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 Fixed point theorems for α-contractive mappings of Meir–Keeler type and applications

2014 ◽  
Vol 19 (2) ◽  
pp. 178-198 ◽  
Author(s):  
Maher Berzig ◽  
Mircea-Dan Rus
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Point Boundary ◽  
Iterative Approximation ◽  
Third Order ◽  
Complete Metric Spaces ◽  
Contractive Mappings

In this paper, we introduce the notion of α-contractive mapping of Meir–Keeler type in complete metric spaces and prove new theorems which assure the existence, uniqueness and iterative approximation of the fixed point for this type of contraction. The presented theorems extend, generalize and improve several existing results in literature. To validate our results, we establish the existence and uniqueness of solution to a class of third order two point boundary value problems.

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 Common Fixed Point Theorems in Metric Spaces with Applications

2018 ◽  
Vol 11 (4) ◽  
pp. 1177-1190
Author(s):  
Pushpendra Semwal
Keyword(s):  
Dynamic Programming ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Existence And Uniqueness ◽  
Functional Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
System Of Functional Equations ◽  
Contractive Type ◽  
Common Fixed Point Theorems

In this paper we investigate the existence and uniqueness of common fixed point theorems for certain contractive type of mappings. As an application the existence and uniqueness of common solutions for a system of functional equations arising in dynamic programming are discuss by using the our results.

scholarly journals The Generalized Weaker(α-ϕ-φ)-Contractive Mappings and Related Fixed Point Results in Complete Generalized Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Maryam A. Alghamdi ◽  
Chi-Ming Chen ◽  
Erdal Karapınar
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Generalized Metric Space ◽  
Generalized Metric Spaces ◽  
Contractive Mappings ◽  
Generalized Metric

We introduce the notion of generalized weaker(α-ϕ-φ)-contractive mappings in the context of generalized metric space. We investigate the existence and uniqueness of fixed point of such mappings. Some consequences on existing fixed point theorems are also derived. The presented results generalize, unify, and improve several results in the literature.

scholarly journals Proving Fixed Point Theorems Employing Fuzzy $(\sigma,\mathcal{Z})$-Contractive Type Mappings

2021 ◽  
Author(s):  
Hayel N. Saleh ◽  
Mohammad Imdad ◽  
Salvatore Sessa ◽  
Ferdinando Di Martino
Keyword(s):  
Fixed Point ◽  
Fuzzy Sets ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Uniqueness Theorems ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Contractive Type

In this article, the concept of fuzzy $(\sigma,\mathcal{Z})$-contractive mapping has been introduced in fuzzy metric spaces which is an improvement over the corresponding concept recently introduced by Shukla et al. [Fuzzy Sets and system. 350 (2018) 85--94]. Thereafter, we utilized our newly introduced concept to prove some existence and uniqueness theorems in $\mathcal{M}$-complete fuzzy metric spaces. Our results extend and generalize the corresponding results of Shukla et al.. Moreover, an example is adopted to exhibit the utility of newly obtained results.

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 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.

Fixed point results for single valued and set valued P-contractions and application to second order boundary value problems

2020 ◽  
Vol 36 (2) ◽  
pp. 205-214
Author(s):  
ISHAK ALTUN ◽  
HATICE ASLAN HANCER ◽  
ALI ERDURAN ◽  
◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Complete Metric Space ◽  
Boundary Value ◽  
Uniqueness Result ◽  
Second Order ◽  
Point Boundary ◽  
Set Valued Mappings

In this paper, by considering the concept of set-valued nonlinear P-contraction which is newly introduced, we present some new fixed point theorems for set-valued mappings on complete metric space. Then by considering a single-valued case we provide an existence and uniqueness result for a kind of second order two point boundary value problem.

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.

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