scholarly journals A Characterization of Quasi-Metric Completeness in Terms of α–ψ-Contractive Mappings Having Fixed Points

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 16 ◽  
Author(s):  
Salvador Romaguera ◽  
Pedro Tirado
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Mappings ◽  
Nonlinear Anal ◽  
Contractive Type ◽  
Surprising Fact

We obtain a characterization of Hausdorff left K-complete quasi-metric spaces by means of α – ψ -contractive mappings, from which we deduce the somewhat surprising fact that one the main fixed point theorems of Samet, Vetro, and Vetro (see “Fixed point theorems for α – ψ -contractive type mappings”, Nonlinear Anal. 2012, 75, 2154–2165), characterizes the metric completeness.

scholarly journals Common fixed point theorems for generalized G- η-χ–contractive type mappings with applications

2017 ◽  
Vol 37 (1) ◽  
pp. 9-20
Author(s):  
Manoj Kumar ◽  
Serkan Araci
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Mappings ◽  
Nonlinear Anal ◽  
Contractive Type ◽  
Common Fixed Point Theorems

Samet et. al. (Nonlinear Anal. 75, 2012, 2154-2165) introduced the concept of alpha-psi-contractive type mappings in metric spaces. In 2013, Alghamdi et. al. [2] introduced the concept of G-β--contractive type mappings in G-metric spaces. Our aim is to introduce new concept of generalized G-η-χ-contractive pair of mappings. Further, we study some fixed point theorems for such mappings in complete G-metric spaces. As an application, we further establish common fixed point theorems for G-metric spaces for cyclic contractive mappings.

scholarly journals αH-ψH-Multivalued Contractive Mappings and Related Results in Complete Metric Spaces with An Application

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 68
Author(s):  
Pooja Dhawan ◽  
Kapil Jain ◽  
Jatinderdeep Kaur
Keyword(s):  
Fixed Point ◽  
Present Article ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Spaces ◽  
Multivalued Contraction ◽  
Contractive Mappings ◽  
Nonlinear Anal ◽  
Contractive Type ◽  
Homotopy Result

In the present article, the notion of αH-ψH-multivalued contractive type mappings is introduced and some fixed point results in complete metric spaces are studied. These theorems generalize Nadler’s (Multivalued contraction mappings, Pac. J. Math., 30, 475–488, 1969) and Suzuki-Kikkawa's (Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal., 69, 2942–2949, 2008) results that exist in the literature. The effectiveness of the obtained results has been verified with the help of some comparative examples. Moreover, a homotopy result has been presented as an application.

scholarly journals α-ψ-contractive type mappings on quasi-metric spaces

Filomat ◽  
2021 ◽  
Vol 35 (5) ◽  
pp. 1649-1659
Author(s):  
Salvador Romaguera ◽  
Pedro Tirado
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Mappings ◽  
Contractive Type

We introduce and discuss several types of ?-?-contractive mappings on quasi-metric spaces. We obtain some fixed point theorems in this setting and present suitable examples to show the validity of our approach and results. Finally, we give a characterization of doubly Hausdorff right K-sequentially complete quasi-metric spaces in terms of ?-?-contractive type mappings having fixed point.

scholarly journals Some tripled coincidence point theorems for almost generalized contractions in ordered metric spaces

2012 ◽  
Vol 44 (3) ◽  
pp. 233-251 ◽  
Author(s):  
Erdal KARAPINAR ◽  
Hassen AYDI ◽  
Zead MUSTAFA
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Ordered Metric Spaces ◽  
Tripled Fixed Point ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered ◽  
Nonlinear Anal ◽  
Contractive Type ◽  
Common Fixed Point Theorems

In this paper, we prove tripledcoincidence and common fixed point theorems for $F: X\times X\times X\to X$ and $g:X\to X$ satisfying almost generalized contractions in partially ordered metric spaces. The presented results generalize the theorem of Berinde and Borcut Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal 74(15) (2011)4889--4897. Also, some examples are presented.

scholarly journals Generalized - Contractive Type Mappings and Related Fixed Point Theorems with Applications

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Erdal Karapınar ◽  
Bessem Samet
Keyword(s):  
Fixed Point ◽  
Partial Order ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
New Class ◽  
Contractive Mappings ◽  
Contractive Type

We establish fixed point theorems for a new class of contractive mappings. As consequences of our main results, we obtain fixed point theorems on metric spaces endowed with a partial order and fixed point theorems for cyclic contractive mappings. Various examples are presented to illustrate our obtained results.

scholarly journals Common Fixed Points for Weakψ-Contractive Mappings in Ordered Metric Spaces with Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Sumit Chandok ◽  
Simona Dinu
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Contractive Condition ◽  
Ordered Metric Spaces ◽  
Contractive Mappings ◽  
Common Fixed Point Theorems

We obtain some new common fixed point theorems satisfying a weak contractive condition in the framework of partially ordered metric spaces. The main result generalizes and extends some known results given by some authors in the literature.

scholarly journals Periodic Points and Fixed Points for the Weaker(ϕ,φ)-Contractive Mappings in Complete Generalized Metric Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Chi-Ming Chen ◽  
W. Y. Sun
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Periodic Points ◽  
Generalized Metric Spaces ◽  
Complete Metric Spaces ◽  
Contractive Mappings ◽  
Generalized Metric

We introduce the notion of weaker(ϕ,φ)-contractive mapping in complete metric spaces and prove the periodic points and fixed points for this type of contraction. Our results generalize or improve many recent fixed point theorems in the literature.

scholarly journals New Contractive Mappings and Their Fixed Points in Branciari Metric Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Hayel N. Saleh ◽  
Mohammad Imdad ◽  
Thabet Abdeljawad ◽  
Mohammad Arif
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Boundary Value ◽  
Contractive Mappings

In this paper, we introduce the notion of generalized L-contractions which enlarge the class of ℒ-contractions initiated by Cho in 2018. Thereafter, we also, define the notion of L∗-contractions. Utilizing our newly introduced notions, we establish some new fixed-point theorems in the setting of complete Branciari’s metric spaces, without using the Hausdorff assumption. Moreover, some examples and applications to boundary value problems of the fourth-order differential equations are given to exhibit the utility of the obtained results.

scholarly journals Fixed Point Results forα-ψ-Contractive Mappings Including Almost Contractions and Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Gonca Durmaz ◽  
Gülhan Mınak ◽  
Ishak Altun
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Theorems ◽  
Uniqueness Result ◽  
Point Boundary ◽  
Contractive Mappings ◽  
Analysis Theory ◽  
Contractive Type

In the recent paper (B. Samet, C. Vetro, and P. Vetro, Fixed point theorems forα-ψ-contractive type mappings, Nonlinear Analysis. Theory, Methods and Applications, 75 (2012), 2154-2165.), the authors introduced the concept ofα-admissible maps on metric spaces. Using this new concept, they presented some nice fixed point results. Also, they gave an existence theorem for integral equation to show the usability of their result. Then, many authors focused on this new concept and obtained a lot of fixed point results, which are used for existence theorems. In this paper, we not only extend some of the recent results about this direction but also generalize them. Then, we give some examples to show our results are proper extensions. Furthermore, we use our results to obtain the existence and uniqueness result for a solution of fourth order two-point boundary value problem.

scholarly journals Cyclic generalized φ-contractions in b-metric spaces and an application to integral equations

Filomat ◽  
2014 ◽  
Vol 28 (10) ◽  
pp. 2047-2057 ◽  
Author(s):  
Kumar Nashine ◽  
Zoran Kadelburg
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Problem ◽  
Contractive Mappings

We introduce the notion of cyclic generalized ?-contractive mappings in b-metric spaces and discuss the existence and uniqueness of fixed points for such mappings. Our results generalize many existing fixed point theorems in the literature. Examples are given to support the usability of our results. Finally, an application to existence problem for an integral equation is presented.

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