دانشگاه آزاداسلامی واحدعلوم وتحقیقات تهران
دانشگاه امیرکبیرتهران(پلی تکنیک)
قضیه نقطه ثابت داربو و تعمیم¬های آن نقش بسیار مهمی در حل وجودی معادلات انتگرال دارد. قضیه نقطه ثابت برای نگاشتهای میر-کیلر جمع شونده یکی از تعمیمهای قضیه داربو است که بسیاری از تعمیمهای دیگر حالت خاصی از آن هستند. در سالهای اخیر، نویسندگان زیادی از این توسیعها برای حل تعدادی از معادلات انتگرال استفاده کرده¬اند. برخی از آنها با استفاده از اندازه نافشردگی و الهام گرفتن از انقباض¬های میر-کیلر در فضاهای متری، یک مشخص سازی برای نگاشتهای میر-کیلر جمع شونده ارایه کرده اند. اما از آنجا که این مشخصه سازی ها نیازمند وجود یک - تابع هستند و پیدا کردن یک - تابع نیازمند تلاش زیادی است بنابراین چنین مشخص سازی هایی عملا بی فایده اند. لذا بر آن شدیم که یک مشخصه سازی جدید برای این نوع عملگرها بیابیم. در این مقاله، با استفاده از مفهوم اندازه نافشردگی یک مشخص سازی جدید برای نگاشتهای میر-کیلر جمع شونده را ارایه می¬کنیم. مشخص سازی حاضر معیاری را بدست می¬دهد که بوسیله آن می¬توان بررسی کرد که یک تعمیم ارایه شده از قضیه داربو یک انقباض میر-کیلر جمع شونده است یا خیر. در پایان با استفاده از مشخص سازی ارایه شده نشان می¬دهیم که بسیاری از تعمیمهای قضیه داربو که تا کنون ارایه شده اند از نوع میر-کیلر جمع شونده هستند.
In this paper, we give a generalization of Sadovski i˘ ’s fixed-point theorem for condensing operators, which is slightly more flexible than this result in applying to some different problems. We apply our extension to prove some results in integral equations. At the end, we illustrate our results by concrete examples to confirm that our method can be used effectively to solve some integral equations.
In this manuscript we introduce the notion of S-operators and as a result we present a new characterization of Meir-Keeler contractions. Also it is shown that the set of S-operators includes the set of continuous R-contractions, and by providing an example it is justified that this inclusion is proper. We use our Meir-Keeler characterization as a tool to show that many different contractions are Meir-Keeler. Finally we extend some fixed point results.
In this manuscript the notion of S-operators is introduced and as a result a new characterization of Meir–Keeler contractions is presented. Also it is shown that the set of S-operators includes the set of continuous R-contractions, and by providing an example it is justified that this inclusion is proper. Then Edelstein’s theorem for contractive mappings on compact metric spaces is generalized to S0 -operators. Finally the set of S-operators is extended to the set of orbitally S-operators that includes Matkowski contractions.
In this paper, a numerical solution (Euler method) for solving first-order fully fuzzy differential equations (FFDE) in the form y′(t)=a⊗y(t), y(0)=y0,t∈[0,T] under strongly generalized H-differentiability is considered. First, we will show that under H-differentiability the FFDE can be divided into four differential equations. Then, we will prove that each of divided differential equations satisfies the Lipschitz condition, therefore, FFDE has a unique solution and Euler method can be used to find an approximate solution in each case. Convergence of this method is proved and an algorithm by which the exact solution can be approximated in each case will be provided.
We use two appropriate bounded invertible operators to define a controlled frame with optimal frame bounds. We characterize those operators that produces Parseval controlled frames also we state a way to construct nearly Parseval controlled frames. We introduce a new perturbation of controlled frames to obtain new frames from a given one. Also we reduce the distance of frames by appropriate operators and produce nearly dual frames from two given frames which are not dual frames for each other.
In this paper, a new approach for solving the second order fuzzy di erential equations (FDE) with fuzzy initial value, under strongly generalized H-di erentiability is presented. Solving rst order fuzzy di erential equations by extending 1-cut solution of the original problem and solving fuzzy integro- di erential equations has been investigated by some authors (see for example [5, 6]), but these methods have been done for fuzzy problems with triangular fuzzy initial value. Therefore by extending the r-cut solutions of the original problem we will obviate this de ciency. The presented idea is based on: if a second order fuzzy di erential equation satisfy the Lipschitz condition then the initial value problem has a unique solution on a speci c interval, therefore our main purpose is to present a method to nd an interval on which the solution is valid.
In this work, partial answers to Reich, Mizoguchi and Takahashi’s and Amini-Harandi’s conjectures are presented via a light version of Caristi’s fixed point theorem. Moreover, we introduce the idea that many of known fixed point theorems can easily be derived from the Caristi theorem. Finally, the existence of bounded solutions of a functional equation is studied.
In this paper, we present a solution of an arbitrary general fully fuzzy linear systems (FFLS) in the form A⊗ x= b. Where coefficient matrix A is an m× n fuzzy matrix and all of this system are elements of LR type fuzzy numbers. Our method discuss a general FFLS (square or rectangle fully fuzzy linear systems with trapezoidal or triangular LR fuzzy numbers). To do this, we transform fully fuzzy linear system in to two crisp linear systems, then obtain the solution of this two systems by using the pseudo inverse matrix method. Numerical examples are given to illustrate our method.
Replacing the set of real numbers by an ordered Banach space in the definition of a metric, Guang and Xian  introduced the concept of a cone metric and obtained some fixed point Theorems for contractive mappings on cone metric spaces. It has been shown that every cone metric space is metrizable [2-4]. In this paper we review and simplify some results of  and as a consequence of our earlier results and in a totally different way will show again that every cone metric space is metrizable and finally prove some fixed point theorems.
In this paper we give generalize some common fixed point results for multi-valued contractive mappings on complete metric spaces. Our results extend recent results of Y. Feng and S. Liu and of N. Mizoguchi and W. Takahashi. We show that some common fixed point contraction theorems for multi-valued mappings are straightforward consequence of our results.
Let (E, τ) be a topological vector space and P a cone in E. We shall define a topology τ P on E so that (E, τ P ) is a normable topological vector space and P is a normal cone with normal constant M = 1. Then by using the norm, we shall give some results about common fixed points of two multifunctions on cone metric spaces.
In this paper we give some theorems of generalized contractive mappings on ordered metric spaces and extend some results of Zhang Xian [Zhang. Xian, Common fixed point theorems for some new generalized contractive type mappings, Trans. Amer. Math. Soc. 266(1977)257- 290] to ordered metric spaces and generalize a result of Agarwal, Ravi. P, El-gebeily, M. A. and D. O’Regan, donal [Agarwal, Ravi. P, Elgebeily, M. A. and D. O’Regan, donal(2008)Generalized contractions in partially ordered metric spaces, Applicable Analysis, 87:1, 109-116]. We also introduce some new type of contractive mappings on ordered metric spaces and prove some related results for them.