Abstract

In this paper we have generalized the extended interpolative Ciric-Reich-Rus type $\psi F$-contraction given in [22] by introducing extended interpolative Ciric-Reich-Rus type $(\alpha,\beta,\gamma F)$ of type-I and type-II contractions. Using these type contractions we have established some unique fixed point results in $S$-complete Hausdorff uniform spaces. We have discussed about some basic definitions, properties, lemmas and theorems on uniform spaces in the introduction and preliminary sections. Some corollaries and examples are also given on the basis of the results.

Keywords and Phrases

$(\alpha,\beta)$-admissible function, $S$-complete Hausdorff uniform space, $E$-distance, $p$-Cauchy sequence, extended interpolative Ciric-Reich-Rus type $(\alpha,\beta,\gamma F)$-contractions of type-I and type-II.

A.M.S. subject classification

47H10, 54H25.

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