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Ciric type p-cyclic contraction results for discontinues mappings

Journal: Journal of the International Mathematical Virtual Institute (Vol.4, No. 1)

Publication Date:

Authors : ; ;

Page : 27-42

Keywords : Menger space; Cauchy sequence; xed point; -function; -function.;

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Abstract

Cyclic mappings constitute a recently introduced class of map- pings which have appeared in a number of papers in the contexts of xed point theory and in the theory of optimization. In this paper we consider p-cyclic contraction type mappings which are generalized cyclic contractions through p number of subsets of a probabilistic metric space. Moreover the contractive mappings are discontinuous. We use Hadzic type t-norms in our theorems which is characterized by the equicontinuities of its iterates. We deduce two xed point theorems. In one of the theorems we use a control function which is the counterpart of a function widely used in xed point the- ory in metric spaces. The theorems are supported with examples. The work is in the line of research developing probabilistic xed point theory.

Last modified: 2015-01-07 20:03:33