1,720,972 research outputs found
Common Fixed Point of Generalized Rational Type Contraction Mappings in Partially Ordered Metric Spaces
No full textCHANDOK, SUMIT/0000-0003-1928-2952Some common fixed point results for generalized weak contractive condition satisfying rational type expressions in the frame work of partially ordered metric spaces are obtained. The proved results generalize and extend some known results in the literature.Emerging Sources Citation Inde
Construction of Iterated Function System using Contraction Mapping Principle
No full textFractals, briefly defined as self-similar structure or mathematically they are subsets of simple geometrical spaces such as and . Fractals are viewed as significant on the grounds that they characterize pictures that are generally cannot be characterized by Euclidean geometry. Fractals are depicted utilizing calculations and manages objects that do not have whole number measurements. Some of the examples of fractals are the Cantor set, the Koch curve, the Sierpinski triangle, and the Julia set etc.
In Chapter 1, we give a brief introduction of fractals, their existence in nature or real life and some of their applications. Also we discuss the two vital properties of fractals that is self-similarity and fractional dimension with the help of Koch curve. We also give a brief introduction of Hutchinson operator, iterated function system and an attractor of iterated function system.
The study of Picard operator is similar to the study of contractive type mappings in the context of metric spaces. It is easy to see that almost all contractive type mappings on a complete metric space are Picard operators. In Chapter 2, we introduce weak -contraction and give some results on the existence of Picard operator for such class of mappings in the setting of metric spaces.
In Chapter 3, we define weak iterated function system and present some results on the existence of a unique attractor for such an iterated function system. Also we define weak multifunction iterated system and prove some results on the existence of the attractor for such iterated multifunction system
Best Approximation and Best Co-approximation in Metric Linear Space and Normed Linear Space
No full textMaster of Science -Mathematics & ComputingApproximation theory is an old and rich branch of analysis and a large number of researchers
have studied this subject. The theory has many applications in mathematical
analysis, nonlinear problems arising in physical sciences, engineering and social sciences.
Since the particular examples of approximation often arise from the problems of Science
and Technology, they provide proper motivation for the subject of Approximation Theory.
In this work, we consider the problem of characterization, existence and uniqueness
of best approximation and best co-approximation in the setting of metric linear space and
normed linear space
Existence and Uniqueness of Common Coupled Fixed Point Results Via Auxiliary Functions
No full textCHANDOK, SUMIT/0000-0003-1928-2952The purpose of this paper is to establish some coupled coincidence point theorems for mappings having a mixed g-monotone property in partially ordered metric spaces. Also, we present a result on the existence and uniqueness of coupled common fixed points. The results presented in the paper generalize and extend several well-known results in the literature.Science Citation Index Expande
Existence of Picard operator and iterated function system
Full text link[EN] In this paper, we define weak θm− contraction mappings and give a new class of Picard operators for such class of mappings on a complete metric space. Also, we obtain some new results on the existence and uniqueness of attractor for a weak θm− iterated multifunction system. Moreover, we introduce (α, β, θm)− contractions using cyclic (α, β)− admissible mappings and obtain some results for such class of mappings without the continuity of the operator. We also provide an illustrative example to support the concepts and results proved herein.The authors are thankful to the learned referee for valuable suggestions. The second author is also thankful to AISTDF, DST for the research grant vide project No. CRD/2018/000017.Garg, M.; Chandok, S. (2020). Existence of Picard operator and iterated function system. Applied General Topology. 21(1):57-70. https://doi.org/10.4995/agt.2020.11992OJS5770211S. Alizadeh, F. Moradlou and P. Salimi, Some fixed point results for (α, β) − (ψ, φ)- contractive mappings, Filomat 28 (2014), 635-647. https://doi.org/10.2298/FIL1403635AM. F. Barnsley, Fractals Everywhere, Revised with the Assistance of and with a Foreword by Hawley Rising, III. Academic Press Professional, Boston (1993).R. M. T. Bianchini, Su un problema di S. Reich riguardante la teoria dei punti fissi, Boll. Un. Mat. Ital. 5 (1972), 103-108.E. L. Fuster, A. Petrusel and J. C. Yao, Iterated function system and well-posedness, Chaos Sol. Fract. 41 (2009), 1561-1568. https://doi.org/10.1016/j.chaos.2008.06.019R. H. Haghi, Sh. Rezapour and N. Shahzad, Some fixed point generalizations are not real generalizations, Nonlinear Anal. 74 (2011), 1799-1803. https://doi.org/10.1016/j.na.2010.10.052N. Hussain, V. Parvaneh, B. Samet and C. Vetro, Some fixed point theorems for generalized contractive mappings in complete metric spaces, Fixed Point Theory Appl. 2015, 185 (2015). https://doi.org/10.1186/s13663-015-0433-zJ. E. Hutchinson, Fractals and self similarity, Indiana Univ. Math. J. 30, no. 5 (1981), 713-747. https://doi.org/10.1512/iumj.1981.30.30055M. Imdad, W. M. Alfaqih and I. A. Khan, Weak θ−contractions and some fixed point results with applications to fractal theory, Adv. Diff. Eq. 439 (2018). https://doi.org/10.1186/s13662-018-1900-8M. Jleli and B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl. 38 (2014). https://doi.org/10.1186/1029-242X-2014-38M. Radenovic and S. Chandok, Simulation type functions and coincidence points, Filomat, 32, no. 1 (2018), 141-147. https://doi.org/10.2298/FIL1801141RB. E. Rhoades, A comparison of various definitions of contractive mappings, Trans. American Math. Soc. 226 (1977), 257-290. https://doi.org/10.1090/S0002-9947-1977-0433430-4I. A. Rus, Picard operators and applications, Sci. Math. Jpn. 58, no. 1 (2003), 191-219.I. A. Rus, A. Petrusel and G. Petrusel, Fixed Point Theory, Cluj University Press, Cluj-Napoca, 2008.N. A. Secelean, Countable Iterated Function Systems, LAP LAMBERT Academic Publishing (2013). https://doi.org/10.1186/1687-1812-2013-277N. A. Secelean, Iterated function systems consisting of F-contractions, Fixed Point Theory Appl. 2013, 277 (2013). https://doi.org/10.1186/1687-1812-2013-277V. M. Sehgal, On fixed and periodic points for a class of mappings, J. London Math. Soc. 5 (1972), 571-576. https://doi.org/10.1112/jlms/s2-5.3.571S.-A. Urziceanu, Alternative charaterizations of AGIFSs having attactors, Fixed Point Theory 20 (2019), 729-740. https://doi.org/10.24193/fpt-ro.2019.2.4
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe 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
Variations on the Author
Full text link“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
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Existence of solutions to multivalued problems in incomplete metric spaces with applications
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