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.

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 Product-Normed Linear Spaces

2018 ◽  
Vol 11 (3) ◽  
pp. 740-750
Author(s):  
Benedict Barnes ◽  
I. A. Adjei ◽  
S. K. Amponsah ◽  
E. Harris
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Differential Equations ◽  
Linear Space ◽  
Linear Algebra ◽  
Functional Properties ◽  
Normed Linear Space ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Space Product

In this paper, both the product-normed linear space $P-NLS$ (product-Banach space) and product-semi-normed linear space (product-semi-Banch space) are introduced. These normed linear spaces are endowed with the first and second product inequalities, which have a lot of applications in linear algebra and differential equations. In addition, we showed that $P-NLS$ admits functional properties such as completeness, continuity and the fixed point.

Gaps between Spheres in Normed Linear Spaces

1980 ◽  
Vol 23 (3) ◽  
pp. 347-354 ◽  
Author(s):  
Robert H. Lohman
Keyword(s):  
Linear Space ◽  
Normed Linear Space ◽  
Linear Spaces ◽  
Infinite Dimensional ◽  
Normed Linear Spaces ◽  
Concentric Spheres ◽  
General Conditions

AbstractThe geometric notions of a gap and gap points between “concentric” spheres in a normed linear space are introduced and studied. The existence of gap points characterizes finitedimensional spaces. General conditions are given under which an infinite-dimensional normed linear space admits concentric spheres such that both these spheres and their dual spheres fail to have gap points.

On the calculation of the Dunkl-Williams constant of normed linear spaces

2013 ◽  
Vol 11 (7) ◽  
Author(s):  
Hiroyasu Mizuguchi ◽  
Kichi-Suke Saito ◽  
Ryotaro Tanaka
Keyword(s):  
Linear Space ◽  
Normed Linear Space ◽  
Normal Structure ◽  
Linear Spaces ◽  
Normed Linear Spaces

AbstractRecently, Jiménez-Melado et al. [Jiménez-Melado A., Llorens-Fuster E., Mazcuñán-Navarro E.M., The Dunkl-Williams constant, convexity, smoothness and normal structure, J. Math. Anal. Appl., 2008, 342(1), 298–310] defined the Dunkl-Williams constant DW(X) of a normed linear space X. In this paper we present some characterizations of this constant. As an application, we calculate DW(ℓ2-ℓ∞) in the Day-James space ℓ2-ℓ∞.

scholarly journals On Exposed and Farthest Points in Normed Linear Spaces

1971 ◽  
Vol 12 (3) ◽  
pp. 301-308 ◽  
Author(s):  
M. Edelstein ◽  
J. E. Lewis
Keyword(s):  
Linear Space ◽  
Normed Linear Space ◽  
Nonempty Subset ◽  
Linear Spaces ◽  
Farthest Points ◽  
Normed Linear Spaces ◽  
Farthest Point ◽  
Image Position

Let S be a nonempty subset of a normed linear space E. A point s0 of S is called a farthest point if for some x ∈ E, . The set of all farthest points of S will be denoted far (S). If S is compact, the continuity of distance from a point x of E implies that far (S) is nonempty.

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 On equidistant sets in normed linear spaces

1974 ◽  
Vol 11 (3) ◽  
pp. 443-454 ◽  
Author(s):  
B.B. Panda ◽  
O.P. Kapoor
Keyword(s):  
Linear Space ◽  
Normed Linear Space ◽  
Metric Projection ◽  
Chebyshev Subspace ◽  
Linear Spaces ◽  
Normed Linear Spaces

In this note some results concerning the equidistant setE(−x, x) and the kernelMθof the metric projectionPM, whereMis a Chebyshev subspace of a normed linear spaceX, have been obtained. In particular, whenX=lp(1 <p< ∞), it has been proved that every equidistant set is closed in thebw-topology of the space. Inc0no equidistant set has this property.

scholarly journals Equivalence results for implicit Jungck–Kirk type iterations

2018 ◽  
Vol 22 (1) ◽  
pp. 75-89
Author(s):  
H. Akewe ◽  
A. A. Mogbademu
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Points ◽  
Fixed Point Iteration ◽  
Linear Spaces ◽  
Mann Iteration ◽  
Normed Linear Spaces ◽  
Weakly Compatible ◽  
The Common

We show that the implicit Jungck–Kirk-multistep, implicit Jungck–Kirk–Noor, implicit Jungck–Kirk–Ishikawa, and implicit Jungck–Kirk–Mann iteration schemes are equivalently used to approximate the common fixed points of a pair of weakly compatible generalized contractive-like operators defined on normed linear spaces. Our results contribute to the existing results on the equivalence of fixed point iteration schemes by extending them to pairs of maps. An example to show the applicability of the main results is included.

scholarly journals Convex sets in proximal relator spaces

Filomat ◽  
2016 ◽  
Vol 30 (13) ◽  
pp. 3411-3414 ◽  
Author(s):  
J.F. Peters
Keyword(s):  
Linear Space ◽  
Normed Linear Space ◽  
Convex Sets ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Finite Dimensional

This article introduces convex sets in finite-dimensional normed linear spaces equipped with a proximal relator. A proximal relator is a nonvoid family of proximity relations R? (called a proximal relator) on a nonempty set. A normed linear space endowed with R? is an extension of the Sz?z relator space. This leads to a basis for the study of the nearness of convex sets in proximal linear spaces.

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.

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