scholarly journals Some New Observations on Generalized Contractive Mappings and Related Results in b-Metric-Like Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Tatjana Došenović ◽  
Manuel De La Sen ◽  
Ljiljana Paunović ◽  
Dušan Rakić ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
New Approach ◽  
Contraction Mappings ◽  
Contractive Mappings

In this paper, we consider, discuss, complement, improve, generalize, and enrich some fixed point results obtained for β − ψ 1 − ψ 2 − contractive conditions in ordered b-metric-like spaces. By using our new approach for the proof that one Picard’s sequence is b b l − Cauchy in the context of b-metric-like spaces, we get much shorter proofs than the ones mentioned in the recent papers. Also, by the use of our method, we complement and enrich some common fixed point results for β q , ϕ s , ψ − contraction mappings. Our approach in this paper generalizes and modifies several comparable results in the existing literature.

scholarly journals On Some Common Fixed Point Results for Weakly Contraction Mappings with Application

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Yan Hao ◽  
Hongyan Guan
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Contraction Mappings ◽  
New Class ◽  
Contractive Mappings ◽  
Weakly Contractive

In this paper, we introduce a new class of generalized weakly contractive mappings and prove common fixed point results by using different algorithms involving this new class of mappings in the framework of b -metric spaces, which generalize the results of Cho. We also provide two examples to show the applicability and validity of our results. As an application of our result, we obtain a solution to an integral equation. Our results extend and improve several comparable results in the existing literature.

scholarly journals Fixed Point and Common Fixed Point Theorems for Generalized Weak Contraction Mappings of Integral Type in Modular Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Chirasak Mongkolkeha ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Weak Contraction ◽  
Integral Type ◽  
Contraction Mappings ◽  
Contractive Mappings ◽  
Modular Spaces ◽  
Generalized Weak Contraction ◽  
Common Fixed Point Theorems

We prove new fixed point and common fixed point theorems for generalized weak contractive mappings of integral type in modular spaces. Our results extend and generalize the results of A. Razani and R. Moradi (2009) and M. Beygmohammadi and A. Razani (2010).

scholarly journals Generalized Contractive Mappings and Related Results in b-Metric Like Spaces with an Application

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 667 ◽  
Author(s):  
Hasanen A. Hammad ◽  
Manuel De la Sen
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Analytical Solution ◽  
Common Fixed Point ◽  
Contractive Mapping ◽  
Contraction Mappings ◽  
Contractive Mappings ◽  
Graphic Contraction

In this article, a general contractive mapping is presented and some fixed point results in complete b-metric-like spaces are studied. The results obtained here extend and improve some related results in the literature. Also, new common fixed point results for a graphic contraction mappings are proved. Some comparative examples are given to support the obtained results. Moreover, an analytical solution of an integral equation has been presented as an application.

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 An alternating iteration algorithm for solving the split equality fixed point problem with L-Lipschitz and quasi-pseudo-contractive mappings

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Meixia Li ◽  
Xueling Zhou ◽  
Haitao Che
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Split Feasibility Problem ◽  
Fixed Point Problem ◽  
Feasibility Problem ◽  
Iteration Algorithm ◽  
Point Problem ◽  
Contractive Mappings ◽  
Common Fixed Point Problem ◽  
Significant Generalization

Abstract In this paper, we are concerned with the split equality common fixed point problem. It is a significant generalization of the split feasibility problem, which can be used in various disciplines, such as medicine, military and biology, etc. We propose an alternating iteration algorithm for solving the split equality common fixed point problem with L-Lipschitz and quasi-pseudo-contractive mappings and prove that the sequence generated by the algorithm converges weakly to the solution of this problem. Finally, some numerical results are shown to confirm the feasibility and efficiency of the proposed algorithm.

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.

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