FIXED POINT THEOREMS FOR CONTRACTIVELY GENERALIZED HYBRID MAPPINGS IN COMPLETE METRIC SPACES

In this paper, we first introduce a broad class of mappings containing the class of contractively generalized hybrid mappings in a metric space defined by Hasegawa, Komiya and Takahashi [5]. Let (X, d) be a metric space. A mapping T : X -> X is called contractively 2-generalized hybrid if there exist alpha 1, alpha(2), beta(1), beta(2) is an element of R and r is an element of [0,1) such that alpha(1)d(T-2 x, Ty)+alpha(2)d(Tx, Ty) + (1 - alpha(1) - alpha(2))d(x, Ty) <= r{beta(1)d(T(2)x, y) + beta(2)d(Tx, y) + (1 - beta(1) - beta(2))d(x, y)} for all x, y is an element of X. Then we prove fixed point theorems which are related to the mappings in a complete metric space. Using these results, we prove new and well-known fixed point theorems in a complete metric space.