scholarly journals Some Convergence and Stability Results for Two New Kirk Type Hybrid Fixed Point Iterative Algorithms

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Faik Gürsoy ◽  
Vatan Karakaya
Keyword(s):  
Fixed Point ◽  
Iterative Algorithms ◽  
Convergence And Stability ◽  
Stability Results

We introduce Kirk-multistep-SP and Kirk-S iterative algorithms and we prove some convergence and stability results for these iterative algorithms. Since these iterative algorithms are more general than some other iterative algorithms in the existing literature, our results generalize and unify some other results in the literature.

scholarly journals Some Convergence and Stability Results for the Kirk Multistep and Kirk-SP Fixed Point Iterative Algorithms

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Faik Gürsoy ◽  
Vatan Karakaya ◽  
B. E. Rhoades
Keyword(s):  
Fixed Point ◽  
Iterative Algorithm ◽  
Iterative Algorithms ◽  
Iterative Processes ◽  
Convergence And Stability ◽  
The Stability ◽  
Stability Results

The purpose of this paper is to introduce a new Kirk type iterative algorithm called Kirk multistep iteration and to study its convergence. We also prove some theorems related to the stability results for the Kirk multistep and Kirk-SP iterative processes by employing certain contractive-like operators. Our results generalize and unify some other results in the literature.

scholarly journals Convergence and stability of an iterative algorithm for strongly accretive Lipschitzian operator with applications

Filomat ◽  
2020 ◽  
Vol 34 (11) ◽  
pp. 3689-3704
Author(s):  
Vivek Kumar ◽  
Nawab Hussain ◽  
Abdul Khan ◽  
Faik Gürsoy
Keyword(s):  
Iterative Algorithm ◽  
Nonlinear Operator ◽  
Iterative Algorithms ◽  
Convergence Result ◽  
Nonlinear Operator Equation ◽  
Inclusion Problem ◽  
Convergence And Stability ◽  
Variational Inclusion Problem ◽  
Convergence Results ◽  
Stability Results

Using different technique and weaker restrictions on parameters, convergence and stability results of an SP iterative algorithm with errors for a strongly accretive Lipschitzian operator on a Banach space are established. Validity of new convergence results is verified through numerical examples and convergence comparison of various iterative algorithms is depicted. As applications of our convergence result, we solve a nonlinear operator equation and a variational inclusion problem. Our results are refinement and generalization of many classical results.

Random iterative algorithms and almost sure stability in Banach spaces

Filomat ◽  
2017 ◽  
Vol 31 (12) ◽  
pp. 3611-3626 ◽  
Author(s):  
Abdul Khan ◽  
Vivek Kumar ◽  
Satish Narwal ◽  
Renu Chugh
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Iterative Algorithms ◽  
Random Operator ◽  
Almost Sure Stability ◽  
Random Fixed Point ◽  
Stochastic Version ◽  
Contractive Type ◽  
Bochner Integrability ◽  
Weakly Contractive

Many popular iterative algorithms have been used to approximate fixed point of contractive type operators. We define the concept of generalized ?-weakly contractive random operator T on a separable Banach space and establish Bochner integrability of random fixed point and almost sure stability of T with respect to several random Kirk type algorithms. Examples are included to support new results and show their validity. Our work generalizes, improves and provides stochastic version of several earlier results by a number of researchers.

scholarly journals Existence and Ulam stability for implicit fractional q-difference equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Nadjet Laledj ◽  
Yong Zhou
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Ulam Stability ◽  
Uniqueness Of Solutions ◽  
Stability Results ◽  
Rassias Stability

AbstractThis paper deals with some existence, uniqueness and Ulam–Hyers–Rassias stability results for a class of implicit fractional q-difference equations. Some applications are made of some fixed point theorems in Banach spaces for the existence and uniqueness of solutions, next we prove that our problem is generalized Ulam–Hyers–Rassias stable. Two illustrative examples are given in the last section.

scholarly journals Iterative Algorithms for Solving the System of Mixed Equilibrium Problems, Fixed-Point Problems, and Variational Inclusions with Application to Minimization Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-29 ◽  
Author(s):  
Tanom Chamnarnpan ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Equilibrium Problems ◽  
Real Hilbert Space ◽  
Nonexpansive Mappings ◽  
Monotone Mapping ◽  
Iterative Algorithms ◽  
Infinite Family ◽  
Common Element ◽  
Mixed Equilibrium Problems ◽  
Mixed Equilibrium

We introduce a new iterative algorithm for solving a common solution of the set of solutions of fixed point for an infinite family of nonexpansive mappings, the set of solution of a system of mixed equilibrium problems, and the set of solutions of the variational inclusion for aβ-inverse-strongly monotone mapping in a real Hilbert space. We prove that the sequence converges strongly to a common element of the above three sets under some mild conditions. Furthermore, we give a numerical example which supports our main theorem in the last part.

scholarly journals Uniqueness and Stability Results on Non-local Stochastic Random Impulsive Integro-Differential Equations

2021 ◽  
Vol 2 (3) ◽  
pp. 9-20
Author(s):  
VARSHINI S ◽  
BANUPRIYA K ◽  
RAMKUMAR K ◽  
RAVIKUMAR K
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Banach Fixed Point Theorem ◽  
Local Conditions ◽  
Non Local ◽  
Inequality Techniques ◽  
Stability Results

The paper is concerned with stochastic random impulsive integro-differential equations with non-local conditions. The sufficient conditions guarantees uniqueness of mild solution derived using Banach fixed point theorem. Stability of the solution is derived by incorporating Banach fixed point theorem with certain inequality techniques.

scholarly journals Convergence and Stability Results of Modified CUIA Iterative Scheme for Hyperbolic Convex Metric space

2021 ◽  
Vol 2089 (1) ◽  
pp. 012040
Author(s):  
Surjeet Singh Chauhan Gonder ◽  
Khushboo Basra
Keyword(s):  
Fixed Points ◽  
Integral Equations ◽  
Metric Space ◽  
Iterative Scheme ◽  
Real Life ◽  
Convex Metric Space ◽  
Convergence And Stability ◽  
Life Problems ◽  
Stability Results ◽  
Differential And Integral Equations

Abstract The iterative fixed points have numerous applications in locating the solution of some real-life problems which can be modelled into linear as well as nonlinear differential and integral equations. In this manuscript, first of all, a new iterative scheme namely Modified CUIA iterative scheme is introduced. We first prove a theorem to check the convergence of this iteration for Hyperbolic Convex metric space. The result is then supported with one example. Further, another theorem is proved establishing the weak T stability of modified CUIA iterative scheme on the above space.

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