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Virtues in Bharathiyar's Kannan Songs
Get PDFMahakavi Bharathiyar’s songs marks the turning point in the world of Tamil literature. Although there are many innovations in his works, he has never left the old and ancient tradition behind. He puts forward his thoughts, needs, expectations and prayers through devotional songs about Lord Ganesha, Muruga, Lakshmi, Saraswati, Kali, Muthumari, Govindan, Shakti, Omshakti, Parashakti and Kannan. Among the poems written by Bharathiyar, the devotional songs, the songs about Kannan deserve much attention. He was so fond of Kannan that he kept his name as his pseudonym. This article examines the manner in his poems by seeing Kannan not only as a male form but also as a female form, it expresses the virtues which Bharathiyar intended to tell people through Kannan songs and how Bharathiyar accepted Kannan as a friend, father, servant, king, disciple, teacher, and mother
Fractals of Interpolative Kannan Mappings
No full textIn 2018, Erdal Karapinar introduced the concept of interpolative Kannan operators, a novel adaptation of the Kannan mapping originally defined in 1969 by Kannan. This new mapping condition is more lenient than the basic contraction condition. In this paper, we study the concept by introducing the IKC-iterated function/multi-function system using interpolative Kannan operators, including a broader area of mappings. Moreover, we establish the Collage Theorem endowed with the iterated function system (IFS) based on the IKC, and show the well-posedness of the IKC-IFS. Interpolative Kannan contractions are meaningful due to their applications in fractals, offering a more versatile framework for creating intricate geometric structures with potentially fewer constraints compared to classical approaches
Verbijohdosten semanttiset funktiot ja kannan tarkoitteen rooli
Get PDFPro gradu -tutkielmani tavoitteena on kartoittaa substantiivikantaisten verbijohdosten semanttisia ominaisuuksia ja selvittää näiden yhteyttä kannan tehtävään ja tarkoitteen merkitykseen. Tutkielmassa tarkastellaan ensiksi kannan semanttisen roolin vaikutusta verbijohdoksen kuvaamaan asiaintilaan. Tätä seuraa asiaintilan tarkastelu kannan tarkoitteen semantiikan näkökulmasta. Kokonaiskuvaa on täydennetty morfosyntaktisella lähestymistavalla, jonka avulla selvitetään kannan semanttisen roolin kuvastumista suomen muoto- ja lauserakenteesta.
Tutkielman teoreettisena lähtökohtana toimii kognitiivisen kielitieteen näkemykset ja olettamukset kielestä. Niistä tutkimukseni kannalta oleelliset ovat seuraavat: ensinnäkin kielessä pidetään keskeisenä merkitystä, joka heijastuu kaikkiin kielen tasoihin. Toiseksi kielenulkoisen referentin semanttinen sisältö ja sen laajuus on kielenkäyttäjän maailmantietouden varassa. Maailmantietous on tällöin kulttuurisidonnaista. Kognitiivinen viitekehys kuvastuu ennen kaikkea tutkielman semanttisessa, mutta myös morfosyntaktisessa tarkastelussa. Tutkimus on synkroninen.
Tutkimusaineistona käytettiin 22 alkuperäistä suomenkielistä kaunokirjallista teosta. Niistä on poimittu tutkittavien substantiivikantaisten verbijohdosten esiintymät. Verbit on valikoitu Suomen kielen käänteissanakirjasta (1980). Teokset esiintyvät InterCorp-tietokannassa, joka on Prahan Kaarlen yliopiston kehittämä digitaalinen kieliaineistokokoelma. Aineistoa analysoitiin kvalitatiivisesti siten, että teoksista valittiin kunkin verbijohdoksen kohdalle esimerkkilause, jota tarkasteltiin verbijohdoksen muodostaman argumenttirakenteen avulla. Analyysissa keskityttiin verbin semanttiseen sisältöön ja argumenttirakenteen osallistujien kantaman semanttisen roolin luonteeseen. Lisäksi huomio kiinnitettiin verbijohdoksen parafraasiin, jonka rakennetta analysoitiin morfosyntaktisesti.
Tutkimus osoittaa substantiivikantaisten verbijohdosten semanttista värikkyyttä, joka perustuu kannan semanttisen roolin ja tarkoitteen merkityksen yhteisvaikutukseen. Kannan tarkoitteelle ominaiset semanttiset piirteet voivat kuvastua verbijohdoksen merkitykseen lisäämällä siihen eri tietoja ja nyansseja. Tutkimuksessa myös havaittiin, että kannan tarkoitteen semantiikka voi lisäksi vaikuttaa verbijohdoksen kuvaaman asiaintilan osallistujien luonteeseen. Tällöin tutkimustuloksista voidaan päätellä, että eniten vaikutusta on saanut aikaan kannan tarkoite, joka edustuu semanttisena roolina VÄLINE. Sen sijaan vähemmän tai ei mitään vaikutusta on aiheuttanut kannan tarkoite, joka on semanttiselta rooliltaan TEEMA tai TULOS. Tutkimuksen morfosyntaktisen analyysin tulokset osoittavat, että kannan semanttisella roolilla on tiettyjä morfologisia ja syntaktisia keinoja, joilla se pystyy koodautumaan suomen kielen rakenteeseen
Some Similarity between contractions and Kannan mappings II
Get PDFIn Kikkawa-Suzuki [Some similarity between contractions and Kannan mappings, Fixed Point Theory Appl. doi: 10.1155/2007/49749], we discussed a similarity between contractions and Kannan mappings. In this paper, we continue to discuss a similarity between contractions and generalized Kannan mappings-M-Kannan mappings.departmental bulletin pape
Paired-Kannan contraction mappings and fixed point results
No full textWe introduce a novel contraction concept for mappings withinmetric spaces called Paired-Kannan contraction. Unlike traditional Kannancontraction mappings, which involve two points, Paired-Kannan contractionmappings extend this concept to three points. We explore their properties,noting that while these mappings may generally be discontinuous, they exhibitcontinuity at fixed points akin to Kannan contractions. Importantly, we estab-lish that Paired-Kannan contraction mappings constitute distinct entities fromtraditional Kannan contractions. We prove a fixed point theorem for PairedKannan contraction mappings and show that conditions like asymptotic reg-ularity and continuity extend these theorems’ applicability. Additionally, wederive two new fixed point theorems for these mappings, applicable even innon-complete metric spaces
Some Similarity between contractions and Kannan mappings II
No full textIn Kikkawa-Suzuki [Some similarity between contractions and Kannan mappings, Fixed Point Theory Appl. doi: 10.1155/2007/49749], we discussed a similarity between contractions and Kannan mappings. In this paper, we continue to discuss a similarity between contractions and generalized Kannan mappings-M-Kannan mappings
Iteration of Operators with Contractive Mutual Relations of Kannan Type
No full textInspired by the ideas of R. Kannan, we define the new concepts of mutual Kannan contractivity and mutual contractivity between two self-maps on a metric space that generalize the concepts of the Kannan map and contraction. We give some examples and deduce the properties of the operators satisfying this type of condition; in particular, we study the case where the space is normed, and the maps are linear. Then we generalize some theorems proposed by this author on the existence of a fixed point of one operator or a common fixed point for two operators. Our results first prove the existence of a common fixed point of a set of self-maps of any cardinal number (countable or uncountable) satisfying the conditions of Kannan type in metric spaces. The same is proved for a set of maps satisfying the mutual relations of classical contractivity. We prove in both cases the convergence of iterative schemes involving operators with mutual relations of contractivity, proposing sufficient conditions for the iteration of the operators on any element of the space to converge to the common fixed point when a different operator is taken in each step. The results obtained are applied to operators acting on real functions, coming from the fractal convolution with the null function
Kannan as a Human in Bharathi's Poems
Get PDFKannan Songs (Kannan Paattu) are an expression of Bharathi's imagination. Bharathi's early education did not expose him to Saivam literature or the Kambaramayanam. During his stay in Puducherry, he became more involved in Andal Pasuram in Tiruvaimozhi due to the contact with Sri Aurobindo. It can be felt that there is an influence of the Azhwars' consciousness and language style. Bharathi is fascinated by seeing Kannan's many struggles, starting from his birth relocation and later in his early life, and Kannan's overcoming these struggles with a smile. His acceptance of good and condemnation of evil is a lively event. Towards this, the study of Bharathi’s Kannan through the songs of Kannan, has been portrayed as a man of purpose and aims to kindle an interest among the readers to live like him
(ρ,η,μ)-Interpolative Kannan Contractions I
No full textWe point out a vital error in the paper of Gaba et al. (2019), showing that a (ρ,η,μ) interpolative Kannan contraction in a complete metric space need not have a fixed point. Then we give an appropriate restriction on a (ρ,η,μ)-interpolative Kannan contraction that guarantees the existence of a fixed point and provide an equivalent formulation. Moreover, we show that this formulation can be extended to the interpolative Reich-Rus-Ćirić type contraction
Fixed point theorem for generalized Kannan type mappings
No full textWe introduce a new type of mappings in metric spaces which are three-point
analogue of the well-known Kannan type mappings and call them generalized
Kannan type mappings. It is shown that in general case such mappings are
discontinuous but continuous at fixed points as well as Kannan type mappings
and that these two classes of mappings are independent. The fixed-point theorem
for generalized Kannan type mappings is proved. Additional conditions of
asymptotic regularity and continuity allow us to extent the class of mappings
for which the fixed-point theorems hold. Following Kannan, we also obtain two
other fixed-point theorems for generalized Kannan type mappings in metric
spaces which are not obligatory complete.Comment: 19 page
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