Some fixed point results for a new three steps iteration process in Banach spaces

We proved that the modified implicit Mann iteration process can be applied to approximate the fixed point of strictly hemicontractive mappings in smooth Banach spaces.

Download Full-text

Fixed Point Approximation of Generalized Nonexpansive Mappings in Hyperbolic Spaces

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/2015/368204 ◽

2015 ◽

Vol 2015 ◽

pp. 1-6 ◽

Cited By ~ 1

Author(s):

Jong Kyu Kim ◽

Ramesh Prasad Pathak ◽

Samir Dashputre ◽

Shailesh Dhar Diwan ◽

Rajlaxmi Gupta

Keyword(s):

Fixed Point ◽

Banach Spaces ◽

Nonexpansive Mappings ◽

Iteration Process ◽

Hyperbolic Spaces ◽

Uniformly Convex ◽

Convergence Theorems ◽

Point Approximation

We prove strong and Δ-convergence theorems for generalized nonexpansive mappings in uniformly convex hyperbolic spaces using S-iteration process due to Agarwal et al. As uniformly convex hyperbolic spaces contain Banach spaces as well as CAT(0) spaces, our results can be viewed as extension and generalization of several well-known results in Banach spaces as well as CAT(0) spaces.

Download Full-text

Approximation of a Common Random Fixed Point for a Finite Family of Random Operators

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/2007/69626 ◽

2007 ◽

Vol 2007 ◽

pp. 1-12 ◽

Cited By ~ 3

Author(s):

Somyot Plubtieng ◽

Poom Kumam ◽

Rabian Wangkeeree

Keyword(s):

Fixed Point ◽

Banach Spaces ◽

Iteration Process ◽

Finite Family ◽

Random Operators ◽

Uniformly Convex ◽

Random Fixed Point ◽

Uniformly Convex Banach Spaces ◽

Random Iteration

We construct implicit random iteration process with errors for a common random fixed point of a finite family of asymptotically quasi-nonexpansive random operators in uniformly convex Banach spaces. The results presented in this paper extend and improve the corresponding results of Beg and Abbas in 2006 and many others.

Download Full-text

Fixed-Point Approximations of Generalized Nonexpansive Mappings via Generalized M-Iteration Process in Hyperbolic Spaces

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/2020/6435043 ◽

2020 ◽

Vol 2020 ◽

pp. 1-8

Author(s):

Preeyalak Chuadchawna ◽

Ali Farajzadeh ◽

Anchalee Kaewcharoen

Keyword(s):

Integral Equation ◽

Fixed Point ◽

Strong Convergence ◽

Fixed Points ◽

Banach Spaces ◽

Nonexpansive Mappings ◽

Iteration Process ◽

Hyperbolic Spaces ◽

Convergence Theorems ◽

Numerical Example

In this paper, we propose the generalized M-iteration process for approximating the fixed points from Banach spaces to hyperbolic spaces. Using our new iteration process, we prove Δ-convergence and strong convergence theorems for the class of mappings satisfying the condition Cλ and the condition E which is the generalization of Suzuki generalized nonexpansive mappings in the setting of hyperbolic spaces. Moreover, a numerical example is given to present the capability of our iteration process and the solution of the integral equation is also illustrated using our main result.

Download Full-text

Controllability for some nonlinear impulsive partial functional integrodifferential systems with infinite delay in Banach spaces

Open Journal of Mathematical Analysis ◽

10.30538/psrp-oma2020.0069 ◽

2020 ◽

Vol 4 (2) ◽

pp. 104-115

Author(s):

Khalil Ezzinbi ◽

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Banach Spaces ◽

Integrodifferential Equation ◽

Resolvent Operator ◽

Measure Of Noncompactness ◽

Infinite Delay ◽

Sufficient Conditions ◽

Mönch Fixed Point Theorem ◽

The Resolvent Operator

This work concerns the study of the controllability for some impulsive partial functional integrodifferential equation with infinite delay in Banach spaces. We give sufficient conditions that ensure the controllability of the system by supposing that its undelayed part admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point Theorem. As a result, we obtain a generalization of the work of K. Balachandran and R. Sakthivel (Journal of Mathematical Analysis and Applications, 255, 447-457, (2001)) and a host of important results in the literature, without assuming the compactness of the resolvent operator. An example is given for illustration.

Download Full-text