Abstract
The aim of this study is to introduce a new interpolative contractive mapping combining the Hardy–Rogers contractive mapping of Suzuki type and mathcal{Z}-contraction. We investigate the existence of a fixed point of this type of mappings and prove some corollaries. The new results of the paper generalize a number of existing results which were published in the last two decades.
Highlights
1 Introduction and preliminaries A century ago, the notion of fixed point theory appeared in the papers that were written to solve certain differential equations
The first independent fixed point result was given by Banach [1] in the setting of a complete normed space
[38], Karapınar used simulation functions to introduce the notion of interpolative Hardy– Rogers-type Z-contraction mappings and prove some related fixed point results
Summary
Introduction and preliminariesA century ago, the notion of fixed point theory appeared in the papers that were written to solve certain differential equations. Metric fixed point theory has advanced in many directions in the setting of several abstract spaces. We mention and use three interesting notions that were proposed for this purpose, namely simulation function (see, e.g., [19,20,21,22,23,24,25,26,27,28,29]), admissible mapping (see, e.g., [9,10,11,12,13,14,15,16,17,18]), and Suzuki-type contraction (see [4, 5]).
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