scholarly journals Admissible Almost Type Z-Contractions and Fixed Point Results

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Said Melliani ◽  
Abdelhamid Moussaoui ◽  
L. S. Chadli
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Complete Metric Spaces ◽  
New Class

In this paper, we introduce a new concept of α-admissible almost type Z-contraction and prove some fixed point results for this new class of contractions in the context of complete metric spaces. The presented results generalize and unify several 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 Generalized Fixed-Point Results for Almost (α,Fσ)-Contractions with Applications to Fredholm Integral Inclusions

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1068 ◽  
Author(s):  
Saleh Abdullah Al-Mezel ◽  
Jamshaid Ahmad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence Theorem ◽  
Unknown Function ◽  
Metric Spaces ◽  
Multivalued Operator ◽  
Complete Metric Spaces ◽  
New Class ◽  
The Family ◽  
Nonempty Compact

The purpose of this article is to define almost ( α , F σ ) -contractions and establish some generalized fixed-point results for a new class of contractive conditions in the setting of complete metric spaces. In application, we apply our fixed-point theorem to prove the existence theorem for Fredholm integral inclusions ϖ ( t ) ∈ f ( t ) + ∫ 0 1 K ( t , s , x ( s ) ) ϑ s , t ∈ [ 0 , 1 ] where f ∈ C [ 0 , 1 ] is a given real-valued function and K : [ 0 , 1 ] × [ 0 , 1 ] × R → K c v ( R ) is a given multivalued operator, where K c v represents the family of nonempty compact and convex subsets of R and ϖ ∈ C [ 0 , 1 ] is the unknown function. We also provide a non-trivial example to show the significance of our main result.

A fixed point problem with constraint inequalities via a contraction in incomplete metric spaces

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3365-3379 ◽  
Author(s):  
Z. Ahmadi ◽  
R. Lashkaripour ◽  
H. Baghani
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Complete Metric Spaces ◽  
New Class ◽  
Constraint Inequalities ◽  
Weaker Conditions

In the present paper, firstly, we review the notion of the SO-complete metric spaces. This notion let us to consider some fixed point theorems for single-valued mappings in incomplete metric spaces. Secondly, as motivated by the recent work of H. Baghani et al.(A fixed point theorem for a new class of set-valued mappings in R-complete (not necessarily complete) metric spaces, Filomat, 31 (2017), 3875-3884), we obtain the results of Ansari et al. [J. Fixed Point Theory Appl. (2017), 1145-1163] with very much weaker conditions. Also, we provide some examples show that our main theorem is a generalization of previous results. Finally, we give an application to the boundary value system for our results.

scholarly journals A fixed point theorem for a new class of set-valued mappings in R-complete (not necessarily complete) metric spaces

Filomat ◽  
2017 ◽  
Vol 31 (12) ◽  
pp. 3875-3884 ◽  
Author(s):  
Hamid Baghani ◽  
Maryam Ramezani
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Condition ◽  
Complete Metric Spaces ◽  
New Class ◽  
Set Valued Mappings

In this paper, firstly, we introduce the notion of R-complete metric spaces. This notion let us to consider fixed point theorem in R-complete instead of complete metric spaces. Secondly, as motivated by the recent work of Amini-Harandi (Fixed Point Theory Appl. 2012, 2012:215), we explain a new generalized contractive condition for set-valued mappings and prove a fixed point theorem in R-complete metric spaces which extends some well-known results in the literature. Finally, some examples are given to support our main theorem and also we find the existence of solution for a first-order ordinary differential equation.

scholarly journals Proinov-Type Fixed-Point Results in Non-Archimedean Fuzzy Metric Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1594
Author(s):  
Antonio Francisco Roldán López de Hierro ◽  
Andreea Fulga ◽  
Erdal Karapınar ◽  
Naseer Shahzad
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Fuzzy Metric Spaces ◽  
Complete Metric Spaces ◽  
Auxiliary Functions ◽  
Fuzzy Metric ◽  
New Class

Very recently, Proinov introduced a great family of contractions in the setting of complete metric spaces that has attracted the attention of many researchers because of the very weak conditions that are assumed on the involved functions. Inspired by Proinov’s results, in this paper, we introduce a new class of contractions in the setting of fuzzy metric spaces (in the sense of George and Veeramani) that are able to translate to this framework the best advantages of the abovementioned auxiliary functions. Accordingly, we present some results about the existence and uniqueness of fixed points for this class of fuzzy contractions in the setting of non-Archimedean fuzzy metric spaces.

scholarly journals Solutions to Fredholm Integral Inclusions via Generalized Fuzzy Contractions

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 808 ◽  
Author(s):  
Hamed H Al-Sulami ◽  
Jamshaid Ahmad ◽  
Nawab Hussain ◽  
Abdul Latif
Keyword(s):  
Fixed Point ◽  
Unknown Function ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
Multivalued Operator ◽  
Complete Metric Spaces ◽  
New Class ◽  
Integral Inclusion ◽  
The Family

The aim of this study is to investigate the existence of solutions for the following Fredholm integral inclusion φ ( t ) ∈ f ( t ) + ∫ 0 1 K ( t , s , φ ( s ) ) ϱ s for t ∈ [ 0 , 1 ] , where f ∈ C [ 0 , 1 ] is a given real-valued function and K : [ 0 , 1 ] × [ 0 , 1 ] × R → K c v ( R ) a given multivalued operator, where K c v represents the family of non-empty compact and convex subsets of R , φ ∈ C [ 0 , 1 ] is the unknown function and ϱ is a metric defined on C [ 0 , 1 ] . To attain this target, we take advantage of fixed point theorems for α -fuzzy mappings satisfying a new class of contractive conditions in the context of complete metric spaces. We derive new fixed point results which extend and improve the well-known results of Banach, Kannan, Chatterjea, Reich, Hardy-Rogers, Berinde and Ćirić by means of this new class of contractions. We also give a significantly non-trivial example to support our new results.

scholarly journals Some new fixed point theorems in complete metric spaces

2012 ◽  
Vol 21 (2) ◽  
pp. 189-196
Author(s):  
M. O. OLATINWO ◽  
◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Complete Metric Spaces ◽  
New Class ◽  
Contractive Mappings

In this paper, we obtain some fixed point theorems for more general classes of mappings than the A−contractions of Akram et al. We also give an example of mappings satisfying our new class of contractive mappings but which does not satisfy the contractive condition of Akram et al. Our results generalize and extend the recent results of Akram et al., and unify several other classical results in the literature.

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.

scholarly journals Discussions on the almost 𝒵-contraction

2020 ◽  
Vol 18 (1) ◽  
pp. 448-457
Author(s):  
Erdal Karapınar ◽  
V. M. L. Hima Bindu
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Complete Metric Spaces ◽  
The Given

Abstract In this paper, we introduce a new contraction, namely, almost {\mathcal{Z}} contraction with respect to \zeta \in {\mathcal{Z}} , in the setting of complete metric spaces. We proved that such contraction possesses a fixed point and the given theorem covers several existing results in the literature. We consider an example to illustrate our result.

scholarly journals Best Proximity Point for Generalized Proximal Weak Contractions in Complete Metric Space

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Erdal Karapınar ◽  
V. Pragadeeswarar ◽  
M. Marudai
Keyword(s):  
Approximate Solution ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Complete Metric Space ◽  
Optimal Approximate Solution ◽  
Weak Contraction ◽  
Complete Metric Spaces ◽  
New Class

We introduce a new class of nonself-mappings, generalized proximal weak contraction mappings, and prove the existence and uniqueness of best proximity point for such mappings in the context of complete metric spaces. Moreover, we state an algorithm to determine such an optimal approximate solution designed as a best proximity point. We establish also an example to illustrate our main results. Our result provides an extension of the related results in the literature.

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