A new Generalization of Wardowski Fixed Point Theorem in Complete Metric Spaces

Abstract

The aim of this paper is to state and prove Wardowski type fixed point theorem in metric spaces. The paper includes an example which shows that our result is a proper extension of some known results.

New classes of Picard operators

“…Examining the proof of the above theorem, we observe that it takes place a more general result: Theorem 7. Let (X, d) be a complete metric space and T : X → X be a contractive mapping, which satisfies the relation (3), where E, F verifies condition (C 2 ). Then T is a CJMP-contraction, hence a Picard operator.…”

“…Important contributions to Wardowski contractions were given in [12], [17], [18], [19], [20] and [3]. See also the survey paper [5].…”

Fixed Points of Proinov E-Contractions

“…The notion of E-contraction was introduced by Fulga and Proca [1]. Later, this concept has been improved by several authors, e.g., [2][3][4].…”

Some Results on S-Contractions of Type E

“…In the last decades, the renowned metric fixed point results of Banach [1] has been improved, extended, and generalized in several ways, see e.g., [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. We first mention that the notion of E-contraction, defined by Fulga and Proca [10,11], is one of the interesting approach to improve the Banach mapping contraction. Another interesting fixed point result was given by Khojasteh et al [19] via the newly defined notion, simulation function.…”