scholarly journals Schauder-Type Fixed Point Theorem in Generalized Fuzzy Normed Linear Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1643
Author(s):  
S. Chatterjee ◽  
T. Bag ◽  
Jeong-Gon Lee
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Linear Space ◽  
Present Article ◽  
Point Theorem ◽  
Normed Linear Space ◽  
Compact Operators ◽  
Linear Spaces ◽  
Basic Properties ◽  
Fuzzy Setting

In the present article, the Schauder-type fixed point theorem for the class of fuzzy continuous, as well as fuzzy compact operators is established in a fuzzy normed linear space (fnls) whose underlying t-norm is left-continuous at (1,1). In the fuzzy setting, the concept of the measure of non-compactness is introduced, and some basic properties of the measure of non-compactness are investigated. Darbo’s generalization of the Schauder-type fixed point theorem is developed for the class of ψ-set contractions. This theorem is proven by using the idea of the measure of non-compactness.

scholarly journals Some results on best proximity pair theorems

2002 ◽  
Vol 3 (1) ◽  
pp. 25
Author(s):  
P.S. Srinivasan ◽  
P. Veeramani
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Linear Space ◽  
Point Theorem ◽  
Normed Linear Space ◽  
Sufficient Conditions ◽  
Best Proximity Pair

<p>Best proximity pair theorems are considered to expound the sufficient conditions that ensure the existence of an element x<sub>o</sub> ϵ A, such that</p> <p>d(x<sub>o</sub>; T x<sub>o</sub>) = d(A;B)</p> <p>where T : A  2<sup>B</sup> is a multifunction defined on suitable subsets A and B of a normed linear space E. The purpose of this paper is to obtain best proximity pair theorems directly without using any multivalued fixed point theorem. In fact, the well known Kakutani's fixed point theorem is obtained as a corollary to the main result of this paper.</p>

ON n-NORMED LINEAR SPACE VALUED STRONGLY (C,1)-SUMMABLE DIFFERENCE SEQUENCES

2010 ◽  
Vol 03 (04) ◽  
pp. 565-575 ◽  
Author(s):  
Hemen Dutta
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Linear Space ◽  
Point Theorem ◽  
Normed Linear Space ◽  
Difference Sequences ◽  
The Fixed Point Theorem ◽  
Bounded Sequences

In this article we extend the notion of famous strongly ( C ,1)-summable or strongly Cesàro summable real sequences to n-normed linear space valued difference sequences. Consequently we introduce the notions of n-normed linear space (n-nls) valued strongly Cesàro [Formula: see text]-summable, strongly Cesàro [Formula: see text]-null and strongly Cesàro [Formula: see text]-bounded sequences. Further we extend and investigate the notion of n-norm and derived (n - l) - norms, for all l = 1, 2, …, n - 1 on the spaces of these three types of sequences. We also prove the Fixed point theorem for these spaces, which are n-Banach spaces under certain conditions and compute the n-isometrically isomorphic spaces. This article also introduces an idea for constructing n-norm on spaces of n-nls valued summable difference sequences.

scholarly journals Fixed Point Theorem in Fuzzy Automata Normed Linear Space

2019 ◽  
Vol 1377 ◽  
pp. 012047
Author(s):  
S. Karpagavalli ◽  
V. Visalakshi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Linear Space ◽  
Point Theorem ◽  
Normed Linear Space ◽  
Fuzzy Automata

New Fixed Point Theorems via Contraction Mappings in Complete Intuitionistic Fuzzy Normed Linear Space

2018 ◽  
Vol 15 (01) ◽  
pp. 65-83
Author(s):  
Nabanita Konwar ◽  
Ayhan Esi ◽  
Pradip Debnath
Keyword(s):  
Fixed Point ◽  
Mathematical Models ◽  
Linear Space ◽  
Fixed Point Theorems ◽  
Normed Linear Space ◽  
Existence Of A Solution ◽  
Linear Spaces ◽  
Contraction Mappings ◽  
Normed Linear Spaces ◽  
Intuitionistic Fuzzy

Contraction mappings provide us with one of the major sources of fixed point theorems. In many mathematical models, the existence of a solution may often be described by the existence of a fixed point for a suitable map. Therefore, study of such mappings and fixed point results becomes well motivated in the setting of intuitionistic fuzzy normed linear spaces (IFNLSs) as well. In this paper, we define some new contraction mappings and establish fixed point theorems in a complete IFNLS. Our results unify and generalize several classical results existing in the literature.

scholarly journals A fixed point theorem for positive k-set contractions

1974 ◽  
Vol 19 (1) ◽  
pp. 93-102 ◽  
Author(s):  
A. J. B. Potter
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Classical Result ◽  
Compact Operators ◽  
Ordered Banach Space ◽  
Abstract Theory ◽  
Partially Ordered

The abstract theory of positive compact operators (acting in a partially ordered Banach space) has proved to be particularly useful in the theory of integral equations. In a recent paper (2) it was shown that many of the now classical theorems for positive compact operators can be extended to certain classes of non-compact operators. One result, proved in (2, Theorem 5), was a fixed point theorem for compressive k-set contractions (k<l). The main result of this paper (Theorem 3.3) shows that some of the hypotheses of (2, Theorem 5) are unnecessary. We use techniques based on those used by M. A. Krasnoselskii in the proof of Theorem 4.12 in (4), which is the classical fixed point theorem for compressive compact operators, to obtain a complete generalisation of this classical result to the k-set contractions (k < 1). It should be remarked that J. D. Hamilton has extended the same result to A-proper mappings (3, Theorem 1). However apparently it is not known, even in the case when we are dealing with a Π1-space, whether k-set contractions are A-proper or not.

scholarly journals ON I- CONVERGENCE OF SEQUENCES IN GRADUAL NORMED LINEAR SPACES

2021 ◽  
pp. 595
Author(s):  
Chiranjib Choudhury ◽  
Shyamal Debnath
Keyword(s):  
Linear Space ◽  
Normed Linear Space ◽  
Linear Spaces ◽  
Basic Properties ◽  
Normed Linear Spaces ◽  
Cauchy Sequences ◽  
Convergence Of Sequences

In this paper, we introduce the concepts of $\mathcal{I}$ and $\mathcal{I^{*}}-$convergence of sequences in gradual normed linear spaces. We study some basic properties and implication relations of the newly defined convergence concepts. Also, we introduce the notions of $\mathcal{I}$ and $\mathcal{I^{*}}-$Cauchy sequences in the gradual normed linear space and investigate the relations between them.

scholarly journals Some generalizations of ascent and descent for linear operators

2021 ◽  
Author(s):  
Zied Garbouj
Keyword(s):  
Linear Operator ◽  
Linear Space ◽  
Positive Operator ◽  
Finite Rank ◽  
Operator Theory ◽  
Compact Operators ◽  
Linear Operators ◽  
Linear Spaces ◽  
Basic Properties ◽  
Stability Results

AbstractThe purpose of this paper is to present in linear spaces some results for new notions called A-left (resp., A-right) ascent and A-left (resp., A-right) descent of linear operators (where A is a given operator) which generalize two important notions in operator theory: ascent and descent. Moreover, if A is a positive operator, we obtain several properties of ascent and descent of an operator in semi-Hilbertian spaces. Some basic properties and many results related to the ascent and descent for a linear operator on a linear space Kaashoek (Math Ann 172:105–115, 1967), Taylor (Math Ann 163:18–49, 1966) are extended to these notions. Some stability results under perturbations by compact operators and operators having some finite rank power are also given for these notions.

On Rank One Commutators and Triangular Representations

1986 ◽  
Vol 29 (3) ◽  
pp. 268-273
Author(s):  
Tsoy-Wo Ma
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Compact Operators ◽  
Locally Convex Spaces ◽  
Rank One ◽  
Locally Convex ◽  
Convex Spaces

AbstractStarting with the extension of Lomonosov's Lemma by Tychonoff fixed point theorem, a result of Daughtry and Kim — Pearcy-Shields on rank-one commutators is extended to the context of locally convex spaces. Non-zero diagonal coefficients, eigenvalues and simultaneous triangular representations of compact operators on locally convex spaces are studied.

Common fixed point of Jungck-Kirk-type iterations for non-self operators in normed linear spaces

2016 ◽  
Vol 56 (1) ◽  
pp. 29-41 ◽  
Author(s):  
Hudson Akewe ◽  
Adesanmi Mogbademu
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Linear Space ◽  
Normed Linear Space ◽  
Linear Spaces ◽  
Iterative Schemes ◽  
Normed Linear Spaces ◽  
The Common ◽  
Stability Results

Abstract In this paper, we introduce Jungck-Kirk-multistep and Jungck-Kirk-multistep-SP iterative schemes and use their strong convergences to approximate the common fixed point of nonself operators in a normed linear Space. The Jungck-Kirk-Noor, Jungck-Kirk-SP, Jungck-Kirk-Ishikawa, Jungck-Kirk-Mann and Jungck-Kirk iterative schemes follow our results as corollaries. We also study and prove stability results of these schemes in a normed linear space. Our results generalize and unify most approximation and stability results in the literature.

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