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. 2020 Sep 22;13(1):451.
doi: 10.1186/s13104-020-05273-1.

Fixed point theorems for nonlinear contractive mappings in ordered b-metric space with auxiliary function

Namana Seshagiri Rao  1 , Karusala Kalyani  2 , Belay Mitiku  3
Affiliations

Fixed point theorems for nonlinear contractive mappings in ordered b-metric space with auxiliary function

Namana Seshagiri Rao et al. BMC Res Notes. .

Abstract

Objectives: In this paper we present some fixed point theorems for self mappings satisfying generalized [Formula: see text]-weak contraction condition in partially ordered complete b-metric spaces. The results presented over here generalize and extend some existing results in the literature. Finally, we illustrate two examples to support our results.

Result: We obtained a unique fixed point of a self mapping satisfying certain contraction condition which is involving an auxiliary function. Also, the results are presented for the existence of a common fixed point and a coincidence point for generalized [Formula: see text]-weak contraction mappings in partially ordered complete b-metric space.

Keywords: Complete metric space; Fixed points; Ordered b-metric space; Rational type generalized contraction mappings.

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Conflict of interest statement

The authors declare that they have no competing interests.

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