scholarly journals A General Fixed Point Theorem for Mappings Satisfying a Cyclical Contractive Condition in S-Metric Spaces

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 638
Author(s):  
Alina-Mihaela Patriciu ◽  
Valeriu Popa
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Implicit Relation ◽  
New Type

In this paper we introduce a new type of implicit relation in S-metric spaces. Our aim is to prove a general fixed point theorem for mappings satisfying the cyclical contractive condition, which extends several results from the literature.

A general fixed point theorem for a pair of multi-valued mappings in partial metric spaces

2016 ◽  
Vol 56 (1) ◽  
pp. 129-141
Author(s):  
Valeriu Popa
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Partial Metric ◽  
Implicit Relation ◽  
Partial Metric Spaces ◽  
New Type

AbstractThe purpose of this paper is to prove a general fixed point theorem for a pair of multi-valued mappings satisfying a new type of implicit relation in partial metric spaces, which generalizes Theorem 2.2 [4], Theorem 3.1 [3], Theorem 3.2 [7], Corollary 2.3 [4], Theorem 2.8 [16] and obtain other particular results.

scholarly journals A common fixed point theorem using implicit relation and property (E.A) in metric spaces

Filomat ◽  
2007 ◽  
Vol 21 (2) ◽  
pp. 211-234 ◽  
Author(s):  
H. Pathak ◽  
Rosana Rodriguez-López ◽  
R.K. Verma
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Implicit Relation ◽  
Weak Compatibility ◽  
Common Fixed Point Theorem

In this paper, we prove a common fixed point theorem for a quadruple of mappings by using an implicit relation [6] and property (E.A) [1] under weak compatibility. Our theorem improves and generalizes the main Theorems of Popa [6] and Aamri and Moutawakil [1] .Various examples verify the importance of weak compatibility and property (E.A) in the existence of common fixed point and examples are also given to the implicit relation and to validate our main Theorem. We also show that property (E.A) and Meir-Keeler type contractive condition are independent to each other. .

scholarly journals A General Fixed Point Theorem for Two Pairs of Absorbing Mappings in Gp -Metric Spaces

2020 ◽  
Vol 34 (2) ◽  
pp. 268-285
Author(s):  
Valeriu Popa
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Integral Type ◽  
Implicit Relation ◽  
Contractive Mappings ◽  
Weak Compatibility ◽  
New Type

AbstractA general fixed point theorem for two pairs of absorbing mappings satisfying a new type of implicit relation ([37]), without weak compatibility in Gp-metric spaces is proved. As applications, new results for mappings satisfying contractive conditions of integral type and for ϕ-contractive mappings are obtained.

scholarly journals Fixed point theorem for new type of auxiliary functions

2020 ◽  
Vol 12 (1) ◽  
pp. 97-111
Author(s):  
Vishal Gupta ◽  
A. H. Ansari ◽  
Naveen Mani
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Auxiliary Function ◽  
Contractive Condition ◽  
Complete Metric Spaces ◽  
Auxiliary Functions ◽  
The Third ◽  
New Type

AbstractIn this paper, we present some fixed point results satisfying generalized contractive condition with new auxiliary function in complete metric spaces. More precisely, the structure of the paper is the following. In the first section, we present some useful notions and results. The main aim of second section is to establish some new fixed point results in complete metric spaces. Finally, in the third section, we show the validity and superiority of our main results by suitable example. Also, as an application of our main result, some interesting corollaries have been included, which make our concepts and results effective. Our main result generalizes some well known existing results in the literature.

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.

scholarly journals Semicompatibility and fixed point theorems in an unboundedD-metric space

2005 ◽  
Vol 2005 (5) ◽  
pp. 789-801
Author(s):  
Bijendra Singh ◽  
Shishir Jain ◽  
Shobha Jain
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Condition ◽  
Restricted Domain

Rhoades (1996) proved a fixed point theorem in a boundedD-metric space for a contractive self-map with applications. Here we establish a more general fixed point theorem in an unboundedD-metric space, for two self-maps satisfying a general contractive condition with a restricted domain ofxandy. This has been done by using the notion of semicompatible maps inD-metric space. These results generalize and improve the results of Rhoades (1996), Dhage et al. (2000), and Veerapandi and Rao (1996). These results also underline the necessity and importance of semicompatibility in fixed point theory ofD-metric spaces. All the results of this paper are new.

scholarly journals Suzuki ψF-contractions and some fixed point results

2018 ◽  
Vol 34 (1) ◽  
pp. 93-102
Author(s):  
NICOLAE-ADRIAN SECELEAN ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Continuity Point ◽  
Picard Operator ◽  
Nonlinear Anal ◽  
New Type

The purpose of this paper is to combine and extend some recent fixed point results of Suzuki, T., [A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (2009), 5313–5317] and Secelean, N. A. & Wardowski, D., [ψF-contractions: not necessarily nonexpansive Picard operators, Results Math., 70 (2016), 415–431]. The continuity and the completeness conditions are replaced by orbitally continuity and orbitally completeness respectively. It is given an illustrative example of a Picard operator on a non complete metric space which is neither nonexpansive nor expansive and has a unique continuity point.

scholarly journals On New Type of F -Contractive Mapping for Quasipartial b -Metric Spaces and Some Results of Fixed-Point Theorem and Application

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
A. M. Zidan ◽  
Asma Al Rwaily
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Banach’S Fixed Point Theorem ◽  
Contractive Type ◽  
New Type

In this paper, we introduce the concept of new type of F -contractive type for quasipartial b-metric spaces and some definitions and lemmas. Also, we will prove a new fixed-point theorem in quasipartial b -metric spaces for F -contractive type mappings. In addition, we give an application which illustrates a situation when Banach’s fixed-point theorem for complete quasipartial b -metric spaces cannot be applied, while the conditions of our theorem are satisfying.

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