Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 4 (2009), 215 -- 238

FIXED POINT THEOREMS FOR GENERALIZED WEAKLY CONTRACTIVE MAPPINGS

Ramendra Krishna Bose and Mrinal Kanti Roychowdhury

Abstract. In this paper several fixed point theorems for generalized weakly contractive mappings in a metric space setting are proved. The set of generalized weakly contractive mappings considered in this paper contains the family of weakly contractive mappings as a proper subset. Fixed point theorems for single and multi-valued mappings, approximating scheme for common fixed point for some mappings, and fixed point theorems for fuzzy mappings are presented. It extends the work of several authors including Bose and Roychowdhury.

2000 Mathematics Subject Classification: 03E72; 47H04; 47H10; 54H25; 54C60.
Keywords: Fixed point; Weakly contractive mapping; Weakly compatible mapping; Mann iteration; Fuzzy mapping.

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Ramendra Krishna Bose Mrinal Kanti Roychowdhury
Department of Mathematics, Department of Mathematics,
The University of Texas-Pan American, The University of Texas-Pan American,
1201 West University Drive, 1201 West University Drive,
Edinburg, TX 78539-2999, USA. Edinburg, TX 78539-2999, USA.
e-mail: rkbose@utpa.edu, rkbose@hotmail.com e-mail: roychowdhurymk@utpa.edu


http://www.utgjiu.ro/math/sma