Optimal Approximate Solution for $$\alpha $$ α -Multiplicative Proximal Contraction Mappings in Multiplicative Metric Spaces

2015 ◽  
Vol 86 (1) ◽  
pp. 15-20
Author(s):  
Chirasak Mongkolkeha ◽  
Wutiphol Sintunavarat
Keyword(s):  
Approximate Solution ◽  
Metric Spaces ◽  
Optimal Approximate Solution ◽  
Proximal Contraction ◽  
Contraction Mappings ◽  
Multiplicative Metric Spaces

scholarly journals The Existence Theorems of an Optimal Approximate Solution for Generalized Proximal Contraction Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Wutiphol Sintunavarat ◽  
Poom Kumam
Keyword(s):  
Approximate Solution ◽  
Best Proximity Point ◽  
Existence Theorems ◽  
Contraction Principle ◽  
Optimal Approximate Solution ◽  
Proximal Contraction ◽  
Contraction Mappings ◽  
Generalized Proximal Contraction ◽  
Banach’S Contraction Principle

Recently, Basha (2011) established the best proximity point theorems for proximal contractions of the first and second kinds which are extension of Banach's contraction principle in the case of non-self-mappings. The aim of this paper is to extend and generalize the notions of proximal contractions of the first and second kinds which are more general than the notion of self-contractions, establish the existence of an optimal approximate solution theorems for these non-self-mappings, and also give examples to validate our main results.

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 Optimal Approximate Solution of Coincidence Point Equations in Fuzzy Metric Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 327 ◽  
Author(s):  
Naeem Saleem ◽  
Mujahid Abbas ◽  
Manuel Sen
Keyword(s):  
Approximate Solution ◽  
Metric Space ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Fuzzy Metric Space ◽  
Optimal Approximate Solution ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric

The purpose of this paper is to introduce α f -proximal H -contraction of the first and second kind in the setup of complete fuzzy metric space and to obtain optimal coincidence point results. The obtained results unify, extend and generalize various comparable results in the literature. We also present some examples to support the results obtained herein.

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