Applied General Topology
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Applied General Topology publica artículos de investigación originales relacionados con las interacciones entre la topología general y otras disciplinas matemáticas así como los resultados topológicos con aplicaciones a otras áreas de la ciencia, y el desarrollo de teorías topológicas de importancia para permitir futuras aplicaciones.
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Browsing Applied General Topology by Sponsor "Council of Scientific and Industrial Research, India"
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- PublicationBest proximity pair theorems for relatively nonexpansive mappings(Universitat Politècnica de València, 2009-04-01) Sankar Raj, V.; Veeramani, P.; Council of Scientific and Industrial Research, India[EN] Let A, B be nonempty closed bounded convex subsets of a uniformly convex Banach space and T : A∪B → A∪B be a map such that T(A) ⊆ B, T(B) ⊆ A and ǁTx − Tyǁ ≤ ǁx − yǁ, for x in A and y in B. The fixed point equation Tx = x does not possess a solution when A ∩ B = Ø. In such a situation it is natural to explore to find an element x0 in A satisfying ǁx0 − Tx0ǁ = inf{ǁa − bǁ : a ∈ A, b ∈ B} = dist(A,B). Using Zorn’s lemma, Eldred et.al proved that such a point x0 exists in a uniformly convex Banach space settings under the conditions stated above. In this paper, by using a convergence theorem we attempt to prove the existence of such a point x0 (called best proximity point) without invoking Zorn’s lemma.
- PublicationBetween continuity and set connectedness(Universitat Politècnica de València, 2010-04-01) Kohli, J.K.; Singh, D.; Kumar, Rajesh; Aggarwal, Jeetendra; University Grants Commission, India; Council of Scientific and Industrial Research, India[EN] Two new weak variants of continuity called 'R-continuity'and 'F-continuity' are introduced. Their basic properties are studied and their place in the hierarchy of weak variants of continuity, that already exist in the literature, is elaborated. The class of R-continuous functions properly contains the class of continuous functions and is strictly contained in each of the three classes of (1) faintly continu-ous functions studied by Long and Herrignton (Kyungpook Math. J.22(1982), 7-14); (2) D-continuous functions introduced by Kohli (Bull.Cal. Math. Soc. 84 (1992), 39-46), and (3) F-continuous functions which in turn are strictly contained in the class of z-continuous functions studied by Singal and Niemse (Math. Student 66 (1997), 193-210).So the class of R-continuous functions is also properly contained in each of the classes of D∗-continuous functions, D-continuous function and set connected functions.
- PublicationBoyd-Wong contractions in F-metric spaces and applications(Universitat Politècnica de València, 2022-04-01) Bera, Ashis; Dey, Lakshmi Kanta; Som, Sumit; Garai, Hiranmoy; Sintunavarat, Wutiphol; Council of Scientific and Industrial Research, India[EN] The main aim of this paper is to study the Boyd-Wong type fixed point result in the F-metric context and apply it to obtain some existence and uniqueness criteria of solution(s) to a second order initial value problem and a Caputo fractional differential equation. We substantiate our obtained result by finding a suitable non-trivial example.
- PublicationFixed point results concerning α-F-contraction mappings in metric spaces(Universitat Politècnica de València, 2019-04-01) Dey, Lakshmi Kanta; Kumam, Poom; Senapati, Tanusri; Council of Scientific and Industrial Research, India[EN] In this paper, we introduce the notions of generalized α-F-contraction and modified generalized α-F-contraction. Then, we present sufficient conditions for existence and uniqueness of fixed points for the above kind of contractions. Necessarily, our results generalize and unify several results of the existing literature. Some examples are presented to substantiate the usability of our obtained results.
- PublicationFrom interpolative contractive mappings to generalized Ciric-quasi contraction mappings(Universitat Politècnica de València, 2021-04-01) Roy, Kushal; Panja, Sayantan; Council of Scientific and Industrial Research, India[EN] In this article we consider a restricted version of Ciric-quasi contraction mapping for showing that this mapping generalizes several known interpolative type contractive mappings. Also here we introduce the concept of interpolative strictly contractive type mapping T and prove a fixed point theorem for such mapping over a T-orbitally compact metric space. Some examples are given in support of our established results. Finally we give an observation regarding (λ, α, β)-interpolative Kannan contractions introduced by Gaba et al.
- PublicationOn rings of Baire one functions(Universitat Politècnica de València, 2019-04-01) Deb Ray, A.; Mondal, Atanu; Council of Scientific and Industrial Research, India[EN] This paper introduces the ring of all real valued Baire one functions, denoted by B1(X) and also the ring of all real valued bounded Baire one functions, denoted by B∗1(X). Though the resemblance between C(X) and B1(X) is the focal theme of this paper, it is observed that unlike C(X) and C∗(X) (real valued bounded continuous functions), B∗1 (X) is a proper subclass of B1(X) in almost every non-trivial situation. Introducing B1-embedding and B∗1-embedding, several analogous results, especially, an analogue of Urysohn’s extension theorem is established.
- PublicationTopological dynamics on hyperspaces(Universitat Politècnica de València, 2010-04-01) Sharma, Puneet; Nagar, Anima; Department of Science and Technology, Ministry of Science and Technology, India; Council of Scientific and Industrial Research, India[EN] In this paper we wish to relate the dynamics of the base map to the dynamics of the induced map. In the process, we obtain conditions on the endowed hyperspace topology under which the chaotic behaviour of the map on the base space is inherited by the induced map on the hyperspace. Several of the known results come up as corollaries to our results. We also discuss some metric related dynamical properties on the hyperspace that cannot be deduced for the base dynamics.