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Very recently Jain et al. (J. Inequal. Appl. 2022:73, 2022) introduced the concept of multivalued F-contraction with altering distance function and investigated the existence of best proximity points for this class of mappings. In this article we prove that the existence of best proximity points for multivalued F-contraction non-self mappings can be obtained from the corresponding fixed point result for multivalued F-contraction self mappings, and so the main conclusion due to Jain et al. is not a real generalization of fixed point theory. [ABSTRACT FROM AUTHOR]

In a recently published theorem on the split common fixed point problem for strict pseudocontractive and asymptotically nonexpansive mappings, Tang et al. (J. Inequal. Appl. 2015:305, 2015) studied a uniformly convex and 2-uniformly smooth real Banach space with the Opial property and best smoothness constant κ satisfying the condition 0 < κ < 1 2 , as a real Banach space more general than Hilbert spaces. A well-known example of a uniformly convex and 2-uniformly smooth real Banach space with the Opial property is E = l p , 2 ≤ p < ∞ . It is shown in this paper that, if κ is the best smoothness constant of E and satisfies the condition 0 < κ ≤ 1 2 , then E is necessarily l 2 , a real Hilbert space. Furthermore, some important remarks concerning the proof of this theorem are presented. [ABSTRACT FROM AUTHOR]

This paper deals with the attraction–repulsion chemotaxis system with nonlinear productions and logistic source, u t = ∇ ⋅ (D (u) ∇ u) − ∇ ⋅ (Φ (u) ∇ v) + ∇ ⋅ (Ψ (u) ∇ w) + f (u) , v t = Δ v + α u k − β v , τ w t = Δ w + γ u l − δ w , τ ∈ { 0 , 1 } , in a bounded domain Ω ⊂ R n (n ≥ 1 ), subject to the homogeneous Neumann boundary conditions and initial conditions, where D , Φ , Ψ ∈ C 2 [ 0 , ∞) are nonnegative with D (s) ≥ (s + 1) p for s ≥ 0 , Φ (s) ≤ χ s q , ξ s g ≤ Ψ (s) ≤ ζ s j , s ≥ s 0 , for s 0 > 1 , the logistic source satisfies f (s) ≤ s (a − b s d) , s > 0 , f (0) ≥ 0 , and the nonlinear productions for the attraction and repulsion chemicals are described via α u k and γ u l , respectively. When k = l = 1 , it is known that this system possesses a globally bounded solution in some cases. However, there has been no work in the case k , l > 0 . This paper develops the global boundedness of the solution to the system in some cases and extends the global boundedness criteria established by Tian, He, and Zheng (2016) for the attraction–repulsion chemotaxis system. [ABSTRACT FROM AUTHOR]

An introduction is presented in which the editor discusses various reports on nonlinear functional analysis and applications including the iteration method for nonexpansive and monotone mappings in Hilbert spaces, the stability of quadratic functional equations through fixed point and direct method, and the comparison for generalized Muirhead and identric means.

In a recent paper the authors proved a nonuniform local limit theorem concerning normal approximation of the point probabilities P (S = k) when S = ∑ i = 1 n X i and X 1 , X 2 , ... , X n are independent Bernoulli random variables that may have different success probabilities. However, their main result contained an undetermined constant, somewhat limiting its applicability. In this paper we give a nonuniform bound in the same setting but with explicit constants. Our proof uses Stein's method and, in particular, the K-function and concentration inequality approaches. We also prove a new uniform local limit theorem for Poisson binomial random variables that is used to help simplify the proof in the nonuniform case. [ABSTRACT FROM AUTHOR]

In continuation of Zayed and Bulboacă work in (J. Inequal. Appl. 2022:158, 2022), this paper discusses the geometric characterization of the normalized form of the generalized Bessel function defined by V ρ , r (z) : = z + ∑ k = 1 ∞ (− r) k 4 k (1) k (ρ) k z k + 1 , z ∈ U , for ρ , r ∈ C ∗ : = C ∖ { 0 } . Precisely, we will use a sharp estimate for the Pochhammer symbol, that is, Γ (a + n) / Γ (a + 1) > (a + α) n − 1 , or equivalently (a) n > a (a + α) n − 1 , that was firstly proved by Baricz and Ponnusamy for n ∈ N ∖ { 1 , 2 } , a > 0 and α ∈ [ 0 , 1.302775637 ... ] in (Integral Transforms Spec. Funct. 21(9):641–653, 2010), and then proved in our paper by another method to improve it using the partial derivatives and the two-variable functions' extremum technique for n ∈ N ∖ { 1 , 2 } , a > 0 and 0 ≤ α ≤ 2 , and used to investigate the orders of starlikeness and convexity. We provide the reader with some examples to illustrate the efficiency of our theory. Our results improve, complement, and generalize some well-known (nonsharp) estimates, as seen in the Concluding Remarks and Outlook section. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the sufficient conditions that guarantee the stability, continuity, and boundedness of solutions for a type of second-order stochastic delay integro-differential equation (SDIDE). To demonstrate the main results, we employ a Lyapunov functional. An example is provided to demonstrate the applicability of the obtained result, which includes the results of this paper and obtains better results than those available in the literature. [ABSTRACT FROM AUTHOR]

This paper studies the inhomogeneous bi-harmonic nonlinear Schrödinger equation i u ˙ + Δ 2 u ± | x | − τ | u | p − 1 u = 0 , where u : = u (t , x) : R × R N → C , τ > 0 and p > 1 . One proves the existence of global solutions with datum in Lebesgue space L ϱ (R N) , for a certain 1 < ϱ < 2 . This work complements the known global well-posedness result in the mass-sub-critical regime, namely 1 < p < 1 + 8 − 2 τ N and with finite mass. This work aims to develop a local theory in non-Hilbert Lebesgue spaces. Moreover, one complements the local solution to a global one under some suitable assumptions on the parameters. To this end, one uses a Strichartz-type estimate based on L ϱ . Moreover, one breaks down the data into two parts: the first is in L 2 , and the second has a small Strichrtz norm under the free bi-harmonic Schrödinger propagator. Then, one uses a standard fix point argument coupled with Strichartz estimates. First, one resolves the above problem in L 2 and then takes the considered equation with a perturbed source term. The local solution is complemented by a global one with induction. Since the free associated kernel e i ⋅ Δ 2 is unitary in L 2 , the Schrödinger equations seem more adapted to be mathematically studied in functional spaces based on L 2 , such as the Sobolev spaces W s , 2 (R N) . The main novelty here is investigating the above inhomogeneous bi-harmonic nonlinear Schrödinger problem in some Lebesgue spaces different from L 2 . One essential challenge is overcoming the lack of conservation laws, namely the mass and the energy, representing standard tools in the Schrödinger context. The second technical difficulty is the presence of an inhomogeneous source term, namely the singular decaying term | x | − τ , which causes some serious complications. In order to deal with the inhomogeneous term, one uses Lorentz spaces with the property | x | − τ ∈ L N τ , ∞ . [ABSTRACT FROM AUTHOR]

This paper focuses on the minimum eigenvalue involving the Fan product. By utilizing the Hölder inequality and the classic eigenvalue inclusion theorem, we introduce two novel lower bounds for τ (A 1 ⋆ A 2) , representing the minimum eigenvalue involving the Fan product of two M-matrices A 1 , A 2 . The newly derived lower bounds are then compared with the traditional findings. Numerical tests are presented to illustrate that the new lower bound formulas significantly enhance Johnson and Horn's results in certain scenarios and are more precise than other existing findings. [ABSTRACT FROM AUTHOR]

In this paper, we study classes of meromorphic harmonic functions defined by Ruscheweyh derivatives. In addition to finding certain analytic criteria, we obtain radii of starlikeness and convexity, and some topological properties for the defined classes of functions. Some applications of these results are also given. [ABSTRACT FROM AUTHOR]

In this paper, an interior penalty method is proposed to solve a parabolic complementarity problem involving fractional Black–Scholes operator arising in pricing American options under a geometric Lévy process. The complementarity problem is first reformulated as a fractional partial differential variational inequality problem using the representations of fractional order operators and appropriate mathematical techniques. A penalty equation is then proposed to approximate the variational inequality problem by introducing a novel interior-point based penalty term. The existence and uniqueness of the solution to the penalized problem are proved, and an upper bound on the distance between the solutions to the penalty equation and the variational inequality problem is established. To test our method, we discretize the penalty equation by a finite difference method in space and the Crank–Nicolson method in time. We then present numerical experimental results to demonstrate the usefulness and effectiveness for the interior penalty method. [ABSTRACT FROM AUTHOR]

This paper defines a family of neural-network interpolation operators. The first derivative of generalized logistic-type functions is considered as a density function. Using the first-order uniform approximation theorem for continuous functions defined on the finite intervals, the interpolation properties of these operators are presented. A Kantorovich-type variant of the operators F n a , ε is also introduced. The approximation of Kantorovich-type operators in L P spaces with 1 ≤ p ≤ ∞ is studied. Further, different combinations of the parameters of our generalized logistic-type activation function θ s , a are examined to see which parameter values might give us a more efficient activation function. By choosing suitable parameters for the operator F n a , ε and the Kantorovich variant of the operator F n a , ε , the approximation of various function examples is studied. [ABSTRACT FROM AUTHOR]

Split problems under linear transformations have been studied extensively in the literature. In this paper, we investigate a split problem under a nonlinear transformation, which consists of two variational inequalities and an equilibrium problem. We propose an iterative sequence for computing a solution to this split problem. Strong convergence theorem is achieved under additional standard conditions. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the fractional p (x , ⋅) -Kirchhoff-type equations M (∫ R N × R N 1 p (x , y) | u (x) − u (y) | p (x , y) | x − y | N + s p (x , y) d x d y) (− Δ p (x ,.)) s u + | u | p ¯ (x) − 2 u = f (x , u). We weaken the conditions on the nonlinear term f and get the existence and multiplicity of solutions via variational methods, which improves some previous results. [ABSTRACT FROM AUTHOR]

Motivated by certain results known from the literature, in this paper we give several new dynamic inequalities for B-monotone functions with respect to time scales nabla calculus. If the time scale represents the set of real numbers, our results reduce to integral inequalities known from the literature. On the other hand, in the setting of positive integers, we obtain new discrete inequalities for B-monotone sequences. [ABSTRACT FROM AUTHOR]

This paper considers parallel and series systems with heterogeneous components having dependent exponential lifetimes. The underlying dependence is assumed to be Archimedean and the component lifetimes are supposed to be connected according to an Archimedean copula. Sufficient conditions are found to dominate a parallel system with heterogenous exponential components, with respect to the dispersive order, by another parallel system with homogenous exponential components where the dependence structure between lifetimes of components is the same. We also compare two series systems (and two parallel systems) with general one-parameter dependent components and with respect to the usual stochastic ordering. Examples are given to illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a system of coupled wave equations featuring boundary fractional damping applied to a portion of the domain. We first establish the well-posedness of the system, proving the existence and uniqueness of solutions through semi-group theory. While the system does not exhibit exponential stability, we demonstrate its strong stability. Furthermore, leveraging Arendt and Batty's general criteria and certain geometric conditions, we prove a polynomial rate of energy decay for the solutions. [ABSTRACT FROM AUTHOR]

This paper studies some stochastic properties of random quantiles according to the newly defined reliability measure called reversed aging intensity function. Preservation property of reversed aging intensity order under random quantile is obtained and using it, a lower bound and an upper bound for the reversed aging intensity function of a random quantile are derived. Preservation of two related monotonic reliability classes under random quantiles is also studied. We finally apply our results for reliability analysis of series systems with heterogeneous component lifetimes. Examples are included to examine and analyze the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we have explored the existence and uniqueness of solutions for a pair of nonlinear fractional integro-differential equations comprising of the Ψ-Caputo fractional derivative and the Ψ-Riemann–Liouville fractional integral. These equations are subject to nonlocal boundary conditions and a variable coefficient. Our findings are drawn upon the Mittage–Leffler function, Babenko's attitude, and topological degree theory for condensing maps and the Banach contraction principle. To further elucidate our principal outcomes, we have presented two illustrative examples. [ABSTRACT FROM AUTHOR]

Strongly convex functions as a subclass of convex functions, still equipped with stronger properties, are employed through several generalizations and improvements of the Jensen inequality and the Jensen–Mercer inequality. This paper additionally provides applications of obtained main results in the form of new estimates for so-called strong f-divergences: the concept of the Csiszár f-divergence for strongly convex functions f, together with particular cases (Kullback–Leibler divergence, χ 2 -divergence, Hellinger divergence, Bhattacharya distance, Jeffreys distance, and Jensen–Shannon divergence.) Furthermore, new estimates for the Shannon entropy are obtained, and new Chebyshev-type inequalities are derived. [ABSTRACT FROM AUTHOR]

This paper offers a comprehensive analysis of solution representations for ϖ-fractional partial differential equations, specifically focusing on the linear case of the Darboux problem. We exhibit a representation of the solutions for the Darboux problem of ϖ-fractional partial differential equations in the linear case in the space of continuous functions. Through the application of the generalized Gronwall inequality, we establish the Ulam–Hyers–Rassias Mittag–Leffler stability in the space of continuous functions. Three numerical examples are presented to show the effectiveness and the applicability of our results. [ABSTRACT FROM AUTHOR]

Let p (z) be a polynomial of degree n having no zero in | z | < k , k ≤ 1 , then Govil [Proc. Nat. Acad. Sci., 50(1980), 50-52] proved max | z | = 1 | p ′ (z) | ≤ n 1 + k n max | z | = 1 | p (z) | , provided | p ′ (z) | and | q ′ (z) | attain their maxima at the same point on the circle | z | = 1 , where q (z) = z n p (1 z ‾) ‾. In this paper, we present integral mean inequalities of Turán- and Erdös-Lax-type for the polar derivative of a polynomial by involving some coefficients of the polynomial, which refine some previously proved results and one of our results improves the above Govil inequality as a special case. These results incorporate the placement of the zeros and some coefficients of the underlying polynomial. Furthermore, we provide numerical examples and graphical representations to demonstrate the superior precision of our results compared to some previously established results. [ABSTRACT FROM AUTHOR]

Inequalities play a main role in pure and applied mathematics. In this paper, we prove a generalization of Milne inequality for any measure space. The argument in the proof of this inequality allows us to obtain other Milne-type inequalities. Also, we improve the discrete version of Milne inequality, which holds for any positive value of the parameter p. Finally, we present a Milne-type inequality in the fractional context. [ABSTRACT FROM AUTHOR]

In this paper, a (p , q) -fractional nonlinear difference equation of different orders is considered and discussed. With the help of (p , q) -calculus for integrals and derivatives properties, we convert the main integral boundary value problem (IBVP) to an equivalent solution in the form of an integral equation, we use the upper–lower solution technique to prove the existence of positive solutions. We present an example of the IBVP to apply and demonstrate the results of our method. [ABSTRACT FROM AUTHOR]

This work is devoted to the analysis for a new class of set-valued inverse mixed variational inequalities (SIMVIs) in reflexive Banach spaces, when both the mapping and the constraint set are perturbed simultaneously by two parameters. Several equivalence characterizations are given for SIMVIs to have nonempty and bounded solution sets. Based on the equivalence conditions, under the premise of monotone mappings, the stability result for the SIMVIs is obtained in the reflexive Banach space. Furthermore, to illustrate the results, an example of the traffic network equilibrium control problem is provided at the end of this paper. The results presented in this paper generalize and extend some known results in this area. [ABSTRACT FROM AUTHOR]

It is known that the damped fractional wave equation has the diffusive structure as t → ∞ . Let u (t , x) = e − t cosh (t L) f (x) + e − t sinh (t L) L (f (x) + g (x)) be the solution of the Cauchy problem for the damped fractional wave equation, where L involves the fractional Laplacian (− △) α on the space variable. We can study the decay estimate of the solution u (t , x) over the time t by means of the Cauchy problem for the parabolic equation. In this paper, we consider, for 0 < α < 1 , the Cauchy problem in the two- and three-dimensional spaces for the damped fractional wave equation and the corresponding parabolic equation and obtain the Triebel–Lizorkin space estimate of the difference of solutions. At the same time, we also consider, for α = 1 , the case of the Cauchy problem in the four-dimensional space and obtain a Triebel–Lizorkin space estimate. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the following fractional p & q -Laplacian problem: { (− Δ) p s u + (− Δ) q s u = λ a (x) | u | θ − 2 u + μ b (x) | u | r − 2 u in Ω , u (x) = 0 in R N ∖ Ω , where Ω ⊂ R N is a bounded domain with smooth boundary, s ∈ (0 , 1) , (− Δ) m s (m ∈ { p , q }) is the fractional m-Laplacian operator, p , q , r , θ ∈ (1 , p s ∗ ] , p s ∗ = N p N − s p , λ , μ > 0 , and the weights a (x) and b (x) are possibly sign changing. Using the concentration compactness principle for fractional Sobolev spaces and the Ekeland variational principle, we prove that the problem admits a nonnegative solution for the critical case r = p s ∗ . Moreover, for the subcritical case r < p s ∗ , we obtain two existence results by applying the Ekeland variational principle and the mountain pass theorem. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of unified interpolative contractions of the Reich–Rus–Ćirić type and give some results about the fixed points for these mappings in the framework of relational metric spaces. We present examples where the results of some previous research are not relevant. Also, we apply our results to solving problems related to nonlinear matrix equations, emphasizing their practical importance. [ABSTRACT FROM AUTHOR]

Singular integral operators play an important role in approximation theory and harmonic analysis. In this paper, we consider a weighted Lebesgue space L p , w , define a modified Gauss–Weierstrass singular integral on it, and study direct and inverse approximation properties of the operator followed by a Korovkin-type approximation theorem for a function f ∈ L p , w . We use the modulus of continuity of the functions to measure the rate of convergence. [ABSTRACT FROM AUTHOR]

Let S n − 1 denote unit sphere in R n equipped with the normalized Lebesgue measure. Let Φ ∈ L s (S n − 1) be a homogeneous function of degree zero such that ∫ S n − 1 Φ (y ′) d σ (y ′) = 0 , where y ′ = y / | y | for any y ≠ 0 . The commutators of variable Marcinkiewicz fractional integral operator is defined as [ b , μ Φ ] β m (f) (x) = (∫ 0 ∞ | ∫ | x − y | ≤ s Φ (x − y) [ b (x) − b (y) ] m | x − y | n − 1 − β (x) f (y) d y | 2 d s s 3) 1 2. In this paper, we obtain the boundedness of the commutators of the variable Marcinkiewicz fractional integral operator on grand variable Herz spaces K ˙ p (⋅) α (⋅) , q) , θ (R n) . [ABSTRACT FROM AUTHOR]

In the present paper, we have obtained common best proximity point theorems of nonself maps in Hausdorff topological space. Further, our results extend the results due to Gerald F. Jungck, thereby proving a generalized version of Kirk's theorem (J. London Math. 1(1):107–111, 1969). [ABSTRACT FROM AUTHOR]

In this paper, a new appropriate diagonal matrix estimation of the Hessian is introduced by minimizing the Byrd and Nocedal function subject to the weak secant equation. The Hessian estimate is used to correct the framework of a nonmonotone trust region algorithm with the regularized quasi-Newton method. Moreover, to counteract the adverse effect of monotonicity, we introduce a new nonmonotone strategy. The global and superlinear convergence of the suggested algorithm is established under some standard conditions. The numerical experiments on unconstrained optimization test functions show that the new algorithm is efficient and robust. [ABSTRACT FROM AUTHOR]

We devise an iterative algorithm incorporating inertial techniques to approximate the shared solution of a generalized equilibrium problem, a fixed point problem for a finite family of relatively nonexpansive multivalued mappings, and a variational inequality problem. Our discussion encompasses the strong convergence of the proposed algorithm and highlights specific outcomes derived from our theorem. Additionally, we provide a computational analysis to underscore the significance of our findings and draw comparisons. The results presented in this paper serve to extend and unify numerous previously established outcomes in this particular research domain. [ABSTRACT FROM AUTHOR]

This paper presents various bifurcations of the McMillan map under perturbations of its coefficients, such as period-doubling, pitchfork, and hysteresis bifurcation. The associated existence regions are located. Using the quasi-Lyapunov function method, the existence of asymptotically stable fixed point is also demonstrated. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of a quasimodular and we prove that the respective Minkowski functional of the unit quasimodular ball becomes a quasinorm. In this way, we refer to and complete the well-known theory related to the notions of a modular and a convex modular that lead to the F-norm and to the norm, respectively. We use the obtained results to consider the basic properties of quasinormed Calderón–Lozanovskiĭ spaces E φ , where the lower Matuszewska–Orlicz index α φ plays the key role. Our studies are conducted in a full possible generality. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce two new subclasses R sin m (ℑ) and R sin (ℑ) of analytic functions by making use of subordination involving the sine function and the modified sigmoid activation function ℑ (v) = 2 1 + e − v , v ≥ 0 in the open unit disc E. Our purpose is to obtain some initial coefficients, Fekete–Szego problems, and upper bounds for the third- and fourth-order Hankel determinants for the functions belonging to these two classes. All the bounds that we will find here are sharp. We also highlight some known consequences of our main results. [ABSTRACT FROM AUTHOR]

The notion of A -condensing operators via the measure of noncompactness is proposed, which retains the existing classes of condensing operators. Results concerning the existence of the best proximity point (pair) of cyclic (noncyclic) A -condensing operators along with the coupled best proximity-point theorem for cyclic A -condensing operators have been formulated. An application to a (k , ℷ) -Hilfer fractional differential equation of order 2 < p < 3 , type q ∈ [ 0 , 1 ] satistfying some boundary conditions is presented. The paper is the first to investigate the optimum solution of such a generalized fractional differential equation. The hypothesis involved in the investigation is independent of the incorporated measure of noncompactness, thereby making our result better in application than that present in the literature. Moreover, added numerical examples validate the theoretical conclusions. [ABSTRACT FROM AUTHOR]

In this paper, we establish a novel category of sequence spaces ℓ p q λ and ℓ ∞ q λ by utlizing q-analogue Λ q of Λ-matrix. Our investigation outlines several topological characteristics and inclusion results of these newly introduced sequence spaces, specifically identifying them as BK-spaces. Subsequently, we demonstrate that these novel sequence spaces are of nonabsolute type and establish their isometric isomorphism with ℓ p and ℓ ∞ . Moreover, we obtain the α-, β-, and γ-duals of these sequence spaces. We further characterize the class (ℓ p q λ , X) of matrices, where X is any of the spaces ℓ ∞ , c, or c 0 . Lastly, our study delves into the exploration of specific geometric properties exhibited by the space ℓ p q λ . [ABSTRACT FROM AUTHOR]

In this paper, we establish some reversed dynamic inequalities of Hilbert type on time scales nabla calculus by applying reversed Hölder's inequality, chain rule on time scales, and the mean inequality. As particular cases of our results (when T = N and T = R ), we get the reversed form of discrete and continuous inequalities proved by Chang-Jian, Lian-Ying and Cheung (Math. Slovaca 61(1):15–28, 2011). [ABSTRACT FROM AUTHOR]

In this paper, a modification of general linear positive operators introduced by Ibragimov and Gadjiev in 1970 is constructed. It is shown that this modification preserves exponential mappings and also contains modified Bernstein-, Szász- and Baskakov-type operators as special cases. The convergence properties of corresponding operators on [ 0 , ∞) and in exponentially weighted spaces are investigated. Finally, the quantitative Voronovskaja theorem in terms of modulus of continuity for functions having exponential growth is examined. [ABSTRACT FROM AUTHOR]

The coronavirus disease 2019 (COVID-19) remains serious around the world and causes huge deaths and economic losses. Understanding the transmission dynamics of diseases and providing effective control strategies play important roles in the prevention of epidemic diseases. In this paper, to investigate the effect of delays on the transmission of COVID-19, we propose a delayed SEIR model to describe COVID-19 virus transmission, where two delays indicating the incubation and recovery periods are introduced. For this system, we prove its solutions are nonnegative and ultimately bounded with the nonnegative initial conditions. Furthermore, we calculate the disease-free and endemic equilibrium points and analyze the asymptotical stability and the existence of Hopf bifurcations at these equilibrium points. Then, by taking the weighted sum of the opposite number of recovered individuals at the terminal time, the number of exposed and infected individuals during the time horizon, and the system cost of control measures as the cost function, we present a delay optimal control problem, where two controls represent the social contact and the pharmaceutical intervention. Necessary optimality conditions of this optimal control problem are exploited to characterize the optimal control strategies. Finally, numerical simulations are performed to verify the theoretical analysis of the stability and Hopf bifurcations at the equilibrium points and to illustrate the effectiveness of the obtained optimal strategies in controlling the COVID-19 epidemic. [ABSTRACT FROM AUTHOR]

In this paper, we obtain several results on the global existence, uniqueness and attractivity for fractional evolution equations involving the Riemann-Liouville type by exploiting some results on weakly singular integral inequalities in Banach spaces. Some boundedness conditions of the nonlinear term are considered to obtain the main results that generalize and improve some well-known works. [ABSTRACT FROM AUTHOR]

In this paper, motivated by Reich contraction and tool of measure of noncompactness, some generalizations of Reich, Kannan, Darbo, Sadovskii, and Krasnoselskii type fixed point results are presented by considering a pair of maps A, B on a nonempty closed subset M of a Banach space X into X. The existence of a solution to the equation A x + B x = x , where A is k-set contractive and B is a generalized Reich contraction, is established. As applications, it is established that the main result of this paper can be applied to learn conditions under which a solution of a nonlinear integral equation exists. Further we explain this phenomenon with the help of a practical example to approximate such solutions by using fixed point techniques. The graphs of exact and approximate solutions are also given to attract readers for further research activities. [ABSTRACT FROM AUTHOR]

This paper presents noise-induced transitions in a stochastic avian influenza model with Allee effect. In the deterministic case, one of three disease-free equilibria is always globally asymptotically stable in its attractive domain, and there is a unique endemic equilibrium when the basic reproduction number R 0 > 1 . In the stochastic case, a new dynamic phenomenon of noise-induced transition can be observed, that is, the stochastic trajectory can exit from the neighborhood of the epidemic equilibrium and pass into the vicinity of the trivial equilibrium. More precisely, in this paper, based on the stochastic sensitivity function technique, we construct the confidence ellipse and then estimate the critical value of the noise intensity leading to extinction. We also propose useful control strategies to prevent the noise-induced extinction. [ABSTRACT FROM AUTHOR]

Recently, Baktash et al. (2008) proved the stability of the cubic functional equation f(2x+y)+f(2x-y) = 2f(x + y) ( 2f(x - y) + 12f(x) and the quartic functional equation f(2x+y) + f(2x - y) = 4f(x+y)+4f(x-y)+24f(x)-6f(y) in random normed spaces. In this note, we correct the proofs. [ABSTRACT FROM AUTHOR]

In this paper, we introduce new types of contraction mappings named S-Pata-type contraction mapping and Generalized S-Pata-type contraction mapping in the framework of S-metric space. Then, we prove some new fixed-point results for S-Pata-type contraction mappings and Generalized S-Pata-type contraction mappings. To support our results, we provide examples to illustrate our findings and also apply these results to the ordinary differential equation to strengthen our conclusions. [ABSTRACT FROM AUTHOR]

In this paper, we prove an equality for twice-differentiable convex functions involving the conformable fractional integrals. Moreover, several Bullen-type inequalities are established for twice-differentiable functions. More precisely, conformable fractional integrals are used to derive such inequalities. Furthermore, sundry significant inequalities are obtained by taking advantage of the convexity, Hölder inequality, and power-mean inequality. Finally, we provide our results by using special cases of obtained theorems. [ABSTRACT FROM AUTHOR]

The Ruscheweyh derivative operator is used in this paper to introduce and investigate interesting general subclasses of the function class Σ m of m-fold symmetric bi-univalent analytic functions. Estimates of the initial Taylor-Maclaurin coefficients | a m + 1 | and | a 2 m + 1 | are obtained for functions of the subclasses introduced in this study, and the consequences of the results are discussed. Additionally, the Fekete-Szegö inequalities for these classes are investigated. The results presented could generalize and improve some recent and earlier works. In some cases, our estimates are better than the existing coefficient bounds. Furthermore, within the engineering domain, the utilization of the Ruscheweyh derivative operator can encompass a broad spectrum of engineering applications, including the robotic manipulation control, optimizing optical systems, antenna array signal processing, image compression, and control system filter design. It emphasizes the potential for innovative solutions that can significantly enhance the reliability and effectiveness of engineering applications. [ABSTRACT FROM AUTHOR]

In this paper, we study several properties of an orthonormal basis { N n (z) } for the Newton space N 2 (P) . In particular, we investigate the product of N m and N m and the orthogonal projection P of N n ‾ N m that maps from L 2 (P) onto N 2 (P) . Moreover, we find the matrix representation of Toeplitz operators with respect to such an orthonormal basis on the Newton space N 2 (P) . [ABSTRACT FROM AUTHOR]

We explore the intermixed method for finding a common element of the intersection of the solution set of a mixed variational inequality and the fixed point set of a nonexpansive mapping. We point out that Khuangsatung and Kangtunyakarn's statement [J. Inequal. Appl. 2023:1, 2023] regarding the resolvent utilized in their paper is not correct. To resolve this gap, we employ the epigraphical projection and the product space approach. In particular, we obtain a strong convergence theorem with a weaker assumption. [ABSTRACT FROM AUTHOR]