New theorems on extended b-metric spaces under new contractions

Abstract

The notion of extended b-metric space plays an important role in the field of applied analysis to construct new theorems in the field of fixed point theory. In this paper, we construct and prove new theorems in the filed of fixed point theorems under some new contractions. Our results extend and modify many existing results in the literature. Also, we provide an example to show the validity of our results. Moreover, we apply our result to solve the existence and uniqueness of such equations.

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“…One such generalizations is b-metric spaces in the sense of Bakhtin [2] and Czerwik [6], for some works in b-metric space see [10,12,14,16]. In 2017, Kamran et al [7] introduced the notion of extended b-metric spaces as a generalization of b-metric spaces, for some work in this space see [9,15]. In this paper, we utilize the notion of C-class functions which introduced by Ansari [1] to formulate and prove many fixed point results.…”

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∈φ-contraction and some fixed point results via modified ω-distance mappings in the frame of complete quasi metric spaces and applications

“…Shatanawi, M. Postolache in [3,4] studied some common fixed points of such mappings. For more generalizations of Banach fixed point theory, see [5][6][7][8][9][10][11][12][13][14][15][16][17][18]. In 1931 Wilson [19] introduced the notion of quasi metric space as below:…”