scholarly journals Some Results on Fixed and Best Proximity Points of Multivalued Cyclic Self-Mappings with a Partial Order

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
M. De la Sen
Keyword(s):  
Fixed Points ◽  
Partial Order ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Uniformly Convex ◽  
Best Proximity Points ◽  
Complete Metric Spaces ◽  
Uniformly Convex Banach Spaces ◽  
Nonempty Convex ◽  
Composite Self

This paper is devoted to investigate the fixed points and best proximity points of multivalued cyclic self-mappings on a set of subsets of complete metric spaces endowed with a partial order under a generalized contractive condition involving a Hausdorff distance. The existence and uniqueness of fixed points of both the cyclic self-mapping and its associate composite self-mappings on each of the subsets are investigated, if the subsets in the cyclic disposal are nonempty, bounded and of nonempty convex intersection. The obtained results are extended to the existence of unique best proximity points in uniformly convex Banach spaces.

scholarly journals Best Proximity Points of Generalized Semicyclic Impulsive Self-Mappings: Applications to Impulsive Differential and Difference Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
M. De la Sen ◽  
E. Karapinar
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Impulsive Differential Equations ◽  
The Self ◽  
Uniformly Convex ◽  
Convergence Properties ◽  
Best Proximity Points ◽  
Complete Metric Spaces ◽  
Uniformly Convex Banach Spaces

This paper is devoted to the study of convergence properties of distances between points and the existence and uniqueness of best proximity and fixed points of the so-called semicyclic impulsive self-mappings on the union of a number of nonempty subsets in metric spaces. The convergences of distances between consecutive iterated points are studied in metric spaces, while those associated with convergence to best proximity points are set in uniformly convex Banach spaces which are simultaneously complete metric spaces. The concept of semicyclic self-mappings generalizes the well-known one of cyclic ones in the sense that the iterated sequences built through such mappings are allowed to have images located in the same subset as their pre-image. The self-mappings under study might be in the most general case impulsive in the sense that they are composite mappings consisting of two self-mappings, and one of them is eventually discontinuous. Thus, the developed formalism can be applied to the study of stability of a class of impulsive differential equations and that of their discrete counterparts. Some application examples to impulsive differential equations are also given.

scholarly journals Fixed points results via simulation functions

Filomat ◽  
2016 ◽  
Vol 30 (8) ◽  
pp. 2343-2350 ◽  
Author(s):  
Erdal Karapınar
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Simulation Function ◽  
Complete Metric Spaces ◽  
Admissible Mapping ◽  
Simulation Functions

In this paper, we present some fixed point results in the setting of a complete metric spaces by defining a new contractive condition via admissible mapping imbedded in simulation function. Our results generalize and unify several fixed point theorems in the literature.

scholarly journals A fixed point theorem for mappings satisfying a general contractive condition of integral type

2002 ◽  
Vol 29 (9) ◽  
pp. 531-536 ◽  
Author(s):  
A. Branciari
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Real Number ◽  
Fixed Points ◽  
Compact Subset ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Integral Type ◽  
Complete Metric Spaces ◽  
Integrable Mapping

We analyze the existence of fixed points for mappings defined on complete metric spaces(X,d)satisfying a general contractive inequality of integral type. This condition is analogous to Banach-Caccioppoli's one; in short, we study mappingsf:X→Xfor which there exists a real numberc∈]0,1[, such that for eachx,y∈Xwe have∫0d(fx,fy)φ(t)dt≤c∫0d(x,y)φ(t)dt, whereφ:[0,+∞[→[0,+∞]is a Lebesgue-integrable mapping which is summable on each compact subset of[0,+∞[, nonnegative and such that for eachε>0,∫0εφ(t)dt>0.

scholarly journals Some Results on Fixed and Best Proximity Points of Precyclic Self-Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
M. De la Sen
Keyword(s):  
Limit Cycles ◽  
Existence And Uniqueness ◽  
Contractive Condition ◽  
Uniformly Convex ◽  
Best Proximity Points ◽  
Uniformly Convex Banach Spaces ◽  
Pairwise Intersection ◽  
Finite Set ◽  
Uniqueness Of Limit Cycles ◽  
Number Of Iterations

This paper is devoted to investigating the limit properties of distances and the existence and uniqueness of fixed points, best proximity points and existence, and uniqueness of limit cycles, to which the iterated sequences converge, of single-valued, and so-called, contractive precyclic self-mappings which are proposed in this paper. Such self-mappings are defined on the union of a finite set of subsets of uniformly convex Banach spaces under generalized contractive conditions. Each point of a subset is mapped either in some point of the same subset or in a point of the adjacent subset. In the general case, the contractive condition of contractive precyclic self-mappings is admitted to be point dependent and it is only formulated on a complete disposal, rather than on each individual subset, while it involves a condition on the number of iterations allowed within each individual subset before switching to its adjacent one. It is also allowed that the distances in-between adjacent subsets can be mutually distinct including the case of potential pairwise intersection for only some of the pairs of adjacent subsets.

Some Common Fixed Point Theorem in Complete Metric Space of Integral Type

2018 ◽  
Vol 6 (8) ◽  
pp. 297
Author(s):  
Jagdish C. Chaudhary ◽  
Shailesh T. Patel
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Contractive Condition ◽  
Integral Type ◽  
Complete Metric Spaces ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem

In this paper, we prove some common fixed point theorems in complete metric spaces for self mapping satisfying a contractive condition of Integral  type.

A generalization of Reich’s fixed point theorem for multi-valued mappings

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3295-3305 ◽  
Author(s):  
Antonella Nastasi ◽  
Pasquale Vetro
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Complete Metric Spaces ◽  
New Class ◽  
Banach Contraction ◽  
The Banach Contraction Principle

Motivated by a problem concerning multi-valued mappings posed by Reich [S. Reich, Some fixed point problems, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 57 (1974) 194-198] and a paper of Jleli and Samet [M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl. 2014:38 (2014) 1-8], we consider a new class of multi-valued mappings that satisfy a ?-contractive condition in complete metric spaces and prove some fixed point theorems. These results generalize Reich?s and Mizoguchi-Takahashi?s fixed point theorems. Some examples are given to show the usability of the obtained results.

RANDOM COINCIDENCE AND FIXED POINTS FOR WEAKLY COMPATIBLE MAPPINGS IN CONVEX METRIC SPACES

2009 ◽  
Vol 02 (02) ◽  
pp. 171-182 ◽  
Author(s):  
Izmat Beg ◽  
Adnan Jahangir ◽  
Akbar Azam
Keyword(s):  
Fixed Points ◽  
Metric Spaces ◽  
Weakly Compatible Mappings ◽  
Compatible Mappings ◽  
Coincidence Points ◽  
Random Coincidence ◽  
Complete Metric Spaces ◽  
Random Fixed Points ◽  
Weakly Compatible ◽  
Convex Metric Spaces

Some new theorems on random coincidence points and random fixed points for weakly compatible mappings in convex separable complete metric spaces have been established. These results generalize some recent well known comparable results in the literature.

BEST PROXIMITY POINTS AND FIXED POINTS WITH -FUNCTIONS IN THE FRAMEWORK OF -DISTANCES

2018 ◽  
Vol 99 (03) ◽  
pp. 497-507 ◽  
Author(s):  
ALEKSANDAR KOSTIĆ ◽  
ERDAL KARAPINAR ◽  
VLADIMIR RAKOČEVIĆ
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Best Proximity Points

We study best proximity points in the framework of metric spaces with $w$ -distances. The results extend, generalise and unify several well-known fixed point results in the literature.

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