Small firm auditing using the analytical procedures (APs) in a politically challenging context

Purpose This study aims to explore the use, effectiveness, motives and obstacles of analytical procedures (APs) used by auditors in Palestine, a context characterised by a pool of small and medium enterprises (SMEs), a limited skill set, poor quality of data, political uncertainty and a community-based business culture. Design/methodology/approach The study considers the audit market in Palestine using a sequential mixed-methods approach combining a questionnaire survey and a series of in-depth interviews. A total of 129 Big-4 and non-Big-4 auditors were surveyed. Findings The use of APs is driven by the auditor size (Big-4 vs non-Big-4) and the client size (large vs SMEs). Even though the use of APs has increased over the past decade, audit objectives, know-how, and personal, family and social connections among auditors and clients influence the quality of the audit process. Practical implications Small firms take advantage of the lack of audit governance in Palestine. Our findings suggest that the regulators should help bridge the knowledge-sharing programmes between the small and large audit firms to help improve audit quality. Originality/value Studies on audit quality, particularly using APs, in the context of politically unstable cases such as Palestine are limited. The study has implications for the use of APs in the case of SMEs to prepare for the technological revolution that will modernise audit procedures and quality soon

Time-Fractional Optimal Control of Initial Value Problems on Time Scales

We investigate Optimal Control Problems (OCP) for fractional systems involving fractional-time derivatives on time scales. The fractional-time derivatives and integrals are considered, on time scales, in the Riemann--Liouville sense. By using the Banach fixed point theorem, sufficient conditions for existence and uniqueness of solution to initial value problems described by fractional order differential equations on time scales are known. Here we consider a fractional OCP with a performance index given as a delta-integral function of both state and control variables, with time evolving on an arbitrarily given time scale. Interpreting the Euler--Lagrange first order optimality condition with an adjoint problem, defined by means of right Riemann--Liouville fractional delta derivatives, we obtain an optimality system for the considered fractional OCP. For that, we first prove new fractional integration by parts formulas on time scales.Comment: This is a preprint of a paper accepted for publication as a book chapter with Springer International Publishing AG. Submitted 23/Jan/2019; revised 27-March-2019; accepted 12-April-2019. arXiv admin note: substantial text overlap with arXiv:1508.0075

Fixed point results for generalized cyclic contraction mappings in partial metric spaces

Rus (Approx. Convexity 3:171–178, 2005) introduced the concept of cyclic contraction mapping. P˘acurar and Rus (Nonlinear Anal. 72:1181–1187, 2010) proved some fixed point results for cyclic φ-contraction mappings on a metric space. Karapinar (Appl. Math. Lett. 24:822–825, 2011) obtained a unique fixed point of cyclic weak φ- contraction mappings and studied well-posedness problem for such mappings. On the other hand, Matthews (Ann. New York Acad. Sci. 728:183–197, 1994) introduced the concept of a partial metric as a part of the study of denotational semantics of dataflow networks. He gave a modified version of the Banach contraction principle, more suitable in this context. In this paper, we initiate the study of fixed points of generalized cyclic contraction in the framework of partial metric spaces. We also present some examples to validate our results.S. Romaguera acknowledges the support of the Ministry of Science and Innovation of Spain, grant MTM2009-12872-C02-01.Abbas, M.; Nazir, T.; Romaguera Bonilla, S. (2012). Fixed point results for generalized cyclic contraction mappings in partial metric spaces. Revista- Real Academia de Ciencias Exactas Fisicas Y Naturales Serie a Matematicas. 106(2):287-297. https://doi.org/10.1007/s13398-011-0051-5S2872971062Abdeljawad T., Karapinar E., Tas K.: Existence and uniqueness of a common fixed point on partial metric spaces. Appl. Math. Lett. 24(11), 1894–1899 (2011). doi: 10.1016/j.aml.2011.5.014Altun, I., Erduran A.: Fixed point theorems for monotone mappings on partial metric spaces. Fixed Point Theory Appl. article ID 508730 (2011). doi: 10.1155/2011/508730Altun I., Sadarangani K.: Corrigendum to “Generalized contractions on partial metric spaces” [Topology Appl. 157 (2010), 2778–2785]. Topol. 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