WEAK CONTRACTION CONDITION FOR COMPATIBLE MAPPINGS INVOLVING CUBIC TERMS OF THE METRIC FUNCTION

2018 ◽  
Vol 103 (4) ◽  
pp. 799-818
Author(s):  
Deepak Jain ◽  
Sanjay Kumar ◽  
Shin Min Kang ◽  
Chahn Yong Jung
Keyword(s):  
Compatible Mappings ◽  
Weak Contraction ◽  
Contraction Condition ◽  
Metric Function

scholarly journals Notes on multidimensional fixed-point theorems

2017 ◽  
Vol 50 (1) ◽  
pp. 360-374 ◽  
Author(s):  
Habibulla Akhadkulov ◽  
Salmi M. Noorani ◽  
Azizan B. Saaban ◽  
Fathilah M. Alipiah ◽  
Habes Alsamir
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Weak Contraction ◽  
Contraction Condition ◽  
Nonlinear Mappings

Abstract In this paper we prove the existence and uniqueness of coincident (fixed) points for nonlinear mappings of any number of arguments under a (ψ, θ, φ)-weak contraction condition without O-compatibility. The obtained results extend, improve and generalize some well-known results in the literature to be discussed below. Moreover, we present an example to show the efficiency of our results.

scholarly journals Weak Contraction Condition Involving Cubic Terms ofdx,yunder the Fixed Point Consideration

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Penumurthy Parvateesam Murthy ◽  
K. N. V. V. Vara Prasad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Complete Metric Space ◽  
Contractive Condition ◽  
Weak Contraction ◽  
Contraction Condition

A fixed point theorem is presented for single-valued map with using generalizedφ-weak contractive condition involving various combinations ofdx,yon a complete metric space. Our result is an extension as well as a generalization of Alber and Guerre-Delabriere (1997) in particular. It also generalizes the results of Rhoades (2001), Choudhury and Dutta, (2000), and Dutta and Choudhury, (2008).

scholarly journals Fixed point theorems for nonlinear contractive mappings in ordered b-metric space with auxiliary function

2020 ◽  
Vol 13 (1) ◽  
Author(s):  
Namana Seshagiri Rao ◽  
Karusala Kalyani ◽  
Belay Mitiku
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Auxiliary Function ◽  
Weak Contraction ◽  
Partially Ordered ◽  
Contractive Mappings ◽  
Contraction Condition

Abstract Objectives In this paper we present some fixed point theorems for self mappings satisfying generalized $$(\phi , \psi )$$ ( ϕ , ψ ) -weak contraction condition in partially ordered complete b-metric spaces. The results presented over here generalize and extend some existing results in the literature. Finally, we illustrate two examples to support our results. Result We obtained a unique fixed point of a self mapping satisfying certain contraction condition which is involving an auxiliary function. Also, the results are presented for the existence of a common fixed point and a coincidence point for generalized $$(\phi , \psi )$$ ( ϕ , ψ ) -weak contraction mappings in partially ordered complete b-metric space.

scholarly journals Set-valued Contractions in b-Metric Spaces with Application

2021 ◽  
Vol 20 ◽  
pp. 312-318
Author(s):  
Duangkamon Kitkuan ◽  
Pakeeta Sukprasert
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Weak Contraction ◽  
Set Valued Mapping ◽  
Contraction Condition

In this article, we present a (α, F)-set-valued mapping in setting b-metric space by characterizing the weak contraction condition with the C function and the α-set-valued function of type S. There are examples and implementations accessible that illustrate the validity of our findings.

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