Remarks on occasionally weakly compatible maps versus occasionally weakly compatible maps

• Autorzy: Deepmala , Pathak H. K.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we discuss some important and interesting remarks on the concept of occasionally weakly compatible (owc) mappings, which is an active and interesting area of research in the present era. Also, we discuss here the lapses of several authors in quoting the definition of owc maps and provide the corrected proof by including some additional conditions on their results.

Słowa kluczowe

EN

occasionally weakly compatible maps; common fixed points

PL

wspólny punkt stały

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2014
• Tom: Vol. 47, nr 3
• Strony: 695--703
• Opis fizyczny: Bibliogr. 31 poz.

Twórcy

autor

Deepmala

• School of Studies in Mathematics, Pt. Ravishankar Shukla University, Raipur (C.G.), 492010, India

autor

Pathak H. K.

• School of Studies in Mathematics, Pt. Ravishankar Shukla University, Raipur (C.G.), 492010, India

Bibliografia

• [1] A. Aliouche, V. Popa, Common fixed point theorems for occasionally weakly compatible mappings via implicit relations, Filomat 22(2) (2008), 99–107.
• [2] A. Aliouche, V. Popa, General common fixed point theorems for occasionally weakly compatible hybrid mappings and applications, Novi Sad J. Math. 39(1) (2009), 89–109.
• [3] A. Bhatt, H. Chandra, D. R. Sahu, Common fixed point theorems for occasionally weakly compatible mappings under relaxed conditions, Nonlinear Anal. 73 (2010), 176–182.
• [4] A. Bhatt, H. Chandra, Occasionally weakly compatible mapping in cone metric space, Appl. Math. Sci. 6(55) (2012), 2711–2717.
• [5] B. D. Pant, S. Chauhan, Common fixed point theorem for occasionally weakly compatible mappings in Menger space, Surveys Math. Appl. 6 (2011), 1–7.
• [6] C. T. Aage, J. N. Salunke, On fixed point theorems in fuzzy metric spaces, Int. J. Open Problems Compt. Math. 3(2) (2010), 123–131.
• [7] H. Bouhadjera, General common fixed point theorems for occasionally weakly compatible maps, Math. Sci. 3(3) (2009), 263–272.
• [8] H. Bouhadjera, Fixed points for occasionally weakly compatible maps, Gen. Math. 18(3) (2010), 13–18.
• [9] H. Bouhadjera, A. Djoudi, Common fixed point theorems for subcompatible D-maps of integral type, Gen. Math. 18(4) (2010), 163–174.
• [10] H. Chandra, A. Bhatt, Fixed point theorems for occasionally weakly compatible maps in probabilistic semi-metric space, Int. J. Math. Anal. 3(12) (2009), 563–570.
• [11] H. K. Pathak, S. Tiwari, Common fixed point and best simultaneous approximations theorems under releaxed conditions, Journal of International Academy of Physical Sciences 15 (2011), 17–22.
• [12] K. P. R. Sastry, G. A. Naidu, P. V. S. Prasad, V. M. Latha, S. S. A. Sastri, A critical look at fixed point theorems for occasionally weakly compatible maps in probabilistic semi-metric spaces, Int. J. Math. Anal. 4(27) (2010), 1341–1348.
• [13] L. Ciric, B. Samet, C. Vetro, Common fixed point theorems for families of occasionally weakly compatible mappings, Math. Comput. Modelling 53 (2011), 631–636.
• [14] M. Aamri, D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl. 270 (2002), 181–188.
• [15] M. A. Al-Thagafi, N. Shahzad, Generalized I-nonexpansive selfmaps and invariant approximations, Acta Math. Sinica 24 (2008), 867–876.
• [16] M. A. Al-Thagafi, N. Shahzad, A note on occasionally weakly compatible maps, Int. J. Math. Anal. (Ruse) 3(1–4) (2009), 55–58.
• [17] M. Abbas, Common fixed point for Lipschitzian mappings satisfying rational contractive conditions, Ital. J. Pure Appl. Math. 27 (2010), 141–146.
• [18] N. Hussain, M. A. Khamsi, A. Latif, Common fixed points for JH-operators and occasionally weakly biased pairs under relaxed conditions, Nonlinear Anal. 74 (2011), 2133–2140.
• [19] M. Imdad, A. H. Soliman, Some common fixed point theorems for a pair of tangential mappings in symmetric spaces, Appl. Math. Lett. 23 (2010), 351–355.
• [20] M. Imdad, J. Ali, V. Popa, Impact of occasionally weakly compatible property on common fixed point theorems for expansive mappings, Filomat 25(2) (2011), 79–89.
• [21] G. Jungck, Commuting mappings and fixed points, Amer. Math. Monthly 83 (1976), 261–263.
• [22] G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci. 9 (1986), 771–779.
• [23] G. Jungck, H. K. Pathak, Fixed point via “biased maps”, Proc. Amer. Math. Soc. 123 (1995), 2049–2060.
• [24] G. Jungck, B. E. Rhoades, Fixed points for set valued functions without continuity, Indian J. Pure Appl. Math. 29(3) (1998), 227–238.
• [25] G. Jungck, B. E. Rhoades, Fixed point theorems for occasionally weakly compatible mappings, Fixed Point Theory 7(2006), 287–296.
• [26] G. Jungck, N. Hussain, Compatible maps and invariant approximations, J. Math. Anal. Appl. 325 (2007), 1003–1012.
• [27] G. V. R. Babu, G. N. Alemayehu, Common fixed point theorems for occasionally weakly compatible maps satisfying property (E.A.) using an inequality involving quadratic terms, Appl. Math. Lett. 24 (2011), 975–981.
• [28] H. K. Pathak, N. Hussain, Common fixed points for P-operator pair with applications, Appl. Math. Comput. 217 (2010), 3137–3143.
• [29] S. Sessa, On a weak commutativity condition of mappings in fixed point consideration, Publ. Inst. Math. 32 (1982), 149–153.
• [30] R. Sumitra, Common fixed point theorem for more general occasionally noncommuting mappings, Int. J. Contemp. Math. Sci. 5 (2010), 333–340.
• [31] R. K. Verma, A generalized fixed point theorem for occasionally weakly compatible mappings, Int. J. Math. Archive 2(6) (2011), 964–968.