We introduce and analyze a hybrid iterative algorithm by virtue of Korpelevich's extragradient method, viscosity approximation method, hybrid steepest-descent method, and averaged mapping approach to the gradient-projection algorithm. It is proven that under appropriate assumptions, the proposed algorithm converges strongly to a common element of the fixed point set of infinitely many nonexpansive mappings, the solution set of finitely many generalized mixed equilibrium problems (GMEPs), the solution set of finitely many variational inequality problems (VIPs), the solution set of general system of variational inequalities (GSVI), and the set of minimizers of convex minimization problem (CMP), which is just a unique solution of a triple hierarchical variational inequality (THVI) in a real Hilbert space. In addition, we also consider the application of the proposed algorithm to solve a hierarchical fixed point problem with constraints of finitely many GMEPs, finitely many VIPs, GSVI, and CMP. The results obtained in this paper improve and extend the corresponding results announced by many others.
We first introduce and analyze one implicit iterative algorithm for finding a solution of the minimization problem for a convex and continuously Fréchet differentiable functional, with constraints of several problems: the generalized mixed equilibrium problem, the system of generalized equilibrium problems, and finitely many variational inclusions in a real Hilbert space. We prove strong convergence theorem for the iterative algorithm under suitable conditions. On the other hand, we also propose another implicit iterative algorithm for finding a fixed point of infinitely many nonexpansive mappings with the same constraints, and derive its strong convergence under mild assumptions. Θ ( , ) + ( ) − ( ) + ⟨ , − ⟩ ≥ 0, ∀ ∈ . (4)We denote the set of solutions of GMEP (4) by GMEP (Θ, , ).We assume as in [1] that Θ : × → R is a bifunction satisfying conditions (H1)-(H4) and : → R is a lower semicontinuous and convex function with restriction (H5), where (H1) Θ( , ) = 0 for all ∈ ;
To cite this article: Cheng-Wen Liao (2009) Service quality and customers' satisfaction of the food and beverage industry, Journal of Statistics and Management Systems, 12:4, 759-774,
AbstractThe technical entry barrier of the food and beverage industry is low and therefore, it is often the first choice for entrepreneurial. However, due to the ease of imitations and fierce competition, short-lived restaurants and closures are nothing new. Restaurants are faced with many uncertainties because their consumers come far and wide and the information is asymmetric.This paper collected data with a questionnaire survey, and the questionnaire consisted of three parts: (1) the measurement of the personal data of consumers; (2) the attributes of service quality provided by restaurants with assessments provided by consumers after meals; this section is to gain an understanding of the levels of customers' satisfactions as a whole; (3) the relevant consumption experience of customers. This study focused on the items outlined by the survey SERVQUAL on service quality. Meanwhile, other important items based on the characteristics of the food and beverage industry were included to facilitate the research and analysis with better accuracy. An analysis of SPSS was performed so as to derive an accurate analysis result.The conclusion suggested that there are differences in the service quality perceived by customers and the reality based on the assessments concerning the levels of satisfaction and emphasis. The priorities for the satisfaction in service quality are the cleanness of the environment, the comfort of seats, and safety and hygiene. The priorities for the emphasis on service quality are the cleanness of the environment, accuracy of billing, language of greetings and safety and hygiene.
This paper is concerned with the existence of mild and strong solutions on the interval [0, 𝑇] for some neutral partial differential equations with nonlocal conditions. The linear part of the equations is assumed to generate a compact analytic semigroup of bounded linear operators, whereas the nonlinear part satisfies the Carathëodory condition and is bounded by some suitable functions. We first employ the Schauder fixed-point theorem to prove the existence of solution on the interval [𝛿, 𝑇] for 𝛿 > 0 that is small enough, and, then, by letting 𝛿 → 0 and using a diagonal argument, we have the existence results on the interval [0, 𝑇]. This approach allows one to drop the compactness assumption on a nonlocal condition, which generalizes recent conclusions on this topic. The obtained results will be applied to a class of functional partial differential equations with nonlocal conditions.
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