Relational Meir-Keeler Contractions and Common Fixed Point Theorems

In this paper we prove some fixed point theorems for weakly compatible mappings with the notation of A-distance and E-distance in uniform space.

The concept of a W function was introduced very recently by Chen (1) and was used to prove several common fixed point theorems in complete generalized metric spaces. Using a a subclass of these W functions introduced in (1), we prove some fixed point theorems with one, and a pair of self maps on a G-metric space

In this present paper, we establish Cantor's intersection like theorem in a locally convex topological vector spaces. Some fixed point and common fixed point theorems are proved for Reich and Caccioppoli type contractive mappings in such a locally convex topological vector space. Also in this setting we prove a fixed point theorem for some mapping which is the uniform limit of a sequence of Reich type contractive mappings therein. <br><br> Встановлена теорема, подібна теоремі Кантора про перетин, у випадку локально опуклих векторних просторів. Для стискуючих відображень типу Райха і Каччіополі відповідних просторів доведені теореми про нерухому точку та спільну нерухому точку. Також у цій постановці доведена теорема про нерухому точку для відображення, яке є рівномірною границею послідовності стискуючих відображень типу Райха.

In this paper, some results concerning the existence of common fixed points, coincidence points and approximating fixed points with PPF dependence for the pairs of operators in Banach spaces satisfying a generalized contractive condition are proved. The novelty of the present work lies in the fact that the domain and the range spaces of the operators in questions are not same and all the results are obtained via constructive methods. Our results generalize and extend the fixed point theorems with PPF dependence of Bernfeld et al. [S. R. Bernfeld, V. Lakshmikatham and Y. M. Reddy, Applicable Anal. 6 (1977), 271-280] and Dhage [B. C. Dhage, Fixed point Theory, (to appear)] under more general contractive conditions.

Fixed point theory in cone metric spaces obtained via the scalarization method

Common fixed points of nonlinear hybrid mappings under strict contractions in semi-metric spaces

Recently Suzuki (2008) and then Kikkawa and Suzuki (2008) gave a new generalization of the Banach contraction principle. Then, Mot and Petrusel (2009), Dhompapangasa and Yingtaweesttikulue (2009), Bose and Roychowd- hury (2011), Singh and Mishra (2010), and Doric and Lazovic (2011) further extended their work. Recently Bose (2012) obtained some Suzuki-type common fixed point theorems for generalized contractive multivalued mappings using a result of Bose and Mukherjee(1977) which extend the previously obtained re- sults. Recently Damjanovic and Doric(2011) obtained a multivalued generaliza- tion of theorems Kikkawa and Suzuki (2008) concerning Kannan mappings. Also Singh and Mishra (2010) considered coincidence and fixed point theorems for a class of hybrid pair of single-valued and multi-valued maps in metric space setting and Singh et al (2012) prsented a common fixed point theorem for a pair of multi-valued maps in a complete metric space extending a recent theorem of Doric and Lazovic. First we generalize the theorem of Singh et al which also extend the theorem of Singh and Mishra(2010). Then we extend the theorem of Damjanovic and Doric to a common fixed point theorem of a pair of mul- tivalued mappings. As an application, we consider the existence of a common solution for a class of functional equations arising in dynamic programming.

In this paper, we prove some common fixed point theorems using (CLR) property in KM and GV-fuzzy metric spaces. Our results extend and unify several fixed point theorems present in the literature.

&lt;abstract&gt;&lt;p&gt;We introduce a Ćirić type contraction principle in a vector-valued $ b $-metric space that generalizes Perov's contraction principle. We investigate the possible conditions on the mappings $ W, E:G\rightarrow G $ ($ G $ is a non-empty set), for which these mappings admit a unique common fixed point in $ G $ subject to a nonlinear operator $ {\bf F}:\mathbb{P}^{m} \rightarrow \mathbb{R}^{m} $. We illustrate the hypothesis of our findings with examples. We consider an infectious disease model represented by the system of delay integro-differential equations and apply the obtained fixed point theorem to show the existence of a solution to this model.&lt;/p&gt;&lt;/abstract&gt;

The present research paper aims to establish some generalized Banach fixed point theorems on closed Hilbert spaces using the sequence of mappings and satisfying the Banach Fixed point Property. The Banach fixed point theory plays an important role in modern areas of mathematics, mathematical Science, and different branches of Science. Koparde P. V; Waghmode B. B [5]; Pandhar, M. D and Waghmode, B. B [6] have established some Banach Fixed point theorems on a sequence of mappings on a closed subset S of a Hilbert space H. After that, Veerapandi, T and Kumar, S. A. [9] have introduced some fruitful results in this line. In this research article, some generalized Banach fixed point theorems of Veerapandi, T and Kumar, S. A. [9] are stated above. The mathematician established a theory on Hilbert spaces in sequences of mappings on closed spaces.

In the context of a complete metric space, we will consider the common fixed point problem for two self operators. The operators are assumed to satisfy a general contraction type condition inspired by the Ćirić fixed point theorems. Under some appropriate conditions we establish existence, uniqueness and approximation results for the common fixed point. In the same framework, the second problem is to study various stability properties. More precisely, we will obtain sufficient conditions assuring that the common fixed point problem is well-posed and has the Ulam–Hyers stability, as well as the Ostrowski property for the considered problem. Some examples and applications are finally given in order to illustrate the abstract theorems proposed in the first part of the paper. Our results extend and complement some theorems in the recent literature.

The aim of this manuscript is to improve certain results established in a recent paper of Imdad et al on the existence of a common fixed point for contractive mappings in fuzzy metric spaces. Further, we generalize and extend some common fixed point theorems due to Ali and Imdad and some fixed point theorems due to Mihet to the case of fuzzy metric‐like spaces. We also furnish an illustrative example to demonstrate the validity of the hypotheses and degree of generality of our main result.

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Presented are some new common fixed point theorems which generalize some well-known results in papers [ 1-10, 12-19 ]. The method used in this paper defers from that used by other authors

Fixed point theorems in Boolean vector spaces