scholarly journals Double Controlled Quasi-Metric Type Spaces and Some Results

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Abdullah Shoaib ◽  
Sabeena Kazi ◽  
Asifa Tassaddiq ◽  
Shaif S. Alshoraify ◽  
Tahair Rasham
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Unique Fixed Point ◽  
Type Spaces ◽  
Proper Generalization

Abdeljawad et al. (2018) introduced a new concept, named double controlled metric type spaces, as a generalization of the notion of extended b-metric spaces. In this paper, we extend their concept and introduce the concept of double controlled quasi-metric type spaces with two incomparable functions and prove some unique fixed point results involving new types of contraction conditions. Also, we introduce the concept of α−μ−k double controlled contraction and prove some related fixed point results. We give several examples to show that our results are the proper generalization of the existing works.

scholarly journals Fixed Points of Geraghty-Type Mappings in Various Generalized Metric Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Dušan Ðukić ◽  
Zoran Kadelburg ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric ◽  
Generalized Metric Spaces ◽  
Generalized Metric ◽  
Partial Metric Spaces ◽  
Type Spaces

Fixed point theorems for mappings satisfying Geraghty-type contractive conditions are proved in the frame of partial metric spaces, ordered partial metric spaces, and metric-type spaces. Examples are given showing that these results are proper extensions of the existing ones.

scholarly journals On Complex-Valued Triple Controlled Metric Spaces and Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Nabil Mlaiki ◽  
Thabet Abdeljawad ◽  
Wasfi Shatanawi ◽  
Hassen Aydi ◽  
Yaé Ulrich Gaba
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Spaces ◽  
Polynomial Equations ◽  
Degree Polynomial ◽  
Fredholm Type ◽  
Type Integral ◽  
Type Spaces ◽  
Complex Valued

In this manuscript, we introduce the concept of complex-valued triple controlled metric spaces as an extension of rectangular metric type spaces. To validate our hypotheses and to show the usability of the Banach and Kannan fixed point results discussed herein, we present an application on Fredholm-type integral equations and an application on higher degree polynomial equations.

scholarly journals Common fixed point theorems for contractive mappings satisfying Φ-maps in S-metric spaces

2016 ◽  
Vol 8 (2) ◽  
pp. 298-311 ◽  
Author(s):  
Shaban Sedghi ◽  
Mohammad Mahdi Rezaee ◽  
Tatjana Došenović ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Unique Fixed Point ◽  
Contractive Mappings ◽  
Weakly Compatible ◽  
Common Fixed Point Theorems

Abstract In this paper we prove the existence of the unique fixed point for the pair of weakly compatible self-mappings satisfying some Ф-type contractive conditions in the framework of S-metric spaces. Our results generalize, extend, unify, complement and enrich recently fixed point results in existing literature.

Some non-unique fixed point or periodic point results in JS-metric spaces

2019 ◽  
Vol 21 (2) ◽  
Author(s):  
Tanusri Senapati ◽  
Lakshmi Kanta Dey ◽  
Ankush Chanda ◽  
Huaping Huang
Keyword(s):  
Fixed Point ◽  
Periodic Point ◽  
Metric Spaces ◽  
Unique Fixed Point

scholarly journals Non-Unique Fixed Point Theorems in Modular Metric Spaces

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 549
Author(s):  
Sharafat Hussain
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Unique Fixed Point ◽  
Periodic Points ◽  
Modular Metric Spaces ◽  
Modular Spaces

This paper is devoted to the study of Ćirić-type non-unique fixed point results in modular metric spaces. We obtain various theorems about a fixed point and periodic points for a self-map on modular spaces which are not necessarily continuous and satisfy certain contractive conditions. Our results extend the results of Ćirić, Pachpatte, and Achari in modular metric spaces.

scholarly journals Double Controlled Metric Type Spaces and Some Fixed Point Results

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 320 ◽  
Author(s):  
Thabet Abdeljawad ◽  
Nabil Mlaiki ◽  
Hassen Aydi ◽  
Nizar Souayah
Keyword(s):  
Fixed Point ◽  
Triangle Inequality ◽  
Metric Spaces ◽  
Type Space ◽  
Control Functions ◽  
Right Hand ◽  
Type Spaces ◽  
The Right ◽  
The Given

In this article, in the sequel of extending b-metric spaces, we modify controlled metric type spaces via two control functions α ( x , y ) and μ ( x , y ) on the right-hand side of the b - triangle inequality, that is, d ( x , y ) ≤ α ( x , z ) d ( x , z ) + μ ( z , y ) d ( z , y ) , for all x , y , z ∈ X . Some examples of a double controlled metric type space by two incomparable functions, which is not a controlled metric type by one of the given functions, are presented. We also provide some fixed point results involving Banach type, Kannan type and ϕ -nonlinear type contractions in the setting of double controlled metric type spaces.

scholarly journals Fixed point theorems in modular G-metric spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Godwin Amechi Okeke ◽  
Daniel Francis ◽  
Manuel de la Sen ◽  
Mujahid Abbas
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Unique Fixed Point ◽  
Weakly Compatible ◽  
Special Cases

AbstractWe prove the existence and uniqueness of fixed points of some generalized contractible operators defined on modular G-metric spaces and also prove the modular G-continuity of such operators. Furthermore, we prove that some generalized weakly compatible contractive operators in modular G-metric spaces have a unique fixed point. Our results extend, generalize, complement and include several known results as special cases.

scholarly journals On Orthogonal Partial b -Metric Spaces with an Application

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Khalil Javed ◽  
Hassen Aydi ◽  
Fahim Uddin ◽  
Muhammad Arshad
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Unique Fixed Point ◽  
Contractive Type

In this paper, we initiate the concept of orthogonal partial b -metric spaces. We ensure the existence of a unique fixed point for some orthogonal contractive type mappings. Some useful examples are given, and an application is also provided in support of the obtained results.

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