Optimal Approximate Solution for (α,β )γ-Contraction Mappings in Metric Spaces with Applications

2016 ◽  
Vol 10 (2) ◽  
pp. 507-518
Author(s):  
Chirasak Mongkolkeha ◽  
Wutiphol Sintunavarat
Keyword(s):  
Approximate Solution ◽  
Metric Spaces ◽  
Optimal Approximate Solution ◽  
Contraction Mappings

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.

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 Optimal Approximate Solutions of Fixed Point Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
S. Sadiq Basha ◽  
N. Shahzad ◽  
R. Jeyaraj
Keyword(s):  
Fixed Point ◽  
Approximate Solution ◽  
Banach Spaces ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Approximate Solutions ◽  
Uniformly Convex ◽  
Optimal Approximate Solution ◽  
Uniformly Convex Banach Spaces

The main objective of this paper is to present some best proximity point theorems for K-cyclic mappings and C-cyclic mappings in the frameworks of metric spaces and uniformly convex Banach spaces, thereby furnishing an optimal approximate solution to the equations of the form where is a non-self mapping.

scholarly journals Multivalued weak cyclic δ-contraction mappings

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Pulak Konar ◽  
Samir Kumar Bhandari ◽  
Sumit Chandok ◽  
Aiman Mukheimer
Keyword(s):  
Fixed Point ◽  
Distance Function ◽  
Metric Spaces ◽  
Multivalued Mappings ◽  
Cyclic Contraction ◽  
Contraction Mappings ◽  
Multivalued Contraction ◽  
New Type

AbstractIn this paper, we propose some new type of weak cyclic multivalued contraction mappings by generalizing the cyclic contraction using the δ-distance function. Several novel fixed point results are deduced for such class of weak cyclic multivalued mappings in the framework of metric spaces. Also, we construct some examples to validate the usability of the results. Various existing results of the literature are generalized.

SOME FIXED POINT RESULTS FOR A GENERALIZED $\psi$-WEAK CONTRACTION MAPPINGS IN b-METRIC SPACES

2021 ◽  
Vol 10 (5) ◽  
pp. 2449-2468
Author(s):  
E. Bashayreh ◽  
A. Talafhah ◽  
W. Shatanawi
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Weak Contraction ◽  
Contraction Mappings

In this paper, we will present the definitions and notation of generalized $\psi$-weak contraction mappings in b-metric spaces, and establish some results besides the most important properties of fixed point in orbitally complete b-metric spaces. Our results generalize several well-known comparable results in the literature. As an application of our results we generalize the results of Shatanawi [7]. Some examples are given to illustrate the useability of our results.

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