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In this article, a class of cyclic (noncyclic) operators are defined on Banach spaces via concept of measure of noncompactness using some abstract functions. The best proximity point (pair) results are manifested for the said operators. The obtained main results are applied to demonstrate the existence of optimum solutions of a system of fractional differential equations involving (k,ψ)\left(k,\psi )-Hilfer fractional derivatives.

This paper derives some generalized Schur-type stability results of polynomials based on several forms and generalizations of the Eneström–Kakeya theorem combined with the Rouché theorem. It is first investigated, under sufficiency-type conditions, the derivation of the eventually generalized Schur stability sufficient conditions which are not necessarily related to the zeros of the polynomial lying in the unit open circle. In a second step, further sufficient conditions were introduced to guarantee that the above generalized Schur stability property persists within either the same above complex nominal stability region or in some larger one. The classical weak and, respectively, strong Schur stability in the closed and, respectively, open complex unit circle centred at zero are particular cases of their corresponding generalized versions. Some of the obtained and proved results are further generalized "ad hoc" for the case of quasi-polynomials whose zeros might be interpreted, in some typical cases, as characteristic zeros of linear continuous-time delayed time-invariant dynamic systems with commensurate constant point delays. [ABSTRACT FROM AUTHOR]

This paper considers a nominal undelayed and time-varying second-order Sturm–Liouville differential equation on a finite time interval which is a nominal version of another perturbed differential equation subject to a delay in its dynamics. The nominal delay-free differential equation is a Sturm–Liouville system in the sense that it is subject to prescribed two-point boundary conditions. However, the perturbed differential system is not a Sturm–Liouville system, in general, due to the presence of delayed dynamics. The main objective of the paper is to investigate the loss of the boundary values of the Sturm–Liouville nominal undelayed system in the presence of the delayed dynamics. Such a delayed dynamics is considered a perturbation of the nominal dynamics related to the Sturm–Liouville system with given two-point boundary values. In particular, this loss of the Sturm–Liouville exact tracking of the prescribed two-point boundary values might happen because the nominal boundary values may become lost by the state trajectory solution in the presence of delays, related to the undelayed case, due to the presence of the delayed dynamics. The worst-case error description of the deviation of the two-point boundary values of the current perturbed differential with respect to those of the nominal Sturm–Liouville system is characterized in terms of error norms related to the nominal system. Under sufficiently small deviations of the parameterization of the perturbed system with respect to the nominal one, such a worst-error characterization makes the current perturbed system an approximate Sturm–Liouville system of the nominal undelayed one. [ABSTRACT FROM AUTHOR]

We get the strong and Δ\Delta -convergence of the Picard-Krasnoselskii hybrid iteration scheme to a fixed point of a self-map endowed with the condition (Bγ,μ)\left({B}_{\gamma ,\mu }). We use the nonlinear context of CAT(0) spaces for establishing these results. We present a new example of a self-map endowed with (Bγ,μ)\left({B}_{\gamma ,\mu }) condition and prove that its Picard-Krasnoselskii hybrid iterative process is more effective than the Picard and Krasnoselskii hybrid iterative processes. This improves and extends some recently announced results of the current literature.

For the classical Jensen inequality of convex functions, i.e., [Formula: see text] an equivalent condition is proved in the framework of the generalized Sugeno integral. Also, the necessary and sufficient conditions for the validity of the discrete form of the Jensen inequality for the generalized Sugeno integral are given.

Some boundedness and convergence properties of generalized Fibonacci's‐type recurrences and their associated iterated recurrence ratios between pairs of consecutive terms are discussed under a wide number of initial conditions. Also, a more general, so‐called (k, q) Fibonacci's recurrence and the associated Fibonacci's ratio recurrences are investigated, where the constants k and q are the prefixed gains used to generate each new member of the recurrences from the two preceding ones. Some oscillation and periodicity conditions are also discussed depending on the initial conditions, while convergence and stability properties are also dealt with. The initial conditions of the recurrences can be fixed arbitrarily, so that both the well‐known standard Fibonacci recurrence and the Lucas recurrence are just particular cases. In the most general case, the initial conditions can be integer or real and of alternate signs. Later on, the manuscript deals with some further boundedness, oscillation, convergence, and stability properties of generalized Fibonacci recurrences and associated Fibonacci ratio recurrences being generated under, in general, recurrence‐dependent gain sequences. [ABSTRACT FROM AUTHOR]

This present work develops a nonlinear SIRS fractional-order model with a system of four equations in the Caputo sense. This study examines the impact of positive and negative attitudes towards vaccination, as well as the role of government actions, social behavior and public reaction on the spread of infectious diseases. The local stability of the equilibrium points is analyzed. Sensitivity analysis is conducted to calculate and discuss the sensitivity index of various parameters. It has been established that the illness would spread across this system when the basic reproduction number is larger than 1, the system becomes infection-free when the reproduction number lies below its threshold value of 1. Numerical figures depict the effects of positive and negative attitudes towards vaccination to make the system disease-free sooner. A comprehensive study regarding various values of the order of fractional derivatives together with integer-order derivatives has been discussed in the numerical section to obtain some useful insights into the intricate dynamics of the proposed system. The Pontryagin principle is used in the formulation and subsequent discussion of an optimum control issue. The study also reveals the significant role of government actions in controlling the epidemic. A numerical analysis has been conducted to compare the system's behavior under optimal control and without optimal control, aiming to discern their differences. The policies implemented by the government are regarded as the most adequate control strategy, and it is determined that the execution of control mechanisms considerably diminishes the ailment burden. [ABSTRACT FROM AUTHOR]

The collaborative R&D of new products between enterprises is prone to the "free‐rider effect" due to knowledge spillover. To avoid that, this paper establishes a three‐stage dynamic game to explore the collaborative R&D co‐competition behavior between asymmetric horizontal supplier enterprises. In this paper, we incorporate the uncertainty of R&D success probability into the model and reverse induction is applied to solve it. In the model, two asymmetric enterprises play dynamic games under three modes: complete noncooperation, semicooperation, and complete cooperation. We discuss the sensitivity of various asymmetric factors to the R&D investment level and profit of enterprises. The results indicate that the R&D investment level of supplier enterprises is positively correlated with the absorptive capacity, technology spillover, and R&D success probability, and negatively correlated with the initial R&D investment and innovation efficiency under the three co‐competition modes. Especially, when the absorptive capacity of the enterprise or the degree of technological spillover of the other party exceeds a certain value, the profits of the enterprise in the mode of complete noncooperation and semicooperation will intersect, which can easily lead to "free‐riding" behavior. It provides a decision‐making basis for the direction and extent of enterprises' R&D efforts. In addition, some methods are proposed to improve the level of R&D investment and increase the income of enterprises under three modes. [ABSTRACT FROM AUTHOR]

We consider the class of functions u ∈ C²((0, ∞)) satisfying second-order differential inequalities in the form u'(x) + k/x²u(x) ≥ 0 for all x > 0. For this class of functions, we establish Hermite-Hadamard-type inequalities in both cases (k = 1/4 and 0 < k < 1/4 ). We next extend our obtained results to the two-dimensional case. In the limit case k → 0+ we deriver some existing results from the literature that are related to convex functions and convex functions on the coordinates. In our approach, we make use of some tools from ordinary differential equations. [ABSTRACT FROM AUTHOR]

Many scholars have lately explored fractional-order boundary value issues with a variety of conditions, including classical, nonlocal, multipoint, periodic/anti-periodic, fractional-order, and integral boundary conditions. In this manuscript, the existence and uniqueness of solutions to sequential fractional differential inclusions via a novel set of nonlocal boundary conditions were investigated. The existence results were presented under a new class of nonlocal boundary conditions, Carath'eodory functions, and Lipschitz mappings. Further, fixed-point techniques have been applied to study the existence of results under convex and non-convex multi-valued mappings. Ultimately, to support our findings, we analyzed an illustrative example. [ABSTRACT FROM AUTHOR]