Fixed-Point Convergence Results of a Three-Step Iterative Process in CAT(0) Spaces

In this article, we suggest some Δ and strong convergence results of a three-step Sahu–Thakur iteration process for Garcia-Falset maps in the nonlinear setting of CAT(0) spaces. We furnish a new example of Garcia-Falset maps and prove that its three-step Sahu–Thakur iterative process is more effective than the many well-known iterative processes. Our results improve and extend some recently announced results of the current literature.

An Improved Iterative Polynomial Fitting Algorithm for Baseline Correction in X-Ray Spectrum

An iterative polynomial fitting method is proposed for the estimate of the baseline of the X-ray fluorescence spectrum signal. The new method generates automatic thresholds by comparing the X-ray fluorescence spectrum signal with the calculated signal from polynomial fitting in the iterative processes. The signal peaks are cut out consecutively in the iterative processes so the polynomial fitting will finally give a good estimation of the baseline. Simulated data and real data from the soil analysis spectrum are used to demonstrate the feasibility of the proposed method.

Design Science and Co-Designing of Hybrid Workplaces

Background: Future places for learning and working are digitally and physically integrated hybrid environments. The archetypical context of learning is the classroom, and context of working is the office; especially in knowledge work. New information and communication technologies enable the spatial reconfiguration of work opening possibilities for work to take place across multiple locations. This paper aims to explore how the conceptual framework of design-science research in Information Systems can be applied when the design object is a hybrid working environment.; Methods: The case study method as a qualitative approach was chosen; because it involves an empirical investigation of a particular contemporary phenomenon within its real life context using multiple sources of evidence. The empirical analysis of two hybrid working environments is based on Action Design Research (ADR)-entry points; where one analyzes two case studies stage by stage. By analyzing various stages in both case studies; one can identify co-designing challenges of hybrid working environments. Results: The results present four recommendations for co-designing of hybrid working environments. The use of hybrid working environment; the design of spatial solution; the identification of iterative processes; and the user experiences of presence and distance are significant. The Entry Point Analysis-tool can be used and further developed in analyzing and developing hybrid working environments. Conclusion: The results contribute to the tradition of usability studies. The usability briefing approach can be further developed by identifying the iterative processes inside the linear project management models. Additionally, design science research can find new insights from identification of the large stakeholder iterations more precisely.

Introduction of new Picard–S hybrid iteration with application and some results for nonexpansive mappings

PurposeIn this paper, Picard–S hybrid iterative process is defined, which is a hybrid of Picard and S-iterative process. This new iteration converges faster than all of Picard, Krasnoselskii, Mann, Ishikawa, S-iteration, Picard–Mann hybrid, Picard–Krasnoselskii hybrid and Picard–Ishikawa hybrid iterative processes for contraction mappings and to find the solution of delay differential equation, using this hybrid iteration also proved some results for Picard–S hybrid iterative process for nonexpansive mappings.Design/methodology/approachThis new iteration converges faster than all of Picard, Krasnoselskii, Mann, Ishikawa, S-iteration, Picard–Mann hybrid, Picard–Krasnoselskii hybrid, Picard–Ishikawa hybrid iterative processes for contraction mappings.FindingsShowed the fastest convergence of this new iteration and then other iteration defined in this paper. The author finds the solution of delay differential equation using this hybrid iteration. For new iteration, the author also proved a theorem for nonexpansive mapping.Originality/valueThis new iteration converges faster than all of Picard, Krasnoselskii, Mann, Ishikawa, S-iteration, Picard–Mann hybrid, Picard–Krasnoselskii hybrid, Picard–Ishikawa hybrid iterative processes for contraction mappings and to find the solution of delay differential equation, using this hybrid iteration also proved some results for Picard–S hybrid iterative process for nonexpansive mappings.

On Berinde’s method for comparing iterative processes

In the literature there are several methods for comparing two convergent iterative processes for the same problem. In this note we have in view mostly the one introduced by Berinde in (Fixed Point Theory Appl. 2:97–105, 2004) because it seems to be very successful. In fact, if IP1 and IP2 are two iterative processes converging to the same element, then IP1 is faster than IP2 in the sense of Berinde. The aim of this note is to prove this almost obvious assertion and to discuss briefly several papers that cite the mentioned Berinde’s paper and use his method for comparing iterative processes.

Drazin inverse: representation, approximation, continuity and illustrations

In this paper, we present some characteristics and expressions of the Drazin inverse for matrices and bounded linear operators in Banach spaces. We give a survey of some of results on the continuity of the Moore-Penrose and Drazin inverse, direct technics for computing the Drazin inverse are discussed, they are based on Euler-Knopp Method and characterized in terms of a limiting process. The examples presented are for illustrative purposes, some of which are provided for testing the considered iterative processes

“Being” an Older Adult Skier: The Phenomenology of Masters Alpine Ski Racers

This research examined the lived experience of older adult Alpine skiers in their continued participation in competitive ski racing. The aim was to gain an understanding of the meaning of the experiences for older adults as they continued to compete in Alpine ski racing. Masters skiers between the ages of 69 and 82 years participated in individual interviews. Data collection and analysis were iterative processes informed by phenomenological methods and visual mind mapping. The overarching theme identified in participants’ accounts was the significance of the identity of “Being” a Ski Racer. Supporting subthemes were Enjoying the Feeling of Ski Racing, Adapting in the Sport, and Skiing as a Lifestyle. These insights offer the opportunity to encourage and support the holistic experiences of older adults who maintain their athletic identity as they age. This research highlights how inclusion of older adults’ stories may foster critical reflexivity and challenge assumptions about aging.

Introduction: Design as a Discipline of Alternation

Design is never creating out of nothing—it always has specific cultural points of reference. Design alters and adapts, whereby the discipline always takes what exists as a reference point, which also makes it heretical. Design requires and generates knowledge, because designers always need to engage with specific lifeworlds. Through methods such as ethnography, this knowledge can be made explicit, which makes the discipline of design capable of connecting with other academic disciplines. Ethnography in the context of design differs from ethnography in the social sciences: it is quicker and embedded in the iterative processes that designing involves.