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

Demonstratio Mathematica

Beloul Said¹  Upadhyay Shivangi²  Sharma Ritu²  Tomar Anita³ 

[1] Department of Mathematics, University of El-Oued, P. O. Box 789, El-Oued 39000, Algeria;Department of Mathematics, V. S. K. C. Government P. G. College, Dakpathar (Uttarakhand), India;Department of Mathematics, V. S. K. C. Government P. G. College, Dakpathar(Uttarakhand), India;

关键词: Common fixed point;    weakly compatible;    generalized condition (B);    partial-metric space;    quasipartial metric space;    47H10;    54H25;   

DOI  :  10.1515/dema-2017-0028

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown