Some existence of coincidence point and approximate solution method for generalizedweak contraction in b-generalized pseudodistance fiunctionsy

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6185-6203 ◽  
Author(s):  
Chirasak Mongkolkeha ◽  
Poom Kumam
Keyword(s):  
Approximate Solution ◽  
Contraction Mapping ◽  
Solution Method ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Weak Contraction ◽  
Generalized Weak Contraction ◽  
Approximate Solution Method ◽  
Generalized Pseudodistance

The purpose of this article is to prove some coincidence point and approximate solution method for generalized weak contraction mapping in b??metric spaces by using the concept of b-generalized pseudodistance. Also, we give some examples to illustrate our main results.

Fixed point theorems for generalized weak contraction mapping in generating space of b-dislocated metric spaces

2020 ◽  
pp. 2150120
Author(s):  
Reena Jain
Keyword(s):  
Fixed Point ◽  
Partial Order ◽  
Metric Space ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Weak Contraction ◽  
Dislocated Metric Space ◽  
Generalized Weak Contraction ◽  
Dislocated Metric

In this paper, the concept of generalized weak contraction mapping in the setting of generating space of [Formula: see text]-dislocated metric space endowed with partial order is introduced and some fixed-point theorems for the mappings in space satisfying the generalized weak contraction are proved. Example is also given in order to justify our main result.

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 On approximation by splines of solution of boundary problem

1987 ◽  
pp. 30
Author(s):  
S.G. Dronov
Keyword(s):  
Approximate Solution ◽  
Boundary Problem ◽  
Fourth Order ◽  
Solution Method ◽  
Cubic Spline ◽  
Order Of Accuracy ◽  
Approximate Solution Method

For the boundary problem$$y'' + p(x) y' + q(x) y = r(x), \; y(a) = Y_a, \; y(b) = Y_b$$we give the approximate solution method of fourth order of accuracy in the form of cubic spline. For truncated problem ($p(x) \equiv 0$) we establish the prior estimates of error.

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