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

• Autorzy: Tomar A. , Beloul S. , Sharma R. , Upadhyay S.

Identyfikatory

DOI

10.1515/dema-2017-0028

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

common fixed point; weakly compatible; generalized condition (B); partial metric space; quasi-partial metric space

PL

wspólny stały punkt; kompatybilność niska; warunek uogólniony; przestrzeń metryczna częściowa

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2017
• Tom: Vol. 50, nr 1
• Strony: 278--298
• Opis fizyczny: Bibliogr. 20 poz., rys., wykr.

Twórcy

autor

Tomar A.

• Department of Mathematics, V. S. K. C. Government P. G. College, Dakpathar (Uttarakhand), India

autor

Beloul S.

• Department of Mathematics, University of El-Oued, P. O. Box 789, El-Oued 39000, Algeria

autor

Sharma R.

• Department of Mathematics, V. S. K. C. Government P. G. College, Dakpathar (Uttarakhand), India

autor

Upadhyay S.

• Department of Mathematics, V. S. K. C. Government P. G. College, Dakpathar (Uttarakhand), India

Bibliografia

• [1] Frèchet M., Sur quelques points du calcul fonctionnel, Rendic. Circ. Mat. Palermo, 1906, 22, 1-74
• [2] Künzi H.-P. A., Pajoohesh H., Schellekens M. P., Partial quasi-metrics, Theoret. Comput. Sci., 2006, 365(3), 237-246
• [3] Karapinar E., Erhan M., Öztürk Ali, Fixed point theorems on quasi-partial metric spaces, Math. Comput. Modelling, 2013, 57, 2442-2448
• [4] 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
• [5] Abbas M., Nazir T., Vetro P., Common fied point results for three maps in G-metric spaces, Filomat, 2011, 25(4), 1-17
• [6] Babu G. V. R., Sandhy M. L., Kameshwari M. V. R., A note on a fixed point theorem of Berinde on weak contractions, Carpathian J. Math. , 2008, 24(1), 8-12
• [7] Berinde V., General constructive fixed point theorems for Ċiriċ-type almost contractions in metric spaces, Carpathian J. Math., 2008, 24(2), 10-19
• [8] Chatterjea S. K., Fixed point theorems, C. R. Acad. Bulgare Sci., 1972, 25, 727-730
• [9] Jungck G., Rhoades B. E., Fixed point for set valued functions without continuity, Indian J. Pure Appl. Math., 1998, 29(3), 227-238
• [10] Matthews S. G., Partial metric topology, Proceedings of the 8th Summer Conference on General Topology and Applications, Ann. New York Acad. Sci., 1994, 728, 183-197
• [11] Matthews S. G., Partial metric topology, Research Report 212, Department of Computer Science, University of Warwick, 1992
• [12] Abbas M., Ilic D., Common fixed points of generalized almost nonexpansive mappings, Filomat, 2010, 24(3), 11-18
• [13] Banach S., Sur les opérations dans les ensembles abstraits et leur application aux l’équations integrals Fund. Math., 1922, 3, 133-181
• [14] Kannan R., Some results on fixed points, Bull.Calcutta Math. Soc., 1968, 60, 71-76
• [15] Zamrescu T., Fixed point theorems in metric spaces, Arch. Math. (Basel), 1972, 23, 292-298
• [16] Ċiriċ L.B., A generalization of Banach principle, Proc. Amer. Math. Soc., 1974, 45, 727-730
• [17] Tomar A., Karapinar E., On variants of continuity and existence of xed point via Meir-Keeler contractions in MC-spaces, J. Adv. Math. Stud., 2016, 9(2), 348-359
• [18] Singh S. L., Mishra S. N., Remarks on recent xed point theorems, Fixed Point Theory Appl., 2010, Article ID 452905, 18 pages
• [19] Singh S. L., Mishra S. N., Coincidence theorems for certain classes of hybrid contractions, Fixed Point Theory Appl., 2010, Article ID 898109, 14 pages
• [20] Singh S. L., Tomar A., Weaker forms of commuting maps and existence of fixed points, J. Korea Soc. Math. Educ. Ser. B Pure Appl. Math., 2003, 10(3), 141-161

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).