scholarly journals Discussion on Generalized-(αψ,βφ)-Contractive Mappings via Generalized Altering Distance Function and Related Fixed Point Theorems

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Maher Berzig ◽  
Erdal Karapınar ◽  
Antonio-Francisco Roldán-López-de-Hierro
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Contractive Mapping ◽  
Binary Relations ◽  
Contractive Mappings ◽  
Altering Distance ◽  
Wide Range ◽  
Generalized Altering Distance Function

We extend the notion of (αψ,βφ)-contractive mapping, a very recent concept by Berzig and Karapinar. This allows us to consider contractive conditions that generalize a wide range of nonexpansive mappings in the setting of metric spaces provided with binary relations that are not necessarily neither partial orders nor preorders. Thus, using this kind of contractive mappings, we show some related fixed point theorems that improve some well known recent results and can be applied in a variety of contexts.

Some fixed point results for (β-ψ1-ψ2)-contractive conditions in ordered b-metric-like spaces

Filomat ◽  
2017 ◽  
Vol 31 (14) ◽  
pp. 4587-4612 ◽  
Author(s):  
S.K. Padhan ◽  
Rao Jagannadha ◽  
Hemant Nashine ◽  
R.P. Agarwal
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Existence Of Solution ◽  
Distance Functions ◽  
Point Boundary ◽  
Contractive Mappings ◽  
Altering Distance

This paper extends and generalizes results of Mukheimer [(?,?,?)-contractive mappings in ordered partial b-metric spaces, J. Nonlinear Sci. Appl. 7(2014), 168-179]. A new concept of (?-?1-?2)-contractive mapping using two altering distance functions in ordered b-metric-like space is introduced and basic fixed point results have been studied. Useful examples are illustrated to justify the applicability and effectiveness of the results presented herein. As an application, the existence of solution of fourth-order two-point boundary value problems is discussed and rationalized by a numerical example.

scholarly journals Some Fixed Point Theorems Via Combination of Weak Contraction and Caristi Contractive Mapping

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Kushal Roy ◽  
Sayantan Panja ◽  
Mantu Saha ◽  
Zoran D. Mitrović
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Weak Contraction ◽  
Complete Metric Spaces ◽  
Contractive Mappings

Abstract In this paper we introduce some new types of contractive mappings by combining Caristi contraction, Ćirić-quasi contraction and weak contraction in the framework of a metric space. We prove some fixed point theorems for such type of mappings over complete metric spaces with the help of φ-diminishing property. Some examples are given in strengthening the hypothesis of our established theorems.

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 Unique Fixed Point Theorems for Generalized Contractive Mappings in Partial Metric Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Lakshmi Narayan Mishra ◽  
Shiv Kant Tiwari ◽  
Vishnu Narayan Mishra ◽  
Idrees A. Khan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Unique Fixed Point ◽  
Distance Functions ◽  
Partial Metric ◽  
Contractive Mappings ◽  
Altering Distance ◽  
Partial Metric Spaces

We establish some unique fixed point theorems in complete partial metric spaces for generalized weaklyS-contractive mappings, containing two altering distance functions under certain assumptions. Also, we discuss some examples in support of our main results.

scholarly journals Fixed Point Theorems for Hybrid Rational Geraghty Contractive Mappings in Orderedb-Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Farzaneh Zabihi ◽  
Abdolrahman Razani
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Contractive Mapping ◽  
Contractive Mappings

We introduce the new notion of a hybrid rational Geraghty contractive mapping and investigate the existence of fixed point and coincidence point for such mappings in orderedb-metric spaces. We also provide an example to illustrate the results presented herein. Finally, we establish an existence theorem for a solution of an integral equation.

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 Fixed point theorems in fuzzy metric spaces for mappings with Bγ,µ condition

2021 ◽  
Author(s):  
Nilakshi Goswami ◽  
Bijoy Patir
Keyword(s):  
Fixed Point ◽  
Distance Function ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Altering Distance Function ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Convergence Results ◽  
Altering Distance

In this paper we prove some fixed point theorems in fuzzy metric spaces for a class of generalized nonexpansive mappings satisfying Bγ,µ condition. We introduce a type of convexity in fuzzy metric spaces with respect to an altering distance function and prove convergence results for some iteration schemes to the fixed point. The results are supported by suitable examples.

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.

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