A general fixed point theorem for weakly subsequentially continuous mappings

• Autorzy: Popa Valeriu
• Języki publikacji: EN

Abstrakty

EN

In this paper a general fixed point theorem for two pairs of subsequentially mappings compatible of type E is proved, which generalize the results by [2]-[4], [6] and other results. As applications, new results for mappings satisfying contractive conditions of integral type, φ-contractive conditions and weak contractive conditions are obtained.

Słowa kluczowe

EN

fixed point; almost altering distance; implicit relation; weakly subsequentially continuous; compatible mappings of type E

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2019
• Tom: nr 62
• Strony: 103--119
• Opis fizyczny: Bibliogr. 35 poz.

Twórcy

autor

Popa Valeriu

• ”Vasile Alecsandri” University of Bacau 157 Calea Mărăşeşti Bacau, 600115, Romania

Bibliografia

• [1] Alber Ya.I., Guerre-Delabriere S., Principle of weakly contractive maps in Hilbert spaces. New results in aferente theory, Adv. Appl. Math. (Eds. Y. Gahbery and Yu. Lybrch), Birkhauser, Berlag, Basel, 98(1997), 7-22.
• [2] Areefi S., Ravendra Babu J.A.Y., Sundesh Babu E., Yara Lak- SHIMI Р., Common fixed point theorems for weakly subsequentially continuous generalized contractions maps with rational expresion, Int. J. Inovative Research in Science, Engineering and Technology, 6(3)(2017), 4134-4138.
• [3] Beloul S., A common fixed point theorem for weakly subsequentially continuous mappings satisfying implicit relations, Malaya J. Mathematik, 3(4)(2015), 409-418.
• [4] Beloul S., Common fixed point theorems for weakly subsequentially continuous generalized contractions with applications, Applied Math. E-Notes, 15(2015), 173-186.
• [5] Beloul S., Some fixed point theorems for weakly subsequentially continuous and compatible of type (E) mappings with applications, Intern. J. Nonlinear Anal. Appl., 7(1)(2016), 53-62.
• [6] Beloul S., Chauhan S., Gregus type fixed point theorems for weakly subsequentially continuous mappings satisfying strict contractive conditions of integral type, Le Matematiche, LXXI (2016), Fasc. II, 3-15.
• [7] Bouhadjera H., More fixed point theorems under a new concept, Demonstr. Math., 49(1)(2016), 64-78.
• [8] Bouhadjera H., Godet Thobie C., Common fixed point theorems for pairs of subcompatible maps, arriv, 0906.3159v1 (math FA), 17 July (2009) (Old version).
• [9] Bouhadjera H., Godet Thobie C., Common fixed point theorems for pairs of subcompatible maps, arriv, 0906.3159v2 (math FA), 23 May (2011) (New version).
• [10] Branciari A., A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci., 29(9)(2002), 531-536.
• [11] Chauhan S., Kadelburg Z., Dalal S., A common fixed point theorem in metric space under general contractive conditions, J. Appl. Math. 2013(2013), Article ID 510691, 7 pages.
• [12] Chauhan S., Aydi H., Shatanawi W., Yetro C., Some integral type fixed-point theorems and an application to systems of functional equations, Vietnam J. Math., 42(1)(2014), 17-37.
• [13] Diwan S.D., Gupta R., A common fixed point theorem for Gregus type mappings, Thai J. Math., 12(1)(2014), 103-112.
• [14] Djoudi A., Aliouche A., Common fixed point of Gregus type for weak compatible mappings satisfying contractive conditions of integral type, J. Math. Anal. Appl., 329(2007), 31-45.
• [15] Jungck G., Compatible mappings and common fixed points, Int. J. Math. Math. Sci., 9(4)(1986), 771-779.
• [16] Jungck G., Murthy P.P., Cho Y.J., Compatible mappings if type (A) and common fixed points, Math. Japonica, 38(1993), 381-394.
• [17] Khan M.S., Swaleh M., Kumar R., Fixed point theorems by altering distances between points, Bull. Austral. Math. Soc., 30(1984), 1-9.
• [18] Matkowski M., Fixed point theorems for mappings with a contractive iterate at a point, Proc. Amer. Math. Soc., 62(2)(1977), 344-348.
• [19] Pant R.P., Common fixed point theorems for four mappings, Bull. Calcutta Math. Soc., 9(1998), 281-286.
• [20] Pant R.P., A common fixed point theorems under a new condition, Indian J. Pure Appl. Math., 30(20)(1999), 147-152.
• [21] Pant R.P., Discontinuity and fixed points, J. Math. Anal. Appl., 240(1)(1999), 284-289.
• [22] Pathak H.K., Khan M.S., Compatible of type (B) and common fixed point theorems of Gregus type, Czechoslovac Math. J., 45(120)(1995), 685-698.
• [23] Pathak H.K., Cho Y.J., Kang S.M., Lee B.S., Fixed point theorems for compatible mappings of type (P) and applications to dynamic programming, Le Matematiche, 50(1)(1995), 15-32.
• [24] Pathak H.K., Cho Y.J., Khan M.S., Madhari B.M., Compatible mappings of type (C) and common fixed point theorems of Gregus type, Demonstr. Math., 31(3)(1998), 499-518.
• [25] Pathak H.K., Shahzad N., Gregus type fixed point results for tangential mappings satisfying contractive conditions of integral type, Bull. Belg. Math. Soc. Simon Stevin, 16(2)(2009), 277-288.
• [26] Popa V., Fixed point theorems for implicit contractive mappings, Stud. Cerc. Știinţ., Ser. Mat., Univ. Bacău, 7(1997), 127-134.
• [27] Popa V., Some fixed point theorems for compatible mappings satisfying an implicit relation, Demonstr. Math., 32(1)(1999), 157-163.
• [28] Popa V., Some fixed point theorems for weakly compatible mappings, Rad. Mat., 10(2001), 245-252.
• [29] Popa V., Mocanu M., Altering distance and common fixed points under implicit relations, Hacet. J. Math. Stat., 38(3)(2009), 329-337.
• [30] Popa V., Patriciu A.-M., A general fixed point theorem for a pair of self mappings with common limit range property in G-metric spaces, Facta Univ. Ser. Math. Inform., 29(4)(2014), 351-370.
• [31] Rhoades B.E., Some theorems of weakly contractive mappings, Nonlinear Analysis, 47(2001), 2683-2693.
• [32] Sastry K.P.R., Babu G.V.R., Fixed point theorems in metric spaces by altering distances, Bull. Calcutta Math. Soc., 90(3)(1998), 175-182.
• [33] Sastry K.P.R., Babu G.V.R., Some fixed point theorems by altering distances between two points, Indian J. Pure Appl. Math., 30(1999), 641-647.
• [34] Singh M.R., Singh Y.M., Compatible mappings of type (E) and common fixed point theorems of Meir-Keeler type, Intern. J. Math. Sci. and Engin. Appl., 1(2)(2007), 299-316.
• [35] Singh M.R., Singh Y.M., On various type of compatible maps and common fixed point theorems for non-continuous maps, Hacet. J. Math. Stat., 40(4)(2011), 503-513.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).