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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.

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]

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.

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]

We introduce the class of ψ-convex functions f: [0, ∞) → R, where ψ ∈ C([0, 1]) satisfies ψ ≥ 0 and ψ(0) ̠ ψ(1). This class includes several types of convex functions introduced in previous works. We first study some properties of such functions. Next, we establish a double Hermite-Hadamard-type inequality involving ψ-convex functions and a Simpson-type inequality for functions f ∈ C¹([0, ∞)) such that |f'| is ψ-convex. Our obtained results are new and recover several existing results from the literature. [ABSTRACT FROM AUTHOR]

This research relies on several kinds of Volterra-type integral differential systems and their associated stability concerns under the impulsive effects of the Volterra integral terms at certain time instants. The dynamics are defined as delay-free dynamics contriobution together with the contributions of a finite set of constant point delay dynamics, plus a Volterra integral term of either a finite length or an infinite one with intrinsic memory. The global asymptotic stability is characterized via Krasovskii–Lyapuvov functionals by incorporating the impulsive effects of the Volterra-type terms together with the effects of the point delay dynamics. [ABSTRACT FROM AUTHOR]