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On a three-step iteration process for multivalued Reich-Suzuki type α -nonexpansive and contractive mappings
Get PDF*Maldar, Samet ( Aksaray, Yazar )The aim of this paper is twofold: (a) to revisit the results in Iqbal et al. (Numer Algorithms 1–21, 2019. https:doi.org/10.1007/s11075-019-00854-z) and prove some convergence and stability results for the subclass of multivalued contractive operators under some mild conditions (b) to introduce a multivalued Reich-Suzuki type α-nonexpansive mappings and present some fixed point results for this class of mappings. We considered a more natural notion of stability called weak w2-stability instead of simple stability in Iqbal et al. (Numer Algorithms 1–21, 2019. https:doi.org/10.1007/s11075-019-00854-z). Some illustrative examples to support the results obtained herein are also presented
Iterative approximation of fixed points and applications to two-point second-order boundary value problems and to machine learning
Get PDF*Maldar, Samet ( Aksaray, Yazar )
*Atalan, Yunus ( Aksaray, Yazar )In this paper, we revisit two recently published papers on the iterative approximation of fixed points by Kumam et al. (2019) [17] and Maniu (2020) [19] and reproduce convergence, stability, and data dependency results presented in these papers by removing some strong restrictions imposed on parametric control sequences. We confirm the validity and applicability of our results through various non-trivial numerical examples. We suggest a new method based on the iteration algorithm given by Thakur et al. (2014) [28] to solve the two-point second-order boundary value problems. Furthermore, based on the above mentioned iteration algorithm and S-iteration algorithm, we propose two new gradient type projection algorithms and applied them to supervised learning. In both applications, we present some numerical examples to demonstrate the superiority of the newly introduced methods in terms of convergence, accuracy, and computational time against some earlier methods
The iterative solution of a class of nonlinear equation
No full textSabit nokta teorisinde iterasyon yöntemleri geniş bir literatüre sahip olup bu yöntemler için elde edilen sonuçlar söz konusu iterasyon yönteminden elde edilen dizinin yakınsaklığı, yakınsaklık hızı, yakınsama denkliği, veri bağlılığı ve kararlılık olarak sıralanabilir. Ayrıca bu yöntemler integral veya diferansiyel denklemlerin çözümüne ulaşmada etkin bir araç olarak kullanılmaktadır. Bu tez beş bölümden oluşmaktadır. Birinci bölümde sabit nokta teorisine dair literatür özeti verilmiştir. İkinci bölümde tezde kullanılacak temel kavramlar, tanımlar ve teoremler verilmiştir. Üçüncü bölümde yeni tanımlanmış olan dört adımlı sabit nokta iterasyon yönteminin rasyonel dönüşüm sınıfı kullanılarak belirli koşullar altında bu dönüşümün sabit noktasına yakınsaklığı ve yakınsaklık hızı incelenmiştir. Ayrıca yeni iterasyon yöntemi için kararlılık ve veri bağlılığı kavramları irdelenmiştir. Ek olarak bu sonuçlar için aşikâr olmayan nümerik örnekler verilmiştir. Dördüncü bölümde genelleştirilmiş tipte bir integral denklemin çözümüne yeni iterasyon yöntemi kullanılarak ulaşılabileceği ispatlanmış ayrıca bu denklemin çözümünün veri bağlı olduğu gösterilmiştir. Beşinci bölümde ise, tez boyunca elde edilen sonuçlardan bahsedilmiş ve ileride yapılabilecek çalışmalar hakkında bilgi verilmiştir.Iteration methods in fixed point theory, have a wide literatüre, and the results obtained for these methods can be listed as the convergence of the sequence obtained from the mentioned iteration method, the rate of convergence, the equivalence of convergence, data dependence, and stability. In addition, these methods are used as an effective tool in reaching the solution of integral or differential equations. This thesis consists of five chapters. In the first chapter, a summary of the literature on fixed point theory is given. In the second chapter, the basic concepts, definitions, and theorems to be used in the thesis are given. In the third chapter, the convergence of the newly defined four-step fixed point iteration method and the rate of convergence were investigated under certain conditions by using the rational mapping class. In addition, the concepts of stability and data dependency were examined for the new iteration method. Also, nontrivial numerical examples are given for these results. In the fourth chapter, it is proved that the solution of a generalized type integral equation can be reached by using the new iteration method, and it is shown that the solution of this equation is data-dependent. In the fifth chapter, the results obtained during the thesis are mentioned and information about the possible future studies is given
Iterative algorithms of generalized nonexpansive mappings and monotone operators with application to convex minimization problem
No full textIn this paper, we present some convergence results for various iterative algorithms built from Hardy-Rogers type generalized nonexpansive mappings and monotone operators in Hilbert spaces. We obtain some comparison results for the rates of convergence of these algorithms to the solution of variational inequality problem including Hardy-Rogers type generalized nonexpansive mappings and monotone operators. A numerical example is given to validate these results. We apply the iterative algorithms handled herein to solve convex minimization problem and illustrate this result by providing a non-trivial numerical example
Common fixed point theorems for complex-valued mappings with applications
No full textThe aim of this paper is to obtain some results which belong to fixed point theory such as strong convergence, rate of convergence, stability, and data dependence by using the new Jungck-type iteration method for a mapping defined in complex-valued Banach spaces. In addition, some of these results are supported by nontrivial numerical examples. Finally, it is shown that the sequence obtained from the new iteration method converges to the solution of the functional integral equation in complex-valued Banach spaces. The results obtained in this paper may be interpreted as a generalization and improvement of the previously known results
New parallel fixed point algorithms and their application to a system of variational inequalities
Get PDFn this study, considering the advantages of parallel fixed point algorithms arising from their symmetrical behavior, new types of parallel algorithms have been defined. Strong convergence of these algorithms for certain mappings with altering points has been analyzed, and it has been observed that their convergence behavior is better than existing algorithms with non-simple samples. In addition, the concept of data dependency for these algorithms has been examined for the first time in this study. Finally, it has been proven that the solution of a variational inequality system can be obtained using newly defined parallel algorithms under suitable conditions
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Convergence of Jungck-Kirk type iteration ethod with applications
No full textThe aim of this article is to define a new Jungck-Kirk type iteration method and to examine the convergence result under appropriate conditions together with other Jungck-Kirk type iteration methods in the literature. It is also to analyze whether the newly defined iteration method is stable. In addition, it has been shown through numerical examples that the new iteration method has a better convergence rate than the others. Finally, to show the validity of convergence and stability results, some examples are given. The results obtained in this paper may be interpreted as a refinement and improvement of the previously known results
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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