Common fixed point theorems for hybrid pairs of mappings with some weaker conditions

• Autorzy: Sharma S. , Deshpande B. , Pathak R.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we prove a common fixed point theorem for hybrid pairs of set and single valued mappings without assuming compatibility and continuity of any mapping on noncomplete metric spaces. To prove the theorem, we use a noncompatible condition, that is, weak commutativity of type (KB). We show that completeness of the whole space is not necessary for the existence of common fixed point. Our result improves, extends and generalizes the results of Fisher [5], Sastry and Naidu [18]. We give an example to validate our result. We also prove a common fixed point theorem on compact metric spaces. At the end, we improve our theorem by omitting the assumption of compactness. We also improve and generalize the results of Ahmed [2] and Fisher [5].

Słowa kluczowe

EN

coincidence point; common fixed point; noncompatible maps

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2008
• Tom: Nr 39
• Strony: 71--86
• Opis fizyczny: Bibliogr. 21 poz.

Twórcy

autor

Sharma S.

autor

Deshpande B.

autor

Pathak R.

• Madhav Vigyan Mahavidyalaya, Ujjain (M.P.), India,

Bibliografia

• [1]AAMRI M., EL MOUTAWAKII D., Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl., 270(2002), 181-188.
• [2]AHMED Μ.Α., Common fixed point theorems for weakly compatible mappings,Rocky Mountain Journal of Mathematics, Vol. 33, November 4, Winter 2003.
• [3]CHANG T.H., Fixed point theorems of contractive type set valued mappings, Math. Japonica, 38(4)(1993), 675-690.
• [4]DJOUDI A., KHEMIS R., Fixed points for set and single valued maps without continuity, Demonstratio Mathematica, XXXVIII (3)(2005), 739-751.
• [5]FISHER B., Common fixed points of mappings and set valued mappings on a metric space, Kyungpook Math. J., 25(1985), 35-42.
• [6]FISHER B., S ESS A S., TWO common fixed point theorems for weakly commuting mappings, Periodica Math. Hungarica, 20(3)(1989), 207-218.
• [7]JUNGCK G., Compatible mappings and common fixed points, Internat. J. Math. Math. Sci., 9(1986), 771-779.
• [8]JUNGCK G., RHOADES B.E., Some fixed point theorems for compatible maps, Internat. J. Math. Math. Sci., 16(3)(1993), 417-428.
• [9]JUNGCK G., RHOADES B.E., Fixed points for set valued functions without continuity, Indian J. of Pure Appl. Math., 16(3)(1998), 227-238.
• [10]KANNAN R., Some results on fixed points, Bull. Cal. Math. Soc., 60(1968), 71-76.
• [11]KUBIACZYK I., DESHPANDE B., Noncompatibility, discontinuity in consideration of common fixed point of set and single valued maps, SEA Bull. Math, accepted for publication.
• [12]KYZYSKA S., KUBIACZYK L, Fixed point theorems for upper semicontinuous and weakly-weakly upper semicontinuous multivalued mappings, Math.Japonica, 47(2)(1998), 237-240.
• [13]PANT R . P . , Common fixed points of noncommuting mappings, J. Math. Anal.Appl, 188(1994), 436-440.
• [14]PANT R.P., Common fixed point theorems for contractive maps, J. Math.Anal Appl, 226(1998), 284-289.
• [15]PANT R.P., Common fixed points of Lipschitz type mappings pairs, J. Math.Anal Appl, 240(1999), 280-283.
• [16]PANT R.P., Discontinuity and fixed points, J. Math. Anal Appl, 240(1999), 284-289.
• [17]PATHAK H.K., CHO Y.J., KANG, Remarks on R-weakly commuting mappings and common fixed point theorems, Bull Korean Math. Soc., 34(1997), 247-257.
• [18]SASTRY K.P.R., NAIDU S.V.R., Fixed point theorems for generalized contraction mappings, Yokohama Math. J., 28(1980), 15-29.
• [19]SESSA S., On a weak commutativity condition of mappings in fixed point considerations, Publ Inst. Math. (Beograd) 32, 46(1982), 149-153.
• [20]SESSA S., KHAN M.S., Some remarks in best approximation theory, Math.J. Toyoma Univ., 17(1994), 151-165.
• [21]SHARMA S., DESHPANDE B., Fixed point theorems for set and single valued maps without continuity and compatibility, Demonstratio Mathematica, XL (3)(2007), 649-658.