Graph convergence for the H(·, ·)-accretive operator in Banach spaces with an application

In this paper, a concept of graph convergence concerned with the H(·, ·)-accretive operator is introduced in Banach spaces and some equivalence theorems between of graph-convergence and resolvent operator convergence for the H(·, ·)-accretive operator sequence are proved. As an application, a perturbed algorithm for solving a class of variational inclusions involving the H(·, ·)-accretive operator is constructed. Under some suitable conditions, the existence of the solution for the variational inclusions and the convergence of iterative sequence generated by the perturbed algorithm are also given.     

Generalized composition operators from F(p, q, s) spaces to Bloch-type spaces

Let H(B) denote the space of all holomorphic functions on the unit ball B of Cⁿ. Let φ be a holomorphic self-map of B and g ∈ H(B) such that g(0) = 0. In this paper, we investigate the boundedness and compactness of the generalized composition operator

     

Projection algorithms for the system of generalized mixed variational inequalities in Banach spaces

Some projection algorithms are suggested for solving the system of generalized mixed variational inequalities, and the convergence of the proposed iterative methods are proved without any monotonicity assumption for the mappings in Banach spaces. Our theorems generalize some known results.     

Composition operators from F(p, q, s) spaces to the nth weighted-type spaces on the unit disc

In this note we characterize the boundedness and compactness of the composition operator from the general function space F(p, q, s) to the nth weighted-type space on the unit disk, where the nth weighted-type space has been recently introduced by Stevo Stevi?.     

System of generalized variational inclusions with -accretive operators in uniformly smooth Banach spaces

In this paper, we consider and study a system of generalized variational inclusions with H-accretive operators in uniformly smooth Banach spaces. We prove the convergence of iterative algorithm for this system of generalized variational inclusions. A new definition of H-resolvent operator as a retraction is introduced, and in support of the definition, we have constructed an example and a numerical example through Matlab programming. Some special cases are also discussed.     

Soliton solutions for (2 + 1)-dimensional and (3 + 1)-dimensional K(m, n) equations

We consider the nonlinear dispersive K(m,n) equation with the generalized evolution term and derive analytical expressions for some conserved quantities. By using a solitary wave ansatz in the form of sech^p function, we obtain exact bright soliton solutions for (2 + 1)-dimensional and (3 + 1)-dimensional K(m,n) equations with the generalized evolution terms. The results are then generalized to multi-dimensional K(m,n) equations in the presence of the generalized evolution term. An extended form of the K(m,n) equation with perturbation term is investigated. Exact bright soliton solution for the proposed K(m,n) equation having higher-order nonlinear term is determined. The physical parameters in the soliton solutions are obtained as function of the dependent model coefficients.     

The existence and uniqueness of solution and the convergence of a multi-step iterative algorithm for a system of variational inclusions with (<Emphasis Type="Italic">A</Emphasis>, <Emphasis Type="Italic">η</Emphasis>, <Emphasis Type="Italic">m</Emphasis>)-accretive operators

In this paper, we introduce and study a new system of variational inclusions with (A, η, m)-accretive operators which contains variational inequalities, variational inclusions, systems of variational inequalities and systems of variational inclusions in the literature as special cases. By using the resolvent technique for the (A, η, m)-accretive operators, we prove the existence and uniqueness of solution and the convergence of a new multi-step iterative algorithm for this system of variational inclusions in real q-uniformly smooth Banach spaces. The results in this paper unifies, extends and improves some known results in the literature.      

Reliability of a consecutive (r, s)-out-of-(m, n):F lattice system with conditions on the number of failed components in the system

A consecutive(r, s)-out-of-(m, n):F lattice system which is defined as a two-dimensional version of a consecutive k-out-of-n:F system is used as a reliability evaluation model for a sensor system, an X-ray diagnostic system, a pattern search system, etc. This system consists of m × n components arranged like an (m, n) matrix and fails iff the system has an (r, s) submatrix that contains all failed components. In this paper we deal a combined model of a k-out-of-mn:F and a consecutive (r, s)-out-of-(m, n):F lattice system. Namely, the system has one more condition of system down, that is the total number of failed components, in addition to that of a consecutive (r, s)-out-of-(m, n):F lattice system. We present a method to obtain reliability of the system. The proposed method obtains the reliability by using a combinatorial equation that does not depend on the system size. Some numerical examples are presented to show the relationship between component reliability and system reliability.     

Recursive algorithm for the reliability of a connected-(1, 2)-or-(2, 1)-out-of-(m, n):F lattice system

The connected-(1, 2)-or-(2, 1)-out-of-(m, n):F lattice system is included by the connected-X-out-of-(m, n):F lattice system defined by Boehme et al. [Boehme, T.K., Kossow, A., Preuss, W., 1992. A generalization of consecutive-k-out-of-n:F system. IEEE Transactions on Reliability 41, 451–457]. This system fails if and only if at least one subset of connected failed components occurs which includes at least a (1, 2)-matrix (that is, a row and two columns) or a (2, 1)-matrix(that is, two rows and a column) of failed components. This system is applied to two-dimensional network problems with adjacent constraints, and various systems, for example, a supervision system, etc.     

The equivalence of curves in SL(n, R) and its application to ruled surfaces

The generating system of the differential algebra for invariant differential polynomials with two parametric curves is obtained. Conditions for the equivalence of two parametric curves families are given. We are also proved that the generating differential invariants of two parametric curves are independent. Finally, we reduce the SL(n, R)-equivalent problem for ruled surfaces to that of parametric curves.     

Iterative approximation of a solution of multi-valued variational-like inclusion in Banach spaces: A P-η-proximal-point mapping approach

In this paper, we introduce a class of P-η-accretive mappings, an extension of η-m-accretive mappings [C.E. Chidume, K.R. Kazmi, H. Zegeye, Iterative approximation of a solution of a general variational-like inclusion in Banach spaces, Int. J. Math. Math. Sci. 22 (2004) 1159-1168] and P-accretive mappings [Y.-P. Fang, N.-J. Huang, H-accretive operators and resolvent operator technique for solving variational inclusions in Banach spaces, Appl. Math. Lett. 17 (2004) 647-653], in real Banach spaces. We prove some properties of P-η-accretive mappings and give the notion of proximal-point mapping, termed as P-η-proximal-point mapping, associated with P-η-accretive mapping. Further, using P-η-proximal-point mapping technique, we prove the existence of solution and discuss the convergence analysis of iterative algorithm, for multi-valued variational-like inclusions in real Banach space. The theorems presented in this paper extend and improve many known results in the literature.     

On contracts for VMI program with continuous review (r, Q) policy

Based on continuous review (r, Q) policy, this paper deals with contracts for vendor managed inventory (VMI) program in a system comprising a single vendor and a single retailer. Two business scenarios that are popular in VMI program are “vendor with ownership” and “retailer with ownership”. Taking the system performance in centralized control as benchmark, we define a contract “perfect” if the contract can enable the system to be coordinated and can guarantee the program to be trusted. A revenue sharing contract is designed for vendor with ownership, and a franchising contract is designed for retailer with ownership. Without consideration of order policy and related costs at the vendor site, it is shown that one contract can perform satisfactorily and the other one is a perfect contract. With consideration of order policy and related costs at the vendor site, it is shown that one contract can perform satisfactorily and the performance of the other one depends on system parameters.     

The <Emphasis Type="Italic">p</Emphasis>-step iterative algorithm for a system of generalized mixed quasi-variational inclusions with (<Emphasis Type="Italic">H</Emphasis>,η)-monotone operators

In this paper, we introduce and study a new system of generalized mixed quasi-variational inclusions with (H,η)-monotone operators which contains variational inequalities, variational inclusions, systems of variational inequalities and systems of variational inclusions in the literature as special cases. By using the resolvent technique for the (H,η)-monotone operators, we prove the existence of solutions and the convergence of some new p-step iterative algorithms for this system of generalized mixed quasi-variational inclusions and its special cases. The results in this paper unifies, extends and improves some known results in the literature.     

An algorithm for mean residual life computation of (n − k + 1)-out-of-n systems: An application of exponentiated Weibull distribution

In this paper, we establish an algorithm for the computation of the mean residual life of a (n − k + 1)-out-of-n system in the case of independent but not necessarily identically distributed lifetimes of the components. An application for the exponentiated Weibull distribution is given to study the effect of various parameters on the mean residual life of the system. Also the relationship between the mean residual life for the system and that of its components is investigated.     

A simple cost minimization procedure for the (Q, r) inventory system with a specified fixed cost per stockout occasion

For fast-moving A items, Silver et al. [E.A. Silver, D.F. Pyke, R. Peterson, Inventory Management and Production Planning and Scheduling, third ed., John Wiley & Sons, New York, NY, 1998] explore the (Q, r) inventory system with a specified cost per stockout occasion. However, a number of difficulties have impeded the implement of their solution procedure. That is, the total relevant cost function is not convex in general, so the convergence of the Silver et al.’s solution procedure to the optimal solution of the total relevant cost function is not necessarily true. An easier and more accurate solution procedure is proposed to overcome the shortcoming of the Silver et al.’s solution procedure.     

A parallel projection method for a system of nonlinear variational inequalities

In this paper, we introduce and consider a new system of nonlinear variational inequalities involving two different operators. Using the parallel projection technique, we suggest and analyze an iterative method for this system of variational inequalities. We establish a convergence result for the proposed method under certain conditions. Our results can be viewed as a refinement and improvement of the previously known results for variational inequalities.     

The p-step iterative algorithm for a system of generalized mixed quasi-variational inclusions with -accretive operators in q-uniformly smooth banach spaces

In this paper, we introduce and study a new system of generalized mixed quasi-variational inclusions with (A,η)-accretive operators in q-uniformly smooth Banach spaces. By using the resolvent operator technique associated with (A,η)-accretive operators, we construct a new p-step iterative algorithm for solving this system of generalized mixed quasi-variational inclusions in real q-uniformly smooth Banach spaces. We also prove the existence of solutions for the generalized mixed quasi-variational inclusions and the convergence of iterative sequences generated by algorithm. Our results improve and generalize many known corresponding results.