scholarly journals ϵ -Compatible Map and New Approach for Common Fixed Point Theorems in Partial Metric Space Endowed with Graph

2020 ◽  
Vol 8 (3) ◽  
pp. 254-261
Author(s):  
Anuradha Anuradha ◽  
SeemaMehra SeemaMehra
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Partial Metric Space ◽  
Partial Metric ◽  
New Approach ◽  
Common Fixed Point Theorems

scholarly journals The Existence and Uniquenes Solution of Nonlinear Integral Equations via Common Fixed Point Theorems

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1179
Author(s):  
Gunaseelan Mani ◽  
Arul Joseph Gnanaprakasam ◽  
Yongjin Li ◽  
Zhaohui Gu
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Partial Metric Space ◽  
Partial Metric ◽  
Nonlinear Integral Equations ◽  
Common Fixed Point Theorems

In this paper, we prove some common fixed-point theorems on complex partial metric space. The presented results generalize and expand some of the well-known results in the literature. We also explore some of the applications of our key results.

scholarly journals Common fixed point theorems via generalized condition (B) in quasi-partial metric space and applications

2017 ◽  
Vol 50 (1) ◽  
pp. 278-298
Author(s):  
Anita Tomar ◽  
Said Beloul ◽  
Ritu Sharma ◽  
Shivangi Upadhyay
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric Space ◽  
Partial Metric ◽  
Open Problems ◽  
Common Fixed Point Theorems ◽  
Condition B

Abstract The aim of this paper is to introduce generalized condition (B) in a quasi-partial metric space acknowledging the notion of Künzi et al. [Künzi H.-P. A., Pajoohesh H., Schellekens M. P., Partial quasi-metrics, Theoret. Comput. Sci., 2006, 365, 237-246] and Karapinar et al. [Karapinar E., Erhan M.,Öztürk A., Fixed point theorems on quasi-partial metric spaces, Math. Comput.Modelling, 2013, 57, 2442-2448] and to establish coincidence and common fixed point theorems for twoweakly compatible pairs of self mappings. In the sequelwe also answer affirmatively two open problems posed by Abbas, Babu and Alemayehu [Abbas M., Babu G. V. R., Alemayehu G. N., On common fixed points of weakly compatible mappings satisfying generalized condition (B), Filomat, 2011, 25(2), 9-19]. Further in the setting of a quasi-partial metric space, the results obtained are utilized to establish the existence and uniqueness of a solution of the integral equation and the functional equation arising in dynamic programming. Our results are also justified by explanatory examples supported with pictographic validations to demonstrate the authenticity of the postulates.

scholarly journals Solving a System of Nonlinear Integral Equations via Common Fixed Point Theorems on Bicomplex Partial Metric Space

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1584
Author(s):  
Zhaohui Gu ◽  
Gunaseelan Mani ◽  
Arul Joseph Gnanaprakasam ◽  
Yongjin Li
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Partial Metric Space ◽  
Partial Metric ◽  
Nonlinear Integral Equations ◽  
Common Fixed Point Theorems

In this paper, we introduce the notion of bicomplex partial metric space and prove some common fixed point theorems. The presented results generalize and expand some of the literature’s well-known results. An example and application on bicomplex partial metric space is given.

scholarly journals Existence and Uniquenes Solution of Integral Equations via Common Fixed Point Theorems

2021 ◽  
Author(s):  
Gunaseelan Mani ◽  
Arul Joseph Gnanaprakasam ◽  
Yongjin Li ◽  
Zhaohui Gu
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Partial Metric Space ◽  
Partial Metric ◽  
Common Fixed Point Theorems

In this paper, we prove some common fixed point theorems on complex partial metric space. The presented results gener- alize and expand some of the literature well-known results. We also explore some of the application of our key results.

scholarly journals S ∗ p ‐ b -Partial Metric Spaces with some Results in Common Fixed Point Theorems

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
A. M. Zidan
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric Space ◽  
Partial Metric ◽  
Topological Properties ◽  
Partial Metric Spaces ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem

In this paper, we introduce the notion of S ∗ P ‐ b -partial metric spaces which is a generalization each of S ‐ b -metric spaces and partial-metric space. Also, we study and prove some topological properties, to know the convergence of the sequences and Cauchy sequence. Finally, we study a new common fixed point theorem in these spaces.

scholarly journals Some Common Fixed Point Theorems in Partial Metric Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Erdal Karapınar ◽  
Uğur Yüksel
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Triangle Inequality ◽  
Metric Spaces ◽  
Applied Mathematics ◽  
Partial Metric Space ◽  
Partial Metric ◽  
Partial Metric Spaces ◽  
Common Fixed Point Theorems

Many problems in pure and applied mathematics reduce to a problem of common fixed point of some self-mapping operators which are defined on metric spaces. One of the generalizations of metric spaces is the partial metric space in which self-distance of points need not to be zero but the property of symmetric and modified version of triangle inequality is satisfied. In this paper, some well-known results on common fixed point are investigated and generalized to the class of partial metric spaces.

scholarly journals Fixed Point Theorems and Asymptotically Regular Mappings in Partial Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Satish Shukla ◽  
Ishak Altun ◽  
Ravindra Sen
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric ◽  
Regular Mapping ◽  
Partial Metric Spaces ◽  
Common Fixed Point Theorems ◽  
Asymptotically Regular

The notion of asymptotically regular mapping in partial metric spaces is introduced, and a fixed point result for the mappings of this class is proved. Examples show that there are cases when new results can be applied, while old ones (in metric space) cannot. Some common fixed point theorems for sequence of mappings in partial metric spaces are also proved which generalize and improve some known results in partial metric spaces.

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