Faik Gürsoy

Fixed Point of a New Three-Step Iteration Algorithm under Contractive-Like Operators over Normed Spaces

We introduce a new three-step iteration scheme and prove that this new iteration scheme is convergent to fixed points of contractive-like operators. Also, by providing an example, we show that our new iteration method is faster than another iteration method due to Suantai (2005). Furthermore, it is shown that this new iteration method is equivalent to some other iteration methods in the sense of convergence. Finally, it is proved that this new iteration method is -stable.

Jungck-Khan iterative scheme and higher convergence rate

In this paper, we continue the theme of analytical and numerical treatment of Jungck-type iterative schemes. In particular, we focus on a special case of Jungck-Khan iterative scheme introduced by Khan et al. [Analytical and numerical treatment of Jungck-type iterative schemes, Appl. Math. Comput. 231 (2014) 521–535] to get an insight in the strong convergence and data dependence results obtained therein. Our investigations show that this special case under different control conditions on parametric sequences provides higher convergence rate and better data dependence estimates as compared to the Jungck-Khan iterative scheme itself.

Statistical Convergence of Sequences of Functions inIntuitionistic Fuzzy Normed Spaces

We study -statistically convergent sequences of functions in intuitionistic fuzzy normed spaces. We define concept of -statistical pointwise convergence and -statistical uniform convergence in intuitionistic fuzzy normed spaces and we give some basic properties of these concepts.

Statistical Convergence of Sequences of Functions in Intuitionistic Fuzzy Normed Spaces

The purpose of this work is to investigate types of convergence of sequences of functions in intuitionistic fuzzy normed spaces and some properties related with these concepts.

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

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.

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

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.

Data Dependence Results for Multistep and CR Iterative Schemes in the Class of Contractive-Like Operators

We intend to establish some results on the data dependence of fixed points of certain contractive-like operators for the multistep and CR iterative processes in a Banach space setting. One of our results generalizes the corresponding results of Soltuz and Grosan (2008) and Chugh and Kumar (2011).

Convergence and Data Dependency of Normal−S Iterative Method for Discontinuous Operators on Banach Space

ABSTRACT We study convergence, rate of convergence and data dependency of normal−S iterative method for a fixed point of a discontinuous operator T on a Banach space. We also prove some Collage type theorems for T. The main aim here is to show that there is a close relationship between the concepts of data dependency of fixed points and the collage theorems and show that the latter provides better estimate. Numerical examples in support of the results obtained are also given.