Common fixed point theorems for hybrid pairs of mappings with some weaker conditions in 2-metric spaces

• Autorzy: Deshpande B. , Chouhan S.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we prove common xed point theorems for hybrid pairs of mappings satisfying an implicit relation in 2-metric spaces by using a new commutativity condition i.e. weak commutativity of type (KB). We also prove common xed point theorem, of Gregus type for hybrid pairs of maps by using weak commutativity of type (KB) in 2-metric spaces. We extend, improve and generalize many known results. We also give examples to validate our results.

Słowa kluczowe

EN

common fixed point; coincidence point; weak commutativity of type ( KB )

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2011
• Tom: Nr 46
• Strony: 37--55
• Opis fizyczny: Bibliogr. 33 poz.

Twórcy

autor

Deshpande B.

• Bhavana Deshpande Department of Mathematics Govt. Arts & Science P.G. College Ratlam- 457001 (M.P.) India

autor

Chouhan S.

Bibliografia

• [1] Abd El-Monsef, Abu-Donia H.M., Abd-Rabou Kb., New types of common fixed point theorems in 2-metric spaces, Chaos Solitons and Fractals, 41(2009), 1435-1441.
• [2] Aliouche A., Common fixed point theorems via an implicit relation and new properties, Soochow J. Math, 33(4)(2007), 593-601.
• [3] Aliouche A., Djoudi A., Common fixed point theorems for mappings satisfying an implicit relation without decreasing assumption, Hacet. J. Math. Stat., 36(1)(2007), 11-18.
• [4] Dhage B.C., Generalized metric space and mappings with fixed point, Bulletin of Calcutta Mathematical Society, 84(6)(1992), 329-334.
• [5] Dhage B.C., Generalized metric spaces and topological structure I, Analele Stiintifice ale Universitatii Al. I. Cuza Din Iasi Serie Noud. Mathematica, 46(1)(2000), 3-24.
• [6] Dhage B.C., On generalized metric spaces and topological structure II, Pure and Applied Mathematika Sciences, 40(1-2)(1994), 37-41.
• [7] Dhage B.C., On continuity of mappings in D-metric spaces, Bulletin of Calcutta Mathematical Society, 86(6)(1994), 503-508.
• [8] Djoudi A., Nisse L., Gregus type fixed points for weakly compatible maps, Bull. Belg. Math. Soc. Simon Steven, 10(3)(2003), 369-378.
• [9] Djoudi A., Khemis R., Fixed point for set and single valued maps without continuity, Demonstratio Math., 38(3)(2005), 739-751.
• [10] El. Naschie MS, Wild topology hyperbolic geometry and fusion algebra of high energy particle physics, Choas, Solitons & Fractals, 13(2002), 1935-1945.
• [11] Gahler S., Uber die niformisierbakait 2-metrische Raume, Math. Nacher, 28(1965), 235-244.
• [12] Gahler S., Zur geometric 2-metrische Raume, Rev Raum, Math. Pures Et Appl., 11(1966), 655-664.
• [13] Gahler S., 2-metrische Raume und ihre topologische structure, Math. Nacher, 26(1963), 115-48.
• [14] Hsiao A., Property of contractive type mappings in 2-metric spaces, Tnan- abha, 16(1986), 223-239.
• [15] Iseki K., Fixed point theorems in 2-metric spaces, Math. Sem. Notes, 3(1975), 13-36.
• [16] Jungck G., Compatible mappings and common fixed points, Int. J. Math. Sci., 9(1986), 771-779.
• [17] Jungck G., Rhoades BE., Some fixed point theorems for compatible maps, Int. J. Math. Sci., 16(1993), 417-28.
• [18] Jungck G., Rhoades BE., Fixed point theorems for set valued functions without continuity, Indian J. Pure and Appl. Math., 29(1998), 227-38.
• [19] Krzyska S., Kubiaczyk I., Fixed point theorems for upper semicontinuous and weakly-weakly upper semicontinuous multivalued mappings, Math. Japonica, 47(2)(1998), 237-240.
• [20] Kubiaczyk I., Deshpande B., Noncompatibility. Discontinuity inconsideration of common fixed point of set and single-valued maps, Southeast Asian Bull. of Math., 32(2008), 467-474.
• [21] Khan M.D., A Study of Fixed Point Theorems Doctoral Thesis, Aligarh Muslim University, 1984.
• [22] Mustafa Z., Sims U., Some remarks concerning D-metric spaces, International Conference of Fixed point Theory and Applications, Yokohama 2004, 189-198.
• [23] Mustafa Z., Sims U., A new approach to generalized metric spaces, Journal of Nonlinear and Convex Analysis, 7(2)(2006), 289-297.
• [24] Naidu S.V.R., Prasad J.R., Fixed point theorem in 2-metric spaces, Indian J. Pure and Appl. Math., 17(1986), 974-93.
• [25] Pant R.P., Common fixed points of noncommuting mappings, J. Math. Anal. Appl., 188(1994), 436-440.
• [26] Pant R.P., Common fixed point theorems for contractive maps, J. Math. Anal. Appl., 226(1998), 251-258.
• [27] Pant R.P., Discontinuity and fixed points, J. Math. Anal. Appl., 240(1999), 284-289.
• [28] Pathak H.K., Cho Y.J., Kang, Remarks on R-weakly commuting map- pings and common fixed points theorems, Bull. Korean Math. Soc., 34(1997), 247-257.
• [29] Pathak H.K., Kang S.M., Baek J.H., Weak compatible mappings of type (A) and common fixed points, Kyungpook Math J., 35(1995), 345-59.
• [30] Sessa S., On weak commutativity condition of mappings in fixed point con- siderations, Publ. Inst. Math. (Beograd), 32(46)(1982), 149-153.
• [31] Sessa S., Khan M.S., Some remarks in best approximation theory, Math. J. Toyoma Univ., 17(1994), 151-165.
• [32] Sharma S., Deshpande B., Fixed point theorems for set and single valued maps without continuity and compatibility, Demonst. Math., Vol. XL 3(2007), 649-658.
• [33] Sharma S., Deshpande B., Pathak R., Common fixed point theorems for hybrid pairs of mappings with some weaker conditions, Fasc. Math., 39(2008), 71-86.