scholarly journals Three-Step Fixed Point Iteration for Generalized Multivalued Mapping in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Zhanfei Zuo
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Banach Spaces ◽  
Multivalued Mapping ◽  
Fixed Point Iteration ◽  
Iterative Processes ◽  
Multivalued Nonexpansive Mapping

The convergence of three-step fixed point iterative processes for generalized multivalued nonexpansive mapping was considered in this paper. Under some different conditions, the sequences of three-step fixed point iterates strongly or weakly converge to a fixed point of the generalized multivalued nonexpansive mapping. Our results extend and improve some recent results.

WEAK CONVERGENCE OF AN IMPLICIT ITERATIVE PROCESS WITH ERRORS FOR AN ASYMPTOTICALLY QUASI I-NONEXPANSIVE MAPPING IN BANACH SPACES

2011 ◽  
Vol 04 (02) ◽  
pp. 309-319 ◽  
Author(s):  
Farrukh Mukhamedov ◽  
Mansoor Saburov
Keyword(s):  
Fixed Point ◽  
Weak Convergence ◽  
Nonexpansive Mapping ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Iterative Process

In this paper we prove the weak convergence of the implicit iterative process with errors to a common fixed point of an asymptotically quasi I-nonexpansive mapping T and an asymptotically quasi-nonexpansive mapping I in Banach spaces.

APPROXIMATING THE SOLUTION OF A FRACTIONAL ORDER MODEL OF NOVEL CORONAVIRUS (COVID-2019) UNDER CAPUTO–FABRIZIO DERIVATIVE

2021 ◽  
Vol 11 (1) ◽  
pp. 35-46
Author(s):  
F.A. Adie ◽  
G.I. Ogban ◽  
S.E. Ekoro ◽  
O. Joseph ◽  
A.E. Ofem
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Fractional Order ◽  
Iteration Method ◽  
Order Model ◽  
Fixed Point Iteration ◽  
Fractional Order Model ◽  
Novel Coronavirus

This paper presents a fixed point iteration method for approximating the solution of a fractional order model of novel coronavirus (COVID-2019) under Caputo--Fabrizio derivative in Banach spaces. Our result is new and complements some existing results in the literature.

scholarly journals Fixed-Point Theorems for Mean Nonexpansive Mappings in Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Zhanfei Zuo
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Nonexpansive Mappings ◽  
Uniqueness Theorems ◽  
Existence And Uniqueness Theorems ◽  
Approximate Fixed Point

We define a mean nonexpansive mappingTonXin the sense thatTx-Ty≤ax-y+bx-Ty,a,b≥0,a+b≤1. It is proved that mean nonexpansive mapping has approximate fixed-point sequence, and, under some suitable conditions, we get some existence and uniqueness theorems of fixed point.

scholarly journals Convergence Theorems for a Common Point of Solutions of Equilibrium and Fixed Point of Relatively Nonexpansive Multivalued Mapping Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
H. Zegeye ◽  
N. Shahzad
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Equilibrium Problem ◽  
Banach Spaces ◽  
Multivalued Mapping ◽  
Iterative Process ◽  
Common Point ◽  
Finite Family ◽  
Relatively Nonexpansive ◽  
Nonexpansive Multivalued Mapping

We introduce an iterative process which converges strongly to a common point of set of solutions of equilibrium problem and set of fixed points of finite family of relatively nonexpansive multi-valued mappings in Banach spaces.

scholarly journals Fixed-point iteration processes for non-Lipschitzian mappings of asymptotically quasi-nonexpansive type

2003 ◽  
Vol 2003 (33) ◽  
pp. 2075-2081 ◽  
Author(s):  
Daya Ram Sahu ◽  
Jong Soo Jung
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Iteration ◽  
Ishikawa Iteration ◽  
Lipschitzian Mappings ◽  
Iteration Processes

We study convergences of Mann and Ishikawa iteration processes for mappings of asymptotically quasi-nonexpansive type in Banach spaces.

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