NON-SELF MAPPINGS UNDER COMMON LIMIT RANGE PROPERTY IN SYMMETRIC SPACES AND FIXED POINTS

Yıl 2018, Cilt: 8 Sayı: 1, 20 - 31, 01.06.2018

S. Chandok D. Kumar

Öz

In this paper, some sucient conditions are provided for the existence of xed points for two pairs of non-self mappings satisfying CLR property without the condition of continuity on mappings in the framework of symmetric spaces. Several interesting corollaries are also deduced. Some examples are also provided which illustrate the usability of the results obtained.

Anahtar Kelimeler

weak compatible mappings, , -weak rational type contraction mappings, metric space.

Kaynakça

• A. Aliouche, A common fixed point theorem for weakly compatible mappings in symmetric spaces satisfying a contrative condition of integral type, J. Math. Anal. Appl. 322(2)(2006), 796-802.
• M. Aamri, D. EI Moutawakil, Common fixed points under contractive conditions in symmetric spaces, Appl. Math. E-notes 3(2003), 156-162.
• I.D. Arandjelovi´c, D. Keˇcki´c, Symmetric spaces approach to some fixed point result, Nonlinear Anal. 75(2012), 5168.
• S.H. Cho, G.Y.Lee, J.S. Bae, On coincidence and fixed-point theorems in symmetric spaces, Fixed Point Theory Appl. (2008) Article ID 562130, 9 pages.
• F. Galvin, S.D. Shore, Completeness in semi-metric, Pacific. J. Math. 113(1)(1984), 67-75.
• M. Imdad, A.H. Soliman, Some common fixed point theorems for a pair of tangential mappings in symmetic spaces, Appl. Math. Lett. 23(4)(2010), 351-355.
• M. Imdad, B.D. Pant, S. Chauhan, Fixed points theorems in Menger spaces using (CLRST) property and applications. J. Nonlinear Anal. Optim. 3(2)(2012), 225-237.
• M. Imdad, S. Chauhan, Z. Kadelburg, C. Vetro, Fixed point theorems for non-self mappings in symmetric spaces under φ-weak contractive conditions and an application to functional equations in dynamic programming, Appl. Math. Comp. 227(2014), 469-479.
• M. Imdad, J. Ali, M. Tanveer, Coincidence and common fixed point theorems for nonlinear contractions in Menger PM spaces, Choas Solitons Fractals 42 (5)(2009), 3121-3129.
• M. Jovanovi´c, Z. Kadelburg, S. Radenovi´c, Common fixed point results in metric-type spaces, Fixed Point Theory Appl. (2010), Article ID 978121 15 pages.
• G. Jungck, Compatible mappings and common fixed points. Int. J. Math. Math. Sci. 9(4)(1986), 771-779.
• G. Jungck, B.E. Rhodes, Fixed points for set valued functions without continuity, Indian J. Pure Appl. Math. (3)(1998), 227-238.
• Y. Liu, J. Wu, Z. Li, Common fixed points of single-valued and multivalued maps, Int. J. Math. Math. Sci. (2005), 3045-3055.
• R.P. Pant, Noncompatible mappings and common fixed points, Soochow J. Math. 26(1)(2000), 29-35.
• S. Radenovi´c, Z. Kadelburg, Quasi-contractions on symmetric and cone symmetric spaces, Banach J. Math. Anal. 5(2011), 38-50.
• W. Sintunavarat, P. Kumam, Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric sapces, J. Appl. Math.(2011) Article ID637958 14pages.
• W.A. Wilson, On semi-metric space, Am. J. Math. 53(1931), 361-373.