scholarly journals Fixed point theory for multivalued generalized nonexpansive mappings

2012 ◽  
Vol 6 (2) ◽  
pp. 265-286 ◽  
Author(s):  
Jesús García-Falset ◽  
Enrique Llorens-Fuster ◽  
Elena Moreno-Gálvez
Keyword(s):  
Fixed Point ◽  
General Class ◽  
Recent Literature ◽  
Fixed Point Theory ◽  
Nonexpansive Mappings ◽  
Point Theory ◽  
The Other

A very general class of multivalued generalized nonexpansive mappings is defined. We also give some fixed point results for these mappings, and finally we compare and separate this class from the other multivalued generalized nonexpansive mappings introduced in the recent literature.

scholarly journals Transfinite methods in metric fixed-point theory

2003 ◽  
Vol 2003 (5) ◽  
pp. 311-324 ◽  
Author(s):  
W. A. Kirk
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Nonexpansive Mappings ◽  
Point Theory ◽  
Transfinite Induction ◽  
Caristi’S Theorem ◽  
Countable Compactness ◽  
Recent Extension

This is a brief survey of the use of transfinite induction in metric fixed-point theory. Among the results discussed in some detail is the author's 1989 result on directionally nonexpansive mappings (which is somewhat sharpened), a result of Kulesza and Lim giving conditions when countable compactness implies compactness, a recent inwardness result for contractions due to Lim, and a recent extension of Caristi's theorem due to Saliga and the author. In each instance, transfinite methods seem necessary.

scholarly journals Relation-Theoretic Fixed Point Theorems for Generalized Weakly Contractive Mappings

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 29
Author(s):  
Priyam Chakraborty ◽  
Binayak S. Choudhury ◽  
Manuel De la Sen
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Fixed Point Theory ◽  
Point Theory ◽  
The Other ◽  
Binary Relations ◽  
Contractive Mappings ◽  
Fixed Point Result ◽  
Weakly Contractive

In recent times there have been two prominent trends in metric fixed point theory. One is the use of weak contractive inequalities and the other is the use of binary relations. Combining the two trends, in this paper we establish a relation-theoretic fixed point result for a mapping which is defined on a metric space with an arbitrary binary relation and satisfies a weak contractive inequality for any pair of points whenever the pair of points is related by a given relation. The uniqueness is obtained by assuming some extra conditions. The metric space is assumed to be R -complete. We use R -continuity of functions. The property of local T-transitivity of the relation R is used in the main theorem. There is an illustrative example. An existing fixed point result is generalized through the present work. We use a method in the proof of our main theorem which is a blending of relation-theoretic and analytic approaches.

scholarly journals Iterative Approximation of Fixed Point of Multivalued ρ-Quasi-Nonexpansive Mappings in Modular Function Spaces with Applications

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Godwin Amechi Okeke ◽  
Sheila Amina Bishop ◽  
Safeer Hussain Khan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Nonexpansive Mappings ◽  
Modular Function ◽  
Point Theory ◽  
Function Spaces ◽  
Initial Value ◽  
Iterative Approximation ◽  
Modular Function Spaces ◽  
Nonlinear Mappings

Recently, Khan and Abbas initiated the study of approximating fixed points of multivalued nonlinear mappings in modular function spaces. It is our purpose in this study to continue this recent trend in the study of fixed point theory of multivalued nonlinear mappings in modular function spaces. We prove some interesting theorems for ρ-quasi-nonexpansive mappings using the Picard-Krasnoselskii hybrid iterative process. We apply our results to solving certain initial value problem.

scholarly journals The Fixed Point Theory for Some Generalized Nonexpansive Mappings

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Enrique Llorens Fuster ◽  
Elena Moreno Gálvez
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Nonexpansive Mappings ◽  
Point Theory

We study some aspects of the fixed point theory for a class of generalized nonexpansive mappings, which among others contain the class of generalized nonexpansive mappings recently defined by Suzuki in 2008.

scholarly journals Iterated nonexpansive mappings in Hilbert spaces

2021 ◽  
Vol 23 (4) ◽  
Author(s):  
Bozena Piatek
Keyword(s):  
Fixed Point ◽  
Hilbert Spaces ◽  
Fixed Point Theory ◽  
Compact Convex ◽  
Nonexpansive Mappings ◽  
Normal Structure ◽  
Point Theory ◽  
Affirmative Answer ◽  
Weakly Compact ◽  
Special Case

AbstractIn [T. Dominguez Benavides and E. Llorens-Fuster, Iterated nonexpansive mappings, J. Fixed Point Theory Appl. 20 (2018), no. 3, Paper No. 104, 18 pp.], the authors raised the question about the existence of a fixed point free continuous INEA mapping T defined on a closed convex and bounded subset (or on a weakly compact convex subset) of a Banach space with normal structure. Our main goal is to give the affirmative answer to this problem in the very special case of a Hilbert space.

scholarly journals Three-step iterations for total asymptotically nonexpansive mappings in CAT(0) spaces

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1317-1330 ◽  
Author(s):  
Gurucharan Saluja ◽  
Mihai Postolache
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Nonexpansive Mappings ◽  
Point Theory ◽  
Convergence Theorems ◽  
Demiclosed Principle ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Total Asymptotically Nonexpansive Mappings ◽  
Appl Math

In this paper, we establish strong and ?-convergence theorems of modified three-step iterations for total asymptotically nonexpansive mapping which is wider than the class asymptotically nonexpansive mappings in the framework of CAT(0) spaces. Our results extend and generalize the corresponding results of Chang et al. [Demiclosed principle and ?-convergence theorems for total asymptotically nonexpansive mappings in CAT(0) spaces, Appl. Math. Comput. 219(5) (2012) 2611-2617], Nanjaras and Panyanak [Demiclosed principle for asymptotically nonexpansive mappings in CAT(0) spaces, Fixed Point Theory Appl. Vol. 2010, Art. ID 268780], and many others.

scholarly journals Transformation Method for Generating Periodic Solutions of Abel’s Differential Equation

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Ni Hua
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Periodic Solutions ◽  
Fixed Point Theory ◽  
Transformation Method ◽  
Point Theory ◽  
The Other ◽  
Alternative Method ◽  
Particular Solution

This paper deals with Abel’s differential equation. We suppose that r=r(t) is a periodic particular solution of Abel’s differential equation and, then, by means of the transformation method and the fixed point theory, present an alternative method of generating the other periodic solutions of Abel’s differential equation.

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