scholarly journals A common fixed point theorem for semigroups of nonlinear uniformly continuous mappings with an application to asymptotic stability of nonlinear systems

Filomat ◽  
2017 ◽  
Vol 31 (7) ◽  
pp. 1949-1957
Author(s):  
Ahmed Soliman
Keyword(s):  
Fixed Point ◽  
Asymptotic Stability ◽  
Common Fixed Point ◽  
Real Banach Space ◽  
Normal Structure ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
Continuous Mappings ◽  
Uniformly Continuous ◽  
Common Fixed Point Theorem

In this paper, we study the existence of a common fixed point for uniformly continuous one parameter semigroups of nonlinear self-mappings on a closed convex subset C of a real Banach space X with uniformly normal structure such that the semigroup has a bounded orbit. This result applies, in particular, to the study of an asymptotic stability criterion for a class of semigroup of nonlinear uniformly continuous infinite-dimensional systems.

Fixed point theorems for uniformly generalized Kannan type semigroup of self-mappings

2017 ◽  
Vol 26 (2) ◽  
pp. 231-240
Author(s):  
AHMED H. SOLIMAN ◽  
MOHAMMAD IMDAD ◽  
MD AHMADULLAH
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Convex Subset ◽  
Fixed Point Theorems ◽  
Real Banach Space ◽  
Normal Structure ◽  
Uniform Normal Structure

In this paper, we consider a new uniformly generalized Kannan type semigroup of self-mappings defined on a closed convex subset of a real Banach space equipped with uniform normal structure and employ the same to show that such semigroup of self-mappings admits a common fixed point provided the underlying semigroup of self-mappings has a bounded orbit.

scholarly journals A Common Fixed Point Theorem in Metric Space under General Contractive Condition

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Sunny Chauhan ◽  
Zoran Kadelburg ◽  
Sumitra Dalal
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Metric Space ◽  
Contractive Condition ◽  
Continuous Mappings ◽  
Common Fixed Point Theorem

We prove a common fixed point theorem for two pairs of compatible and subsequentially continuous (alternately subcompatible and reciprocally continuous) mappings satisfying a general contractive condition in a metric space. Some illustrative examples are furnished to highlight the realized improvements. Our result improves the main result of Sedghi and Shobe (2007).

scholarly journals More general common fixed point theorems under a new concept

2016 ◽  
Vol 49 (1) ◽  
Author(s):  
H. Bouhadjera
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Common Fixed Points ◽  
Implicit Function ◽  
Continuous Mappings ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem

AbstractA general common fixed point theorem for two pairs of weakly subsequentially continuous mappings (recently introduced) satisfying a significant estimated implicit function is proved. An extension of this result is thereby obtained. Our results assert the existence and uniqueness of common fixed points in several cases.

scholarly journals A common fixed point theorem in strictly convex Menger PM-spaces

Filomat ◽  
2014 ◽  
Vol 28 (4) ◽  
pp. 735-743 ◽  
Author(s):  
Sinisa Jesic ◽  
Rale Nikolic ◽  
Natasa Babacev
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Normal Structure ◽  
Strictly Convex ◽  
Common Fixed Point Theorem

In this paper we will define a notions of strictly convex and normal structure in Menger PM-space. Also, existence of a common fixed point for two self-mappings defined on strictly convex Menger PM-spaces will be proved. As a consequence of main result we will give probabilistic variant of Browder's result [3]. Projekat Ministarstva nauke Republike Srbije, br. 174032]

scholarly journals Existence of common fixed points of non-linear semigroups of Enriched Kannan contractive mappings

2021 ◽  
Vol 38 (1) ◽  
pp. 169-178
Author(s):  
SAYANTAN PANJA ◽  
◽  
MANTU SAHA ◽  
RAVINDRA K. BISHT ◽  
◽  
...  
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Convex Subset ◽  
Real Banach Space ◽  
Normal Structure ◽  
Contractive Mapping ◽  
Common Fixed Points ◽  
Contractive Mappings ◽  
Non Linear

In this article, we consider the non-linear semigroup of \textit{enriched Kannan} contractive mapping and prove the existence of common fixed point on a non-empty closed convex subset $\mathcal C$ of a real Banach space $\mathscr X$, having uniformly normal structure.

scholarly journals Common fixed point of four maps in Sm-metric space

2021 ◽  
Vol 19 (6) ◽  
pp. 915-928
Author(s):  
K. Mallaiah ◽  
V. Srinivas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Metric Space ◽  
Well Posedness ◽  
Compatible Mappings ◽  
Weakly Compatible ◽  
Continuous Mappings ◽  
Multiplicative Metric Space ◽  
Common Fixed Point Theorem

In this paper, first, we deal with new metric space Sm-metric space that combines multiplicative metric space and S-metric space. We generate a common fixed point theorem in a Sm-metric space using the notions of reciprocally continuous mappings, faintly compatible mappings and occasionally weakly compatible mappings (OWC). We are also studying the well-posedness of Sm metric space. Further, some examples are presented to support our outcome.

Some Common Fixed Point Theorem in Complete Metric Space of Integral Type

2018 ◽  
Vol 6 (8) ◽  
pp. 297
Author(s):  
Jagdish C. Chaudhary ◽  
Shailesh T. Patel
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Contractive Condition ◽  
Integral Type ◽  
Complete Metric Spaces ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem

In this paper, we prove some common fixed point theorems in complete metric spaces for self mapping satisfying a contractive condition of Integral  type.

scholarly journals Common fixed point theorem on Proinov type mappings via simulation function

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Badr Alqahtani ◽  
Sara Salem Alzaid ◽  
Andreea Fulga ◽  
Seher Sultan Yeşilkaya
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Simulation Function ◽  
Type Mapping ◽  
The Common ◽  
Common Fixed Point Theorem

AbstractIn this paper, we aim to discuss the common fixed point of Proinov type mapping via simulation function. The presented results not only generalize, but also unify the corresponding results in this direction. We also consider an example to indicate the validity of the obtained results.

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