Electronic Journal: Southwest Journal of Pure and Applied Mathematics Internet: http://rattler.cameron.edu/swjpam.html ISSN 1083-0464 Vol. No. 01, 1996, pp. 30–41 Submitted: October 11, 1995. Published: March 8, 1996.

SET-VALUED MAPS WITH FIXED AND

COINCIDENCE POINTS

H.K. Pathak and M.S. Khan

Abstract. In this paper, we prove the existence of solutions of functional equations f_{i}x ∈ Sx ∩ T x and x = f_{i}x ∈ Sx ∩ T x under certain nonlinear hybrid contraction and asymptotic regularity conditions, generalize and improve a recent result due to V. Popa concerning common fixed points of multi-valued mappings weakly commuting with a single-valued mapping and satisfying a generalized contraction type condition. In the sequel, we derive several independent results.

(1991) A.M.S. Subject Classification Codes. 54H25, 47H10.

Key Words and Phrases. Coincidence and common fixed points, Hausdorff metric, orbital complete, proximinal subset & weakly commuting mappings

Department of Mathematics, Kalyan Mahvidyalaya, Bhilai Nagar (M.P.) 490006, India Sultan Qaboos University, Department of Mathematics and Computing, College of Science, P.O Box 36, Postal Code 123, Al-Khod, Muscat, Sultanate of Oman

E-mail Address: n/a \begin{matrix}c \\ ◯ \end{matrix}1996 Cameron University

Typeset by AMS-TEX