify the physio-chemical properties of the chemical graph. In this paper, we computed closed forms of M-polynomials for line graphs of H-naphtalenic nanotubes and chain silicate network. From M-polynomial, we obtained some topological indices based on degrees.

In this paper, we further studied properties of the modulus of n -dimensional U -convexity and the modulus of n -dimensional U -flatness when n = 1 (2-dimensional character) and n = 2 (3-dimensional character). The new properties of these moduli are investigated, and the relationships between these moduli and other geometric parameters of Banach spaces are studied. Some results on fixed point theory for nonexpansive mappings and normal structure in Banach spaces are obtained.

In this paper, by applying the discharging method, we show that if G is a planar graph with a maximum degree of Δ = 6 that does not contain any adjacent 8-cycles, then G is of class 1.

The most important properties of the conformable derivative and integral have been recently introduced. In this paper, we propose and prove some new results on conformable Laplace’s equation. We discuss the solution of this mathematical problem with Dirichlet-type and Neumann-type conditions. All our obtained results will be applied to some interesting examples.

For an ordered subset Q e of vertices in a simple connected graph G , a vertex x ∈ V distinguishes two edges e 1 , e 2 ∈ E , if d x , e 1 ≠ d x , e 2 . A subset Q e having minimum vertices is called an edge metric generator for G , if every two distinct edges of G are distinguished by some vertex of Q e . The minimum cardinality of an edge metric generator for G is called the edge metric dimension, and it is denoted by dim e G . In this paper, we study the edge resolvability parameter for different families of Möbius ladder networks and we find the exact edge metric dimension of triangular, square, and hexagonal Möbius ladder networks.

Isaacs, Passman, and Manz have determined the structure of finite groups whose each degree of the irreducible characters is a prime power. In particular, if G is a nonsolvable group and every character degree of a group G is a prime power, then G is isomorphic to S × A , where S ∈ A 5 , PSL 2 8 and A is abelian. In this paper, we change the condition, each character degree of a group G is a prime power, into the condition, each character degree of the proper subgroups of a group is a prime power, and give the structure of almost simple groups whose character degrees of all proper subgroups are all prime powers.

The aim of this paper is to derive some new fractional analogues of Ostrowski-type inequalities involving bounded functions using the concept of σ -Riemann–Liouville fractional integrals.

This paper studies the problem of determining invertible elements (units) in any n-refined neutrosophic ring. It presents the necessary and sufficient condition for any n-refined neutrosophic element to be invertible, idempotent, and nilpotent. Also, this work introduces some of the elementary algebraic properties of n-refined neutrosophic matrices with a direct application in solving n-refined neutrosophic algebraic equations.

Suppose G is a simple graph with edge set E G . The Randić index R G is defined as R G = ∑ u v ∈ E G 1 / deg G u deg G v , where deg G u and deg G v denote the vertex degrees of u and v in G , respectively. In this paper, the first and second maximum of Randić index among all n − vertex c − cyclic graphs was computed. As a consequence, it is proved that the Randić index attains its maximum and second maximum on two classes of chemical graphs. Finally, we will present new lower and upper bounds for the Randić index of connected chemical graphs.

In this paper, we establish an integral identity associated with m -times differentiable functions. The result is then used to derive some integral estimations for higher-order strongly n -polynomial preinvex functions. Finally, we apply the obtained inequalities to construct new inequalities involving special means.

Let d be a positive integer which is not a perfect square and n be any nonzero fixed integer. Then, the equation x 2 − d y 2 = n is known as the general Pell equation. In this paper, we give some criteria for class numbers of certain real quadratic fields to be greater than one, depending on the solvability of the general Pell equation, ideals in quadratic orders, and the period length of the simple continued fraction expansions of d .

The purpose of this paper is to study annihilators and annihilator ideals in a more general context; in universal algebras.

In this paper, we firstly derived the equations for the curves of a Lorentz–Minkowski space L3 to be f-biharmonic. Then, using these equations, we classify such unit speed curves in L3.