scholarly journals Saturated contraction principles for non self operators, generalizations and applications

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3391-3406 ◽  
Author(s):  
Vasile Berinde ◽  
Ştefan Măruşter ◽  
Ioan Rus
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Closed Subset ◽  
Unique Fixed Point ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Nonempty Closed Subset ◽  
Open Problems ◽  
Displacement Condition ◽  
Well Posed

Let (X; d) be a metric space, Y ? X a nonempty closed subset of X and let f : Y ? X be a non self operator. In this paper we study the following problem: under which conditions on f we have all of the following assertions: 1. The operator f has a unique fixed point; 2. The operator f satisfies a retraction-displacement condition; 3. The fixed point problem for f is well posed; 4. The operator f has the Ostrowski property. Some applications and open problems related to these questions are also presented.

scholarly journals Relevant Classes of Weakly Picard Operators

2016 ◽  
Vol 54 (2) ◽  
pp. 131-147
Author(s):  
Ioan A. Rus
Keyword(s):  
Fixed Point ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Open Problems ◽  
Displacement Condition ◽  
Well Posed

Abstract In this paper we consider the following problems: (1) Which weakly Picard operators satisfy a retraction- displacement condition? (2) For which weakly Picard operators the fixed point problem is well posed? (3) Which weakly Picard operators have Ostrowski property? Some applications and open problems are also presented.

scholarly journals A common unique fixed point theorem for two random operators in Hilbert spaces

2002 ◽  
Vol 32 (3) ◽  
pp. 177-182 ◽  
Author(s):  
Binayak S. Choudhury
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Hilbert Spaces ◽  
Closed Subset ◽  
Separable Hilbert Space ◽  
Unique Fixed Point ◽  
Random Operators ◽  
Nonempty Closed Subset ◽  
Random Fixed Point

We construct a sequence of measurable functions and consider its convergence to the unique common random fixed point of two random operators defined on a nonempty closed subset of a separable Hilbert space. The corresponding result in the nonrandom case is also obtained.

scholarly journals On Multivalued Contractions in Cone Metric Spaces without Normality

2013 ◽  
Vol 2013 ◽  
pp. 1-3 ◽  
Author(s):  
Muhammad Arshad ◽  
Jamshaid Ahmad
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Normal Cone ◽  
Metric Spaces ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Cone Metric Spaces ◽  
The Family ◽  
Multivalued Contractions ◽  
Cone Metric

Wardowski (2011) in this paper for a normal cone metric space(X,d)and for the family𝒜of subsets ofXestablished a new cone metricH:𝒜×𝒜→Eand obtained fixed point of set-valued contraction of Nadler type. Further, it is noticed in the work of Janković et al., 2011 that the…fixed-point problem in the setting of cone metric spaces is appropriate only in the case when the underlying cone is nonnormal. In the present paper we improve Wardowski's result by proving the same without the assumption of normality on cones.

scholarly journals Well-posedness of fixed point problem for mappings satisfying an implicit relation

2010 ◽  
Vol 43 (4) ◽  
Author(s):  
Mohamed Akkouchi ◽  
Valeriu Popa
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Well Posedness ◽  
Implicit Relation ◽  
Complete Metric Spaces ◽  
Well Posed

AbstractThe notion of well-posedness of a fixed point problem has generated much interest to a several mathematicians, for example, F. S. De Blassi and J. Myjak (1989), S. Reich and A. J. Zaslavski (2001), B. K. Lahiri and P. Das (2005) and V. Popa (2006 and 2008). The aim of this paper is to prove for mappings satisfying some implicit relations in orbitally complete metric spaces, that fixed point problem is well-posed.

scholarly journals A fixed point problem under a finite number of equality constraints on b-Banach spaces

Filomat ◽  
2019 ◽  
Vol 33 (18) ◽  
pp. 5837-5849
Author(s):  
Monica-Felicia Bota ◽  
Erdal Karapınar
Keyword(s):  
Fixed Point ◽  
Finite Number ◽  
Banach Spaces ◽  
Metric Space ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Fixed Point Problem ◽  
Equality Constraints ◽  
Point Problem

In this manuscript, we investigate a fixed point problem under a finite number of equality constraints involving a well-known Ciric type mappings in the context of b-metric space. We obtain sufficient conditions for the existence of solutions of such problems. We also express some immediate consequences of our main results.

scholarly journals On some fixed point theorems for implicit almost contractive mappings

2013 ◽  
Vol 29 (2) ◽  
pp. 223-229
Author(s):  
VALERIU POPA ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Implicit Relation ◽  
Contractive Mappings ◽  
Well Posed

In this paper a general fixed point theorem for pairs of general almost contractive mappings satisfying an implicit relation is proved. In the last part of the paper is proved that the fixed point problem for these pairs of mappings is well posed.

scholarly journals SOME FIXED POINT THEOREMS VIA CYCLIC CONTRACTIVE CONDITIONS IN S-METRIC SPACES

2021 ◽  
pp. 377
Author(s):  
Gurucharan Singh Saluja
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Well Posed

We present some fixed point theorems for mappings which satisfy certain cyclic contractive conditions in the setting of $S$-metric spaces. The results presented in this paper generalize or improve many existing fixed point theorems in the literature. We also presented an application of our result to well-posed of fixed point problem. To support our results, we give some examples.

A fuzzy fixed point problem for constraint inequalities

2020 ◽  
Vol 39 (3) ◽  
pp. 3025-3032
Author(s):  
Hüseyin Işık ◽  
Muzeyyen Sangurlu Sezen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Fixed Point Problem ◽  
Point Problem ◽  
New Approach ◽  
Fuzzy Metric ◽  
Constraint Inequalities ◽  
Fuzzy Fixed Point

In this work, we prove a new fixed point theorem in the setting fuzzy metric spaces. The fuzzy metric space considered here is assumed to have two partial orders defined on it. We introduce a new approach to the existence of a fixed point of a function satisfying the two constraint inequalities. An example is included which illustrates new results of this paper. Moreover, an application of our result to the study of integral equations is provided.

scholarly journals Common fixed point theorem for modified Kannan enriched contraction pair in Banach spaces and its applications

Filomat ◽  
2021 ◽  
Vol 35 (8) ◽  
pp. 2485-2495
Author(s):  
Rizwan Anjum ◽  
Mujahid Abbas
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Nonexpansive Mappings ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Existence Of A Solution ◽  
Common Fixed Point Problem ◽  
The Common ◽  
Well Posed ◽  
Common Fixed Point Theorem

The purpose of this paper is to introduce the class of (a,b,c)-modified enriched Kannan pair of mappings (T,S) in the setting of Banach space that includes enriched Kannan mappings, contraction and nonexpansive mappings and some other mappings. Some examples are presented to support the concepts introduced herein. We establish the existence of common fixed point of the such pair. We also show that the common fixed point problem studied herein is well posed. A convergence theorem for the Krasnoselskij iteration is used to approximate fixed points of the (a,b,c)-modified enriched Kannan pair. As an application of the results proved in this paper, the existence of a solution of integral equations is established. The presented results improve, unify and generalize many known results in the literature.

scholarly journals Existence of the Solutions of Nonlinear Fractional Differential Equations Using the Fixed Point Technique in Extended b-Metric Spaces

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 158
Author(s):  
Liliana Guran ◽  
Monica-Felicia Bota
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Boundary Value ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Existence Of A Solution ◽  
Shadowing Property ◽  
Limit Shadowing ◽  
Type Boundary ◽  
Cyclic Type

The purpose of this paper is to prove fixed point theorems for cyclic-type operators in extended b-metric spaces. The well-posedness of the fixed point problem and limit shadowing property are also discussed. Some examples are given in order to support our results, and the last part of the paper considers some applications of the main results. The first part of this section is devoted to the study of the existence of a solution to the boundary value problem. In the second part of this section, we study the existence of solutions to fractional boundary value problems with integral-type boundary conditions in the frame of some Caputo-type fractional operators.

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