arXiv subjects
Publications and source records attributed to Vatan Karakaya.
In this work, we prove the existence of solutions for a tripled system of integral equations using some new results of fixed point theory associated with measure of noncompactness. These results extend some previous works in the literature, since the condition under which the operator admits fixed points is more general than the others in literature.
The main purpose of this work is to extend the properties of multivalued transformations to the integral type transformations and to obtain the existence of fixed points under F-contraction. In addition, the results of this study were evaluated with some interesting example.
In this paper, some results on the existence of n-tuplet fixed points for multi-valued contraction mappings are proved via measure of noncompactness. As an application, the existence of solutions for a system of integral inclusions is studied.
In this paper, we introduce a new iteration method and show that this iteration method can be used to approximate fixed point of almost contraction mappings. Furthermore, we prove that the new iteration method is equivalent to both Mann iteration method and Picard-Mann hybrid iteration method and also converges faster than Picard-Mann hybrid iteration method for the class of almost contraction mappings. In addition to these we give a table and graphics for support this result. Finally, we prove a data dependence result for almost contraction mappings by using the new iteration method.
In this paper, we introduce a new variational inequality problem(VIP) associated with nonself multivalued nonexpansive mappings in $CAT(0)$ spaces.
In this paper, we introduce a new type of Darbo's fixed point theorem by using concept of function sequences with shifting distance property. Afterward, we investigate existence of fixed point under this the theorem. Also we are going to give interesting example held the conditions of sequences of functions
In this paper by using the measure of noncompactness concept, we present new fixed point theorems for multivalued maps. In further we introduce a new class of mappings which are general than Meir-Keeler mappings. Finally, we use these results to investigate the existence of weak solutions to an Evolution differential inclusion with a lack of compactness.
In this study, we give definition of some multivalued hybrid mappings which are general than many mappings in the existing literature, then we give some existence and convergence results for these mappings in CAT(κ)-spaces
A sequence of real numbers $\{x_{n}\}_{n\in \mathbb{N}}$ is said to be $αβ$-statistically convergent of order $γ$ (where $0<γ\leq 1$) to a real number $x$ \cite{a} if for every $δ>0,$ $$\underset{n\rightarrow \infty} {\lim} \frac{1}{(β_{n} - α_{n} + 1)^γ}~ |\{k \in [α_n,β_n] : |x_{k}-x|\geq δ\}|=0.$$ where $\{α_{n}\}_{n\in \mathbb{N}}$ and $\{β_{n}\}_{n\in \mathbb{N}}$ be two sequences of positive real numbers such that $\{α_{n}\}_{n\in \mathbb{N}}$ and $\{β_{n}\}_{n\in \mathbb{N}}$ are both non-decreasing, $β_{n}\geq α_{n}$ $\forall ~n\in \mathbb{N},$ ($β_{n}-α_{n})\rightarrow \infty$ as $n\rightarrow \infty.$ In this paper we study a related concept of convergences in which the value $|x_{k}-x|$ is replaced by $P(|X_{k}-X|\geq \varepsilon)$ and $E(|X_{k}-X|^{r})$ repectively (Where $X, X_k$ are random variables for each $k\in \mathbb{N}$, $\varepsilon>0$, $P$ denote the probability, $E$ denote the expectation) and we call them $αβ$-statistical convergence of order $γ$ in probability and $αβ$-statistical convergence of order $γ$ in $r^{\mbox{th}}$ expectation respectively. The results are applied to build the probability distribution for $αβ$-strong $p$-Ces$\grave{\mbox{a}}$ro summability of order $γ$ in probability and $αβ$-statistical convergence of order $γ$ in distribution. Our main objective is to interpret a relational behavior of above mentioned four convergences.
In this paper, we define concept of approximate fixed point property of a function and a set in intuitionistic fuzzy normed space. Furthermore, we give intuitionistic fuzzy version of some class of maps used in fixed point theory and investigate approximate fixed point property of these maps.
Our aim in this paper is to present results of existence of fixed points for continuous operators in Banach spaces using measure of noncompactness under an integral condition. This results are generalization of results given by A. Aghajania and M. Aliaskaria which are generalization of Darbo's fixed point theorem. As application we use these results to solve an integral equations in Banach spaces.
We introduce a new iteration method called Picard-S iteration. We show that the Picard-S iteration method can be used to approximate fixed point of contraction mappings. Also, we show that our new iteration method is equivalent and converges faster than CR iteration method for the aforementioned class of mappings. Furthermore, by providing an example, it is shown that the Picard-S iteration method converges faster than all Picard, Mann, Ishikawa, Noor, SP, CR, S and some other iteration methods in the existing literature when applied to contraction mappings. A data dependence result is proven for fixed point of contraction mappings with help of the new iteration method. Finally, we show that the Picard-S iteration method can be used to solve differential equations with retarded argument.
We show that iterative scheme due to Karahan and Özdemir (2013) can be used to approximate fixed point of contraction mappings. Furthermore, we prove that CR iterative scheme converges faster than the iterative scheme due to Karahan and Özdemir (2013) for the class contraction mappings. Finally, we prove a data dependence result for contraction mappings by employing iterative scheme due to Karahan and Özdemir (2013).
In this paper, we show that Picard, Krasnoselskij, Mann, Ishikawa, new two step, Noor, multistep, new multistep, SP and S-iterative schemes are equivalent for contractive-like operators.
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 with 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.
In this paper, we prove that convergence of a new iteration and S-iteration can be used to approximate to the fixed points of contractive-like operators. We also prove some data dependence results of this new iteration and S-iteration schemes for contractive-like operators. Our results extend and improve some known results in the literature.
Fuzzy logic was introduced by Zadeh in 1965. Since then, the importance of fuzzy logic has come increasingly to the present.There are many applications of fuzzy logic in the field of science and engineering, e.g. population dynamics (Barros), chaos control (Feng,Fradkov), computer programming (Giles), nonlinear dynamical systems (Hong), etc. The concept of intuitionistic fuzzy set, as a generalization of fuzzy logic, was introduced by Atanassov in 1986. Quite recently Park has introduced the concept of intuitionistic fuzzy metric space, and Saadati and Park studied the notion of intuitionistic fuzzy normed space. Intuitionistic fuzzy analogues of many concept in classical analysis was studied by many authors (Mursaleen, Rsaadati, Jebril, Dinda, etc.). The concept of statistical convergence was introduced by Fast. Mursaleen defined λ-statistical convergence in Muhammed. Also the concept of statistical convergence was studied in intuitionistic fuzzy normed space in Karakus..Quite recently, Karakaya et al. defined and studied statistical convergence of function sequences in intuitionistic fuzzy normed spaces. Mohiuddine and Lohani defined and studied λ-statistical convergence in intuitionistic fuzzy normed spaces (Lohani). In this paper, we shall study concept λ-statistical convergence for function sequences and investigate some basic properties related to the concept in intuitionistic fuzzy normed space.
In general, it is well known the behaviors of the symmetric tri-band matrices on the Hilbert spaces. But the symmetric tri-band matrices have different the behavior on the Banach spaces. The main purpose of this work is to determine the fine spectra of the operator U(s, r, s) defined by symmetric tri-band matrix over the sequence spaces {\ell}_p and bvp.