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The purpose of this paper is to study the coupled fixed point problem and the coupled best proximity problem for single-valued and multi-valued contraction type operators defined on cyclic representations of the space. The approach is based on fixed point results for appropriate operators generated by the initial problems. [ABSTRACT FROM AUTHOR]

Abstract We approximate the fixed points of contraction mappings using the Picard–Krasnoselskii hybrid iterative process, which is known to converge faster than all of Picard, Mann and Ishikawa iterations in complex valued Banach spaces. Moreover, we prove analytically and with a numerical example that the Picard–Mann hybrid iteration and the Picard–Krasnoselskii hybrid iteration have the same rate of convergence. Furthermore, we apply our results in finding solutions of delay differential equations in complex valued Banach spaces. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Harbin Institute of Technology. Social Sciences Edition / Haerbin Gongye Daxue Xuebao. Shehui Kexue Ban is the property of Harbin Institute of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

To reduce the complexity of program comprehension such as program standardization and program matching, a program comprehension oriented construction algorithm of system dependence graph is proposed. This algorithm can be divided into three stages: program information extraction, control dependence sub - graph construction and data dependence sub-graph construction. Control dependency and data dependency are independently computed. Data flow is directly analyzed based on control dependent sub-graph without extra control flow graph, and computed on demand, which reduces the algorithm complexity. Selection statements and loop statements are uniformly represented, and expressions are represented as abstract syntax trees, which can facilitate program transformation and analysis: The system dependence graph has been used in automatic grading system of student programs and program recognition. Application results show that it can facilitate program comprehension and analysis and reduce the complexity of program comprehension and analysis. [ABSTRACT FROM AUTHOR]

In order to correctly analyze the control dependence and data dependence relations of C program, and then can out the program slicing, code redundancy and code duplication detection, a method to extract the static information of C program from GCC AST text was put forward. Firstly, the GCC AST text was standardized and the nodes unrelated to control dependence and data dependence analysis were eliminated. Secondly, control dependence subgraph was constructed. If data flow analysis was necessary, control flow graph was constructed based on control dependence subgraph and data dependence subgraph was constructed based on control flow graph. At last, by the introduction of inter-process analysis, system dependence graph was improved. It is indicated that the research can correctly analyze the control dependence and data dependence relations. [ABSTRACT FROM AUTHOR]

Program slicing is a useful technique for debugging, testing and program integration. Intuitively, by the slice of a program P is meant, for a point n and a variable v in P, the set of statements and expressions in P that affect the value of v at n. To determine a slice, there must be a precise analysis of the dependencies among the statements in the program. It is difficult, on the other hand, to analyze the program containing recursions. This paper presents a static analysis for the dependencies in the program containing recursion, as well as the algorithm to determine the slice based on the result of the analysis. To cope with the recursive definition of the procedure, the proposed algorithm assumes the interprocedure information needed in the computation. This information is modified to the correct direction, and the process is iterated until the result converges. The program dependence graph is extended to hold the interprocedure information. Compared to the conventional algorithm, the proposed algorithm can analyze efficiently the program containing recursions, and can be used in the system to provide interactively the slice information. [ABSTRACT FROM AUTHOR]