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Solving system of linear equations via bicomplex valued metric space

Gnanaprakasam Arul Joseph, Boulaaras Salah Mahmoud, Mani Gunaseelan, Cherif Bahri, Idris Sahar Ahmed

Demonstratio Mathematica

2021

Vol. 54, nr 1

474--487

In this paper, we prove some common fixed point theorems on bicomplex metric space. Our results generalize and expand some of the literature’s well-known results. We also explore some of the applications of our key results.

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

Tomar A., Beloul S., Sharma R., Upadhyay S.

Demonstratio Mathematica

2017

Vol. 50, nr 1

278--298

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 two weakly compatible pairs of self mappings. In the sequel we also answer a rmatively 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.

Coincidence and common fixed point theorems via r-weak commutativity of type (AT)

Aliouche A., Popa V.

Fasciculi Mathematici

2009

Nr 41

5-16

We prove common fixed point theorems for two pairs of hybrid mappings satisfying implicit relations in complete metric spaces using the concept of R—weak commutativity of type At and we correct errors of [1], [3] and [8]. Our theorems generalize results of [1-3], [8], [12-16] and [21],