Common Fixed Point Theorems in Uniform Spaces

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In this paper, we prove some common fixed point theorems in 0-complete partial metric spaces. Our results extend and generalize many existing results in the literature. Some examples are included which show that the generalization is proper.

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

In this paper we prove common and coincidences fixed point theorems for asymptotically regular mappings under various contractive conditions on a Hilbert space setting. We also study the well – posedness of a common fixed point problem. Our results generalize several well known results in the literature.

In the present paper we consider initial value problems for Hilfer fractional differential equations and for system of Hilfer fractional differential equations. By using equivalent integral equations and some fixed point theorems, we study the local existence of solutions. We extend these local existence results globally with the help of continuation theorems and generalized Gronwall inequality.

In this paper we have established fixed point theorems for $dq$-rectangular $b$-cyclic-Banach and $dq$-rectangular $b$-cyclic-Kannan contraction mappings in dislocated quasi rectangular $b$-metric spaces. We have also presented examples to support some of our results.

In this article, we prove some coincidence and common fixed point theorems under the relation-theoretic Meir-Keeler contractions in a metric space endowed with a locally finitely T -transitive binary relation. Our newly proved results generalize, extend, and sharpen some existing coincidence point as well as fixed point theorems existing in the literature. Moreover, we give some examples to affirm the efficacy of our results.

In this paper, we prove a new common random fixed point theorem for a pair of random operators satisfying random F-contraction of rational inequality in polish spaces. An application to a system of random nonlinear integral equations is discussed. Finally, we give some examples to verify our results.

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, we first establish some new types of fixed point theorem which generalize and improve Berinde-Berinde's fixed point theorem, Mizoguchi-Takahashi's fixed point theorem and many results in [W.-S. Du, Some new results and generalizations in metric fixed point theory, Nonlinear Anal. 73 (2010), 1439-1446] and references therein. Applying those new results, we also present some existence theorems of coincidence point and others.

The present paper is concerned with the Ekeland Variational Principle (EkVP) and its equivalents (Caristi–Kirk fixed point theorem, Takahashi minimization principle, Oettli-Théra equilibrium version of EkVP) in quasi-uniform spaces. These extend some results proved by Hamel and Löhne [A minimal point theorem in uniform spaces. In: Nonlinear analysis and applications: to V. Lakshmikantham on his 80th birthday. Vols 1, 2. Dordrecht: Kluwer Academic Publishers; 2003. p. 577–593] and Hamel [Equivalents to Ekeland's variational principle in uniform spaces. Nonlinear Anal. 2005;62:913–924] in uniform spaces, as well as those proved in quasi-metric spaces by various authors. The case of F-quasi-gauge spaces, a non-symmetric version of F-gauge spaces introduced by Fang [The variational principle and fixed point theorems in certain topological spaces. J Math Anal Appl. 1996;202:398–412], is also considered. The paper ends with the quasi-uniform versions of some minimization principles proved by Arutyunov and Gel'man [The minimum of a functional in a metric space, and fixed points. Zh Vychisl Mat Mat Fiz. 2009;49:1167–1174] and Arutyunov [Caristi's condition and existence of a minimum of a lower bounded function in a metric space. Applications to the theory of coincidence points. Proc Steklov Inst Math. 2015;291(1):24–37] in complete metric spaces.

In this paper, we prove some common fixed point theorems for various types of compatible mappings in the setting of complete multiplicative metric spaces.

In this paper, we establish some common fixed point theorems for selfmappings of a uniform space by employing both the concepts of an A—distance and an E—distance introduced by Aamri and El Moutawakil [1] and two contractive conditions of integral type. Our results are generalizations and extensions of the classical Banach's fixed point theorem of [2, 3, 19], some results of Aamri and El Moutawakil [1], Theorem 2.1 of Branciari [5] as well as a result of Jungck [7].

In this article, we study some new coupled coincidence and coupled common fixed point theorems in metric-like spaces for integral type contraction condition involving a pair of mappings satisfying the CRLg property. As an application, we discuss the existence of the solution for a coupled system of functional equations arising in dynamic programming. Our results generalize and modify several comparable results in the literature. Finally, two examples are given to illustrate the usefulness of the theoretical results.