scholarly journals Generalized ψ-weak contraction condition for variants of compatible mappings in G-metric space

2021 ◽  
Keyword(s):  
Metric Space ◽  
Compatible Mappings ◽  
Weak Contraction ◽  
Contraction Condition

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 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.

scholarly journals Fixed point results for weak contractions in partially ordered b-metric space

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
N. Seshagiri Rao ◽  
K. Kalyani ◽  
K. Prasad
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Coupled Coincidence Point ◽  
Weak Contraction ◽  
Partially Ordered ◽  
Contraction Condition ◽  
Generalized Weak Contraction ◽  
Coupled Coincidence

Abstract Objectives We explore the existence of a fixed point as well as the uniqueness of a mapping in an ordered b-metric space using a generalized $$({\check{\psi }}, \hat{\eta })$$ ( ψ ˇ , η ^ ) -weak contraction. In addition, some results are posed on a coincidence point and a coupled coincidence point of two mappings under the same contraction condition. These findings generalize and build on a few recent studies in the literature. At the end, we provided some examples to back up our findings. Result In partially ordered b-metric spaces, it is discussed how to obtain a fixed point and its uniqueness of a mapping, and also investigated the existence of a coincidence point and a coupled coincidence point for two mappings that satisfying generalized weak contraction conditions.

scholarly journals Best Proximity Point for Generalized Proximal Weak Contractions in Complete Metric Space

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Erdal Karapınar ◽  
V. Pragadeeswarar ◽  
M. Marudai
Keyword(s):  
Approximate Solution ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Complete Metric Space ◽  
Optimal Approximate Solution ◽  
Weak Contraction ◽  
Complete Metric Spaces ◽  
New Class

We introduce a new class of nonself-mappings, generalized proximal weak contraction mappings, and prove the existence and uniqueness of best proximity point for such mappings in the context of complete metric spaces. Moreover, we state an algorithm to determine such an optimal approximate solution designed as a best proximity point. We establish also an example to illustrate our main results. Our result provides an extension of the related results in the literature.

scholarly journals A common fixed point theorem of Meir and Keeler type

1993 ◽  
Vol 16 (4) ◽  
pp. 669-674 ◽  
Author(s):  
Y. J. Cho ◽  
P. P. Murthy ◽  
G. Jungck
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Metric Space ◽  
Compatible Mappings ◽  
Common Fixed Point Theorem

In this paper, we introduce the concept of compatible mappings of type (A) on a metric space, which is equivalent to the concept of compatible mappings under some conditions, and give a common fixed point theorem of Meir and Keeler type. Our result extends, generalized and improves some results of Meir-Keeler, Park-Bae, Park-Rhoades, Pant and Rao-Rao, etc.

scholarly journals Fixed Point Theorem for Set Valued Mapping with Rational Condition

2020 ◽  
pp. 805-810
Author(s):  
Liqaa J. Khaleel ◽  
Buthainah A. A. Ahmed
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Partial Metric Space ◽  
Partial Metric ◽  
Set Valued Mapping ◽  
Contraction Condition ◽  
Rational Condition

In this paper, we generalized the principle of Banach contractive to the relative formula and then used this formula to prove that the set valued mapping has a fixed point in a complete partial metric space. We also showed that the set-valued mapping can have a fixed point in a complete partial metric space without satisfying the contraction condition. Additionally, we justified an example for our proof.

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