Remarks on the approximate fixed point sequence of $$(\alpha ,\beta )$$-maps

2021 ◽  
Vol 115 (4) ◽  
Author(s):  
Nguyen Van Dung ◽  
Stojan Radenovic
Keyword(s):  
Fixed Point ◽  
Approximate Fixed Point ◽  
Alpha Beta

scholarly journals A study on controllability of impulsive fractional evolution equations via resolvent operators

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Haide Gou ◽  
Yongxiang Li
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Resolvent Operator ◽  
Evolution Equations ◽  
Validity Study ◽  
Resolvent Operators ◽  
Fractional Evolution Equations ◽  
Mönch Fixed Point Theorem ◽  
Alpha Beta

AbstractIn this article, we study the controllability for impulsive fractional integro-differential evolution equation in a Banach space. The discussions are based on the Mönch fixed point theorem as well as the theory of fractional calculus and the $(\alpha ,\beta )$ ( α , β ) -resolvent operator, we concern with the term $u'(\cdot )$ u ′ ( ⋅ ) and finding a control v such that the mild solution satisfies $u(b)=u_{b}$ u ( b ) = u b and $u'(b)=u'_{b}$ u ′ ( b ) = u b ′ . Finally, we present an application to support the validity study.

scholarly journals Approximate Fixed Point Sequences of an Evolution Family on a Metric Space

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Si Fuan ◽  
Rizwan Ullah ◽  
Gul Rahmat ◽  
Muhammad Numan ◽  
Saad Ihsan Butt ◽  
...  
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Nonlinear Operator ◽  
Iteration Process ◽  
Evolution Family ◽  
Nonlinear Mapping ◽  
Approximate Fixed Point ◽  
The Family ◽  
Ishikawa Iteration Process ◽  
The Common

In this article, we study the approximate fixed point sequence of an evolution family. A family E=Ux,y;x≥y≥0 of a bounded nonlinear operator acting on a metric space M,d is said to be an evolution family if Ux,x=I and Ux,yUy,z=Ux,z for all x≥y≥z≥0. We prove that the common approximate fixed point sequence is equal to the intersection of the approximate fixed point sequence of two operators from the family. Furthermore, we apply the Ishikawa iteration process to construct an approximate fixed point sequence of an evolution family of nonlinear mapping.

scholarly journals On the approximate fixed point property in abstract spaces

2011 ◽  
Vol 271 (3-4) ◽  
pp. 1271-1285 ◽  
Author(s):  
C. S. Barroso ◽  
O. F. K. Kalenda ◽  
P.-K. Lin
Keyword(s):  
Fixed Point ◽  
Fixed Point Property ◽  
Point Property ◽  
Approximate Fixed Point ◽  
Approximate Fixed Point Property ◽  
Abstract Spaces
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