Abstract
We establish a common fixed-point theorem for six self maps under the compatible mappings of type (C) with a contractive condition [1], which is independent of earlier contractive conditions.
Highlights
The study of common fixed point of mappings satisfying contractive type conditions has been a very active field of research activity during the last two decades
We establish a common fixed-point theorem for six self maps under the compatible mappings of type (C) with a contractive condition [1], which is independent of earlier contractive conditions
Singh [1] and prove a fixed point theorem for six self mappings in a complete metric space
Summary
The study of common fixed point of mappings satisfying contractive type conditions has been a very active field of research activity during the last two decades. The contractive conditions (1.2) and (1.3) hold simultaneously whenever (1.2) or (1.3) is assumed with additional conditions on δ and φrespectively It follows, that the known common fixed point theorems can be extended and generalized if instead of assuming one of the contractive condition (1.2) or (1.3) with additional conditions on δ and φ. Definition: Two self mappings A and S of a metric space (X, d) are said to be compatible mappings of type (A). Definition: Two self mappings A and S of a metric space (X,d) are said to be compatible mappings of type (P) (see [8]), if lim n whenever x n is a sequence in X such that lim n t for some t X. We give an example which is compatible mapping of type (C) but is neither compatible nor compatible mapping of type (A), compatible mapping of type (B) and compatible mapping of type (P)
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