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Speaker: Francis Su

We prove three theorems giving fixed points for orientation preserving homeomorphisms of the plane following forgotten results of Brouwer.

This paper is an introduction to soft cone metric spaces. We define the concept of soft cone metric via soft element, investigate soft converges in soft cone metric spaces and prove some fixed point theorems for contractive mappings on soft cone metric spaces.

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The main purpose of this paper is to extend the results of fixed point theorems for lipschitzian semigroups. The proofs we give follow the results of Ishihara, Suantai and Puengrattana theorems. Using one of the proofs, we also develop a fixed point theorem result for nonempty asymptotically total mapping semigroups on uniformly convex Banach spaces.

In this paper we establish the existence of related fixed points theorems for two pairs of mappings with different contraction conditions in two fuzzy metric spaces.

\"{O}zavsar and Cevikel(Fixed point of multiplicative contraction mappings on multiplicative metric space.arXiv:1205.5131v1 [math.GN] 23 may 2012)initiated the concept of the multiplicative metric space in such a way that the usual triangular inequality is replaced by "multiplicative triangle inequality $d(x,y)\leq d(x,z).d(z,y)$ for all $x,y,z\in X$". In this manuscript, we discussed some unique fixed point theorems in the context of multiplicative metric spaces. The established results carry some well known results from the literature to multiplicative metric space. We note that some fixed point theorems can be deduced in multiplicative metric space by using the established results. Appropriate examples are also given.

Using an elementary argument, we prove new fixed point theorems for classical elliptic complexes. We obtain new results for conformal relations and coisotropic intersections. We obtain theorems for the average intersections of families of special lagrangian and lagrangian varieties in certain homogeneous spaces.

We study isometric actions of Steinberg groups on Hadamard manifolds. We prove some rigidity properties related to these actions. In Particular we show that every isometric action of $St_n(F_p\langle t_1,\ldots ,t_k \rangle)$ on Hadamard manifold when $n \geq 3$ is finite. We further study actions on infinite dimensional manifolds and prove a fixed point theorem related to such actions.

Speaker : Francis Su

The main purpose of this paper is to study the existence of a fixed points in fuzzy n-normed spaces. we proved our main results, a fixed point theorem for a self mapping and a common fixed point theorem for a pair of weakly compatible mappings on fuzzy n-normed spaces. Also we gave some remarks on fuzzy n-normed spaces.

In this paper, we study the existence of fixed points for mappings defined on complete (compact) metric space (X, d) satisfying a general contractive (contraction) inequality depended on another function. These conditions are analogous to Banach conditions.

Speaker: Francis Su

We propose some variants of Lefschetz fixed point theorem for Fourier-Mukai functors on a smooth projective algebraic variety. Independently we also suggest a similar theorem for endo-functors on the category of perfect modules over a smooth and proper DG algebra.

We propose some variants of Lefschetz fixed point theorem for Fourier-Mukai functors on a smooth projective algebraic variety. Independently we also suggest a similar theorem for endo-functors on the category of perfect modules over a smooth and proper DG algebra.

The deficiencies of the theories that characterize the maximal compact invariant set of T as asymptotically stable, and that some iterate of T has a fixed point are discussed. It is shown that this fixed point condition is always satisfied for condensing and local dissipative T. Applications are given to a class of neutral functional differential equations.

The deficiencies of the theories that characterize the maximal compact invariant set of T as asymptotically stable, and that some iterate of T has a fixed point are discussed. It is shown that this fixed point condition is always satisfied for condensing and local dissipative T. Applications are given to a class of neutral functional differential equations.

In this article, we prove the existence of common fixed points for a pair of maps on a $q$-spherically complete $T_0$-ultra-quasi-metric space. The present article is a generalization, in the assymmetric setting of the paper of Rao et al.\cite{Rao}. The key point in the proof is the use of Zorn's lemma. We construct an appropriate chain and show that it has a maximal element, from which we extract the fixed point we are looking for. The choice of the sets, here open balls, is characteristic of this type of problems and the contraction condition are essential, specially when we are to establish the uniqueness of the fixed point

This paper deals with a modifed iterative projection method for approximating a solution of hierarchical fixed point problems for nearly nonexpansive mappings. Some strong convergence theorems for the proposed method are presented under certain approximate assumptions of mappings and parameters. As a special case, this projection method solves some quadratic minimization problem. It should be noted that the proposed method can be regarded as a generalized version of Wang et.al. [15], Ceng et. al. [14], Sahu [4] and many other authors.

In this paper we study the existence and uniqueness of fixed points of a class of mappings defined on complete, (sequentially compact) cone metric spaces, without continuity conditions and depending on another function.

A self-map $T$ of a $\nu$-generalized metric space $(X,d\,)$ is said to be a Ciric-Matkowski contraction if $d(Tx,Ty)0$, there is $\delta>0$ such that $d(x,y) 0$, results analogue to those due to P.D. Proiniv (Fixed point theorems in metric spaces, Nonlinear Anal. 46 (2006) 546--557) are obtained.

In this paper, we establish coincidence fixed point and common fixed point theorems for two mapping in complete $C^*$-algebra-valued metric spaces which satisfy new contractive conditions. Some applications of our obtained results are given.

There are many generalization of metric space. Parametric metric space is the generalization of metric space too. Which was introduced and studied by Hussian (a new approach to metric space) in 2014. In present paper we prove two fixed point theorems based on injective mapping using contraction conditions. Moreover, we provide an example to furnish our result and also the usability of our result.

In this paper, we establish a common fixed point theorem for two pairs of occasionally weakly compatible single and set-valued maps satisfying a strict contractive condition in a metric space. Our result extends many results existing in the literature as those of Aliouche and Popa [15-20]. Also we establish another common fixed point theorem for four owc single and set-valued maps of Gregu% \v{s} type which generalizes the results of Djoudi and Nisse, Pathak, Cho, Kang and Madharia and we end our work by giving a third theorem which extends the results given by Elamrani & Mehdaoui and Mbarki.

In this paper we introduce generalized symmetric Meir-Keeler contractions and prove some coupled fixed point theorems for mixed monotone operators $F:X \times X \rightarrow X$ in partially ordered metric spaces. The obtained results extend, complement and unify some recent coupled fixed point theorems due to Samet [B. Samet, \textit{Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces}, Nonlinear Anal. \textbf{72} (2010), 4508-4517], Bhaskar and Lakshmikantham [T.G. Bhaskar, V. Lakshmikantham, \textit{Fixed point theorems in partially ordered metric spaces and applications}, Nonlinear Anal. TMA \textbf{65} (2006) 1379-1393] and some other very recent papers. An example to show that our generalizations are effective is also presented.

We establish a simple and powerful lemma that provides a criterion for sequences in metric spaces to be Cauchy. Using the lemma, it is then easily verified that the Picard iterates $\{T^nx\}$, where $T$ is a contraction or asymptotic contraction of Meir-Keeler type, are Cauchy sequences. As an application, new and simple proofs for several known results on the existence of a fixed point for continuous and asymptotically regular self-maps of complete metric spaces satisfying a contractive condition of Meir-Keeler type are derived. These results include the remarkable fixed point theorem of Proinov in [Petko D. Proinov, Fixed point theorems in metric spaces, Nonlinear Anal. \textbf{46} (2006) 546--557], the fixed point theorem of Suzuki for asymptotic contractions in [Tomonari Suzuki, A definitive result on asymptotic contractions, J. Math. Anal. Appl. \textbf{335} (2007) 707--715], and others. We also prove some new fixed point theorems.

We establish a simple and powerful lemma that provides a criterion for sequences in metric spaces to be Cauchy. Using the lemma, it is then easily verified that the Picard iterates $\{T^nx\}$, where $T$ is a contraction or asymptotic contraction of Meir-Keeler type, are Cauchy sequences. As an application, new and simple proofs for several known results on the existence of a fixed point for continuous and asymptotically regular self-maps of complete metric spaces satisfying a contractive condition of Meir-Keeler type are derived. These results include the remarkable fixed point theorem of Proinov in [Petko D. Proinov, Fixed point theorems in metric spaces, Nonlinear Anal. \textbf{46} (2006) 546--557], the fixed point theorem of Suzuki for asymptotic contractions in [Tomonari Suzuki, A definitive result on asymptotic contractions, J. Math. Anal. Appl. \textbf{335} (2007) 707--715], and others. We also prove some new fixed point theorems.

We establish a simple and powerful lemma that provides a criterion for sequences in metric spaces to be Cauchy. Using the lemma, it is then easily verified that the Picard iterates $\{T^nx\}$, where $T$ is a contraction or asymptotic contraction of Meir-Keeler type, are Cauchy sequences. As an application, new and simple proofs for several known results on the existence of a fixed point for continuous and asymptotically regular self-maps of complete metric spaces satisfying a contractive condition of Meir-Keeler type are derived. These results include the remarkable fixed point theorem of Proinov in [Petko D. Proinov, Fixed point theorems in metric spaces, Nonlinear Anal. \textbf{46} (2006) 546--557], the fixed point theorem of Suzuki for asymptotic contractions in [Tomonari Suzuki, A definitive result on asymptotic contractions, J. Math. Anal. Appl. \textbf{335} (2007) 707--715], and others. We also prove some new fixed point theorems.

In this paper, we introduce several types of correspondences: weakly naturally quasiconvex, *-weakly naturally quasiconvex, weakly biconvex and correspondences with *--weakly convex graph and we prove some fixed point theorems for these kinds of correspondences. As a consequence, using a version of W. K. Kim's quasi-point theorem, we obtain the existence of equilibria for a quasi-game.

In this paper, we introduce new methods for solving the vacuum Einstein constraints equations: the first one is based on Schaefer's fixed point theorem (known methods use Schauder's fixed point theorem) while the second one uses the concept of half-continuity coupled with the introduction of local supersolutions. These methods allow to: unify some recent existence results, simplify many proofs (for instance, the main theorem in arXiv:1012.2188) and weaken the assumptions of many recent results.

In this paper, we introduce an abstract fuzzy economy model with a measure space of agents which generalizes Patriche's model (2009), we obtain a theorem of fuzzy equilibrium existence and we prove the existence of the solutions for two types of random quasi-variational inequalities with random fuzzy mappings. As a consequence, we obtain random fixed point theorems.

In the present article, we introduce a unified notion of multi-tupled fixed points and utilize the same to prove some existence and uniqueness unified multi-tupled fixed point theorems for Boyd-Wong type nonlinear contractions satisfying generalized mixed monotone property in ordered metric spaces. Our results unify several classical and well-known n-tupled (including coupled, tripled and quadrupled ones) fixed point results existing in the literature.

In this paper, we present some new type of contractive mappings and prove new fixed point theorems on S metric Spaces. J. Gayathri | Dr. K. Sathya "Some New Fixed Point Theorems on S-Metric Spaces" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-3 , April 2020, URL: https://www.ijtsrd.com/papers/ijtsrd30311.pdf Paper Url :https://www.ijtsrd.com/other-scientific-research-area/other/30311/some-new-fixed-point-theorems-on-smetric-spaces/j-gayathri

In this paper we extend the coupled fixed point theorems for mixed monotone operators $F:X \times X \rightarrow X$ obtained in [T.G. Bhaskar, V. Lakshmikantham, \textit{Fixed point theorems in partially ordered metric spaces and applications}, Nonlinear Anal. \textbf{65} (2006) 1379-1393] and [N.V. Luong and N.X. Thuan, \textit{Coupled fixed points in partially ordered metric spaces and application}, Nonlinear Anal. \textbf{74} (2011) 983-992], by weakening the involved contractive condition. An example as well an application to nonlinear Fredholm integral equations are also given in order to illustrate the effectiveness of our generalizations.

In this paper, first we have established two sets of sufficient conditions for a mapping to have unique fixed point in a intuitionistic fuzzy metric space and then we have redefined the contraction mapping in a intuitionistic fuzzy metric space and thereafter we proved the Banach Fixed Point theorem.

In this paper we consider partial metric spaces in the sense of O'Neill. We introduce the notions of strong partial metric spaces and Cauchy functions. We prove a fixed point theorem for such spaces and functions that improves Matthews' contraction mapping theorem in two ways. First, the existence of fixed points now holds for a wider class of functions and spaces. Second, our theorem also allows for fixed points with nonzero self-distances. We also prove fixed point theorems for orbitally $r$-contractive and orbitally $\phi_r$-contractive maps. We then apply our results to give alternative proofs of some of the other known fixed point theorems in the context of partial metric spaces.

In this article, we present a new type of fixed point for single valed mapping in a $G$-complete $G$-metric space.

We establish a fixed point theorem for mappings of square matrices of all sizes which respect the matrix sizes and direct sums of matrices. The conclusions are stronger if such a mapping also respects matrix similarities, i.e., is a noncommutative function. As a special case, we prove the corresponding contractive mapping theorem which can be viewed as a new version of the Banach Fixed Point Theorem. This result is then applied to prove the existence and uniqueness of a solution of the initial value problem for ODEs in noncommutative spaces. As a by-product of the ideas developed in this paper, we establish a noncommutative version of the principle of nested closed sets.

In this paper, we prove common fixed point results for a self-mappings satisfying an implicit function which is general enough to cover a multitude of known as well as unknown contractions. Our results modify, unify, extend and generalize many relevant results of the existing literature. Interestingly, unlike several other cases, our main results deduce a nonlinear order-theoretic version of a well-known fixed point theorem (proved for quasi-contraction) due to \'{C}iri\'{c} (Proc. Amer. Math. Soc. (54) 267-273, 1974). Finally, in the setting of metric spaces, we drive a sharpened version of Theorem 1 due to Berinde and Vetro (Fixed Point Theory Appl. 2012:105).

We introduce the notions of weakly *-concave and weakly naturally quasi-concave correspondence and prove fixed point theorems and continuous selection theorems for these kind of correspondences. As applications in the game theory, by using a tehnique based on a continuous selection, we establish new existence results for the equilibrium of the abstract economies. The constraint correspondences are weakly naturally quasi-concave. We show that the equilibrium exists without continuity assumptions.

In this paper intuitionistic fuzzy {\psi}-{\phi}-contractive mappings are introduced. Intuitionistic fuzzy Banach contraction theorem for M-complete non-Archimedean intuitionistic fuzzy metric spaces and intuitionistic fuzzy Elelstein contraction theorem for non-Archimedean intuitionistic fuzzy metric spaces by intuitionistic fuzzy {\psi}-{\phi}-contractive mappings are proved.

We present proofs of basic results, including those developed by Harold Bell, for the plane fixed point problem: does every map of a non-separating plane continuum have a fixed point? Some of these results had been announced much earlier by Bell but without accessible proofs. We define the concept of the variation of a map on a simple closed curve and relate it to the index of the map on that curve: Index = Variation + 1. A fixed point theorem for positively oriented, perfect maps of the plane is obtained. This generalizes results announced by Bell in 1982. A continuous map of an interval to the real line which sends the endpoints in opposite directions has a fixed point. We generalize this to maps on non-invariant continua in the plane under positively oriented maps of the plane (with appropriate boundary conditions). These methods imply that in some cases non-invariant continua in the plane are degenerate. This has important applications in complex dynamics. E.g., a special case of our results shows that if $X$ is a non-separating invariant subcontinuum of the Julia set of a polynomial $P$ containing no fixed Cremer points and exhibiting no local rotation at all fixed points, then $X$ must be a point. It follows that impressions of some external rays to polynomial Julia sets are degenerate.

Sensitivity is a prominent aspect of chaotic behavior of a dynamical system. We study the relevance of nonsensitivity to fixed point theory in affine dynamical systems. We prove a fixed point theorem which extends Ryll-Nardzewski's theorem and some of its generalizations. Using the theory of hereditarily nonsensitive dynamical systems we establish left amenability of Asp(G), the algebra of Asplund functions on a topological group G (which contains the algebra WAP(G) of weakly almost periodic functions). We note that, in contrast to WAP(G), for some groups there are uncountably many invariant means on Asp(G). Finally we observe that dynamical systems in the larger class of tame G-systems need not admit an invariant probability measure.

Sensitivity is a prominent aspect of chaotic behavior of a dynamical system. We study the relevance of nonsensitivity to fixed point theory in affine dynamical systems. We prove a fixed point theorem which extends Ryll-Nardzewski's theorem and some of its generalizations. Using the theory of hereditarily nonsensitive dynamical systems we establish left amenability of Asp(G), the algebra of Asplund functions on a topological group G (which contains the algebra WAP(G) of weakly almost periodic functions). We note that, in contrast to WAP(G), for some groups there are uncountably many invariant means on Asp(G). Finally we observe that dynamical systems in the larger class of tame G-systems need not admit an invariant probability measure.

We establish fixed point theorems for nonlinear contractions on a metric space (not essentially complete) endowed with an arbitrary binary relation. Our results extend, generalize, modify and unify several known results especially those contained in Samet and Turinici [Commun. Math. Anal. 13, 82-97 (2012)] and Alam and Imdad [J. Fixed Point Theory Appl. 17(4), 693-702 (2015)]. Interestingly a corollary to one of our main results proved under symmetric closure of any binary relation remains a sharpened version of a theorem due to Samet and Turinici. Finally, we use examples to highlight the realized improvements in the results proved in this paper.

In this paper, we prove some coupled fixed point theorems for mappings satisfying different contractive conditions in the context of complete $C^*$-algebra-valued metric spaces. Moreover, the paper provides an application to prove the existence and uniqueness of a solution for Fredholm nonlinear integral equations.

The aim of this paper is to establish some metrical coincidence and common fixed point theorems with an arbitrary relation under an implicit contractive condition which is general enough to cover a multitude of well known contraction conditions in one go besides yielding several new ones. We also provide an example to demonstrate the generality of our results over several well known corresponding results of the existing literature. Finally, we utilize our results to prove an existence theorem for ensuring the solution of an integral equation.

We prove two generalizations of results proved by Bruhat and Tits involving metrical completeness and R-buildings. Firstly, we give a generalization of the Bruhat-Tits fixed point theorem also valid for non-complete R-buildings, but with the added condition that the group is finitely generated. Secondly, we generalize a criterion which reduces the problem of completeness to the wall trees of the R-building.

In this paper, first we have established two sets of sufficient conditions for a TS-IF contractive mapping to have unique fixed point in a intuitionistic fuzzy metric space. Then we have defined \,$(\,\epsilon \,,\, \lambda\,)$\, IF-uniformly locally contractive mapping and \,$\eta\,-$\,chainable space, where it has been proved that the \,$(\,\epsilon \,,\, \lambda\,)$\, IF-uniformly locally contractive mapping possesses a fixed point